- CapeTools Calendars
General Description
These functions provide Calendar objects. Calendar objects contain a list of holidays. These Calendar objects can be passed to numerous functions that require date calculation or manipulation. This category does contain a few functions that you can use to query these Calendar objects.
Additionally, you can add and remove dates from these objects. You can also merge Calendar objects.
- CapeTools Indexes
General Description
These functions provide Index creation objects. An index object is used to provide information concerning how an interest rate is fixed over a period of time. They are applied to floating rate legs. A typical index is a LIBOR index fixed by BBA. All indexes have to define the period length (ie - three months) that the interest rate fixing is applied upon, the number of days before the start date of the interest rate period that the fixing must occur, the holiday center etc... A YieldCurve object is also needed in order to acquire the discount factors needed to compute the fixing.
An optional Basis Swap curve can be passed to the Index creation functions which will be stripped in order to compute a spread that will be added to the fixed (Index) rate.
Why a Basis swap curve?
As an example, the United States is awash in one month money (index) from mortgage payments, car payments, and everything else, so you have to pay someone to take it away and turn it into three month money (index). This payment is captured via a basis spread on the three month money (index). Each currency has its preferred index for creating floating legs, for the United States this is 3m Libor, for Euros its 6m Euribor. Whatever these indices are, they are usually called the currency's "cash" leg.
A floating payment (for the interval tSt to tEnd) is valued as:
V = notional * dcf(tSt, tEnd) * Rfwd * DF(tEnd),
where the dcf is the day count fraction of the interval, Rfwd is the forward rate for the index, and DF is ccy's discount factor to the pay date. This is just the definition of the forward rate.
The forward rate is .
RFwd = RTrue + bs(tEnd)
where bs is the forward basis spread for the index, and the true rate is just the rate you'd expect from the discount factor:
RTrue = ((DF(tSt)/DF(tEnd)) - 1) / dcf(tSt, tEnd)
Or if you like...
RTrue = [DF(tSt) - DF(tEnd)] / dcf(tSt,tEnd) * DF(tEnd)
Whenever you see a floating rate index in a deal, immediately replaces it with the basis spread plus the true rate, the true rate is the mathematically idealized rate for the currency. One usually assumes the forward basis spread curve bs(tEnd) doesn't change. The forward basis spread curves are stripped from the basis swap market.
Yon can view the stripped forward spread curve stored within an Index object by executing the ShowIndexFwdSpreads() function. These forward spread curves are the basis for pricing currency basis swaps.
- CapeTools Curves
General Description
Given deposit, futures, FRAs and Swap instruments, these functions can strip out a discount factor (yield) curve. One can also input discount factor rates directly, or strip from zero rates or forward rates.
Usually when pricing a floating leg, you need two yield curves. A fixing curve in order to fix the rate and a discount curve for discounting cashflows. You will see this in numerous functions where a fixing curve is passed to an Index function and a discount curve is passed to legs (or instruments) that require discounting.
Thus basically you have a special discount curve for calculating the forward rates but the discount factors within this curve are NOT used for discounting cashflows.
We have implemented a curve that produces both a fixing curve and a discounting curve within a single yieldcurve object. Thus the same yieldcurve key will be passed to both the FixingCurve parameter and the discountingCurve parameter when pricing an instrument that demands both parameters (see CapeTools XCCY Curves).
These curves can also serve as input to the interest rate risk engine in order to compute DELTA and GAMMA risk parameters for an interest rate structure.
- CapeTools XCCY Curves
General Description
Given deposit, futures, FRAs and Swap instruments, these functions can strip out a discount factor curve. One can also input discount factor rates directly, or strip from zero rates or forward rates.
Usually when pricing a floating leg, you need two yield curves. A fixing curve in order to fix the rate and a discount curve for discounting cashflows. You will see this in numerous functions where a fixing curve is passed to an Index function and a discount curve is passed to legs (or instruments) that require discounting.
Thus basically you have a special discount curve for calculating the forward rates but the discount factors within this curve are NOT used for discounting cashflows.
We have implemented several yieldcurve functions that produce both a fixing curve and a discounting curve within a single yieldcurve object. Thus the same yieldcurve key will be passed to both the FixingCurve parameter and the discountingCurve parameter when pricing an instrument that demands both parameters.
We have achieved this by including a cross currency swap range within this stripper.
Our approach automatically gets the cross currency swap market correct. This method assumes only that USD 3m Libor floating legs have no basis spreads. One then finds say the forward basis spread curve for, say, 6m Euribor by combining the 6m Euribor to 6m USD Libor basis swap with the 6m USD Libor to 3m USD Libor basis swap to obtain the 6m Euribor to 3m USD Libor basis swaps. N-year basis swap at X basis points swaps a 6m Euribor + X bp payments (paid semiannually) for N years against 3m USD Libor payments (paid quarterly) for N years. The basis swaps are liquidly quoted for 1y, 2y, 3y, 5y, 7y, and 10y. From this data, one assumes an interpolation method, and strips to get the forward basis spreads. (see CapeTools Indexes for a definition of a forward basis spread).
The discount factors within these curves we call the cash discount factors. However when one requests a fixing value the correct LIBOR rate will be returned (with the help of the stripped forward basis spread curve).
These curves can also serve as input to the interest rate risk engine in order to compute DELTA and GAMMA risk parameters for an interest rate structure.
The following curves strip out both the discount curve and a forward spread curve :
- MKTYC_XCCY_D() ( interpolation methodology applied to the internally created DISCOUNT FACTORS CURVE. )
- MKTYC_XCCY_Z() ( interpolation methodology applied to the internally created ZERO RATE CURVE. )
- MKTYC_XCCY_F() ( interpolation methodology applied to the internally created FORWARD RATE CURVE. )
You can view the created forward spread curve by executing the ShowYCFwdSpreads() function. The three strippers above require the use of a Multi-dimensional LevenbergMarquardt object and thus are not as fast as the simpler strippers contained within the 'CapeTools Curves' category of functions (uses a one-dimensional Newton object). Thus we have implemented the following three strippers that will take in as input forward spread curves already stripped out from the strippers presented above.
- MKTYC_XCCY_D2() ( interpolation methodology applied to the internally created DISCOUNT FACTORS CURVE. )
- MKTYC_XCCY_Z2() ( interpolation methodology applied to the internally created ZERO RATE CURVE. )
- MKTYC_XCCY_F2() ( interpolation methodology applied to the internally created FORWARD RATE CURVE. )
All the curves presented here, when passed to interest rate instruments that are subject to interest rate risk calculations (see the 'CapeTools IR Risk' category of functions) produce more accurate results (as opposed to specifying separate discounting and fixing curves) because there exists a relationship between the discounting factors and fixing rates. (If you bump the inputs of the yieldcurve, the discount factors are adjusted correctly for the purpose of discounting a cashflow, this is not the case if you specify separate curves, the discounting factors do not move if you bump the market rates).
- CapeTools Bond Curves
General Description
Given deposit, futures, FRAs and Bond instruments, these functions can strip out a discount factor (yield) curve.
- CapeTools Credit Curves
General Description
Given a risk-free curve (most of the curves stripped from the 'CapeTools Curves', 'CapeTools XCCY Curves' or 'CapeTools Bond Curves' category of functions) we can produce a risky curve. A risky curve has additional information regarding default probabilities and thus specific to a single organisation (or sector). A risky curve can be treated as a regular yieldcurve and can be passed to all instruments that require discounting curve. Risky discount factors will be used to discount the cashflows as opposed to the risk-free discount factors.
These risky-curves also serve as inputs to the credit derivative functions.
- CapeTools Credit Transition Matrix
General Description
These functions create and queries credit transition matrix objects. The entries within the credit transition matrix represent one-year ratings migration probabilities with the last column/row representing the default probabilities. Each row within the matrix should sum to 100.
- CapeTools Volatility Curves
General Description
These functions create volatility curves (or grids). These curves (whether one-dimensional or two-dimensional) can utilise a variety of interpolation methodologies in order to acquire a volatility value from the curve.
The following interest rate volatility curves can also serve as input to the interest rate risk engine (CapeTools IR Risk) in order to compute VEGA and VOLGA risk parameters for an interest rate structure :
The ATMVolMatrix object only models At-The-Money volatility. You provide a matrix of option start - underlying length combinations.
The ExpiryKVolMatrix object can model interst rate smiles, however it does this for only one underlying instrument (ie - volatility structure on caps/floors/swaptions where the underlying length (ie - 5Y swap rate) is the same for all points). You provide a matrix of option start - option strike combinations.
A single SABRVolCurve object can model the entire volatilities for all interest rate options within an interst rate market. Thus one object can model the smiles for all caps/floors/swaptions (regardless of instrument length, 3M, 5Y, 10Y or option starting times).
An alternative to the SABRVolCurve object would be a three-dimensional object that would have Option-Length, Underlying-Length and Strike as the three dimensions of the cube. However such an object (although would capture the volatility smile) would not be able to model the true movement of the volatility smile. It is also a difficult object to work with.
You can also use the EquitySABRVolCurve function to model equity type volatility curves via the SABR model.
- CapeTools Grouped Curves
General Description
These functions allow the grouping of several yield curves, credit curves or volatility curves. These are used by the interest rate portfolio functions or the basket default swap functions to help manage a large number of constructed curves.
- CapeTools Repo Curves
General Description
Given a list of repo instruments, these functions construct repurchase (repo) curves.
The repo curves generated here can be passed to the CapeTools Forward Bond or CapeTools Bond Options category of functions.
- CapeTools Display Curves
General Description
These functions query Yieldcurve objects for various information.
There are functions to display data for discount curves, zero rate curves, market curves and FwdSpread curves.
- CapeTools Query Curves
General Description
These functions query VolCurves and Yieldcurve objects for various information.
You can request for the market sensitivity of the instruments used within the underlying Volalility Curve objects (delta, gamma, vega and theta). This is useful if you are conducting risk-management calculations yourself.
You can also generate a market rate matrix for each of the ('UnderlyingStart' / 'UnderlyingEnd') instrument combination (for a unit notional of the underlying deposits/swaps). Basically a rates matrix where the rows are the rate start tenors and the columns are the rate Length (in a Tenor format also).
- CapeTools Query Credit Curves
General Description
Functions to query and price basic credit default swap (CDS) derivative instruments given a credit curve.
You can execute functions to compute the fair premiums from a CDS (including Binary CDS).
You can compute risky discount factors, default probabilities, default densities, hazard rates and survival probabilities.
- CapeTools Credit Default Swaps
General Description
Functions to create regular and binary credit default swap (CDS) objects. These objects can then be queried and priced via functions present within this category.
You can query for the following information :
- Dirty price
- Clean price
- Accrued premium
- Payoff value
- Par premium value
- Premium leg value
- Rho (risk) of the recovery rate (one percent additive change)
- BPV of the risk-free curve
You can also price an option on a CDS contract.
- CapeTools Credit Default Swaps (Bonds/FRN)
General Description
Functions to create regular and binary credit default swap (CDS) objects based on data extracted from a Bond, Floating leg or Fixed leg object. These CDS objects can then be queried and priced via functions present within this category.
The advantages of these functions over those present within the CapeTools Credit Default Swaps category of functions is that you specify the window in which you would like protection upon your chosen instrument.
The chosen instrument can be one of the objects constructed from the following functions or categories :
You can query for the following information :
- Dirty price
- Clean price
- Accrued premium
- Payoff value
- Par premium value
- Premium leg value
- Rho (risk) of the recovery rate (one percent additive change)
- BPV of the risk-free curve
You can also price an option on the CDS object.
- CapeTools Credit Link Bond/Notes
General Description
Functions to create regular and binary credit link bond/notes (CLN) objects based on data extracted from a Bond, Floating leg or Fixed leg object. These CLN objects can then be queried and priced via functions present within this category.
A CLN object is simply the sum of the price of the instrument (priced using the risky curve) plus the value of the default leg over the protection period.
The chosen instrument can be one of the objects constructed from the following functions or categories :
You can query for the following information :
- FairValue
- Accrued interest
- Fair value + accrued interest
- Payoff value
- Risky PV of the instrument
- Rho (risk) of the recovery rate (one percent additive change)
- CapeTools Exotic Options
General Description
Functions that price vanilla and Exotic options using variations of the black-scholes model. These functions do not create objects and take single-valued parameters. Thus these functions are the fastest in terms of execution speed, but not very flexable in terms of portfolio management, scenario analysis and pricing option strategies. However they all return risk numbers for every single double valued parameter (first and second derivatives including cross derivatives). Theta is (of course) computed even though it is a date parameter.
First order derivative risk numbers can be requested by simply passing in the name of the parameter (preceded by the 'd' character) into the 'Greek' parameter of these functions (ie - dStock).
Second order derivative risk numbers can be requested by simply passing in the name of the parameter (preceded by the 'd' character) ( repeated twice) into the 'Greek' parameter of these functions (ie - dStockdStock).
Cross derivative risk numbers can be requested by simply passing in the name of the parameters (preceded by the 'd' character) into the 'Greek' parameter of these functions (ie - dStockdTime or dTimedStock).
You can of course make use of the following (in-built) case-insensitive Greek values :
- DELTA
- GAMMA
- VEGA
- VOLGA
- THETA
However when pricing options composed of two underlyers, we suggest using the former notation for the common risk values.
The risk values computed are the mathematical definition of a derivative (via differentiation). Thus if you wish to compute the risk numbers for a given shift (ie - a one basis point change in the parameter), then you simply multiply the risk number by the requested shift.
All of the functions implemented here have been taken from. 'The Complete Guide To OPTION PRICING FORMULAS' by Espen Gaarder Haug. This book provides an in-depth analysis of every function described here. We have just implemented these functions in C++ and extended their functionality to include risk-numbers.
- CapeTools Storage
General Description
Functions that price vanilla and Exotic options using variations of the black-scholes model. These functions create portfolio objects. The benefit of these functions is that there are external functions to sort and group deals. You can mix option contracts from different currencies and finally you can price the whole portfolio a selection of the portfolio in any currency (via an FX manager object).
In addition, each parameter has a range object (excel range) as an input parameter. You can input a single-valued number in a range and if the function detects that the size of the other input ranges are longer, the function will automatically expand the single range to the same size. Every cell will contain the same constant number. This is used heavily within our examples.
You can commit the trades (portfolio) to disk via the numerous range-to XML and XML to range functions present within the 'CapeTools Utils' category of functions.
Once a portfolio has been created, the 'CapeTools Exotic Options Tools' category of functions is responsible for selecting, grouping and pricing these portfolios.
The SubOptionBook() function is responsible for selecting trades via an SQL type criteria and creating a new portfolio object.
The GroupOptionBook() function is responsible for grouping trades via an SQL type criteria and creating a new portfolio object.
The DisplayOptionGroups() function will display the unique columns of the grouped portfolio
The DisplayGRPOptionBook() function will display the trades within the selected group. A list of possible groups can be determined via the said DisplayOptionGroups() function.
The DisplayOptionBook() function will display the trades within a portfolio, sorted on a list of columns.
The PriceOptionBook() function will price the portfolio. This function holds a 'Greek' parameter and this parameter taylors what number are generated.
When priced, you can request the price for the total portfolio, the price of each trade. In addition you can request detailed information for each trade.
All of the functions implemented here have been taken from : 'The Complete Guide To OPTION PRICING FORMULAS' by Espen Gaarder Haug. This book provides an in-depth analysis of every function described here. We have just implemented these functions in C++ and extended their functionality to include risk-numbers.
- CapeTools Stock Option Portfolio
General Description
Functions that price vanilla and Exotic options using variations of the black-scholes model. These functions create portfolio objects. The benefit of these functions is that there are external functions to sort and group deals. You can mix option contracts from different currencies and finally you can price the whole portfolio a selection of the portfolio in any currency (via an FX manager object).
In addition, each parameter has a range object (excel range) as an input parameter. You can input a single-valued number in a range and if the function detects that the size of the other input ranges are longer, the function will automatically expand the single range to the same size. Every cell will contain the same constant number. This is used heavily within our examples.
Note : These functions are very similar to those contained within the 'CapeTools Storage' category of functions except that the parameter that receives dividend rate, foreign rate or holding costs have been dropped. Internally this value is set to zero (0). This simplifies calling these functions and in addition, some of the functions implemented within the 'CapeTools Storage' category cannot have this dividend rate, foreign rate or holding cost parameter set to zero.
You can commit the trades (portfolio) to disk via the numerous range to XML and XML to range functions present within the 'CapeTools Utils' category of functions.
Once a portfolio has been created, the 'CapeTools Exotic Options Tools' category of functions is responsible for selecting, grouping and pricing these portfolios.
The SubOptionBook() function is responsible for selecting trades via an SQL type criteria and creating a new portfolio object.
The GroupOptionBook() function is responsible for grouping trades via an SQL type criteria and creating a new portfolio object.
The DisplayOptionGroups() function will display the unique columns of the grouped portfolio
The DisplayGRPOptionBook() function will display the trades within the selected group. A list of possible groups can be determined via the said DisplayOptionGroups() function.
The DisplayOptionBook() function will display the trades within a portfolio, sorted on a list of columns.
The PriceOptionBook() function will price the portfolio. This function holds a 'Greek' parameter and this parameter taylors what number are generated.
When priced, you can request the price for the total portfolio, the price of each trade. In addition you can request detailed information for each trade.
All of the functions implemented here have been taken from : 'The Complete Guide To OPTION PRICING FORMULAS' by Espen Gaarder Haug. This book provides an in-depth analysis of every function described here. We have just implemented these functions in C++ and extended their functionality to include risk-numbers.
- CapeTools Futures Option Portfolio
General Description
Functions that price vanilla and Exotic options using variations of the black-scholes model. These functions create portfolio objects. The benefit of these functions is that there are external functions to sort and group deals. You can mix option contracts from different currencies and finally you can price the whole portfolio a selection of the portfolio in any currency (via an FX manager object).
In addition, each parameter has a range object (excel range) as an input parameter. You can input a single-valued number in a range and if the function detects that the size of the other input ranges are longer, the function will automatically expand the single range to the same size. Every cell will contain the same constant number. This is used heavily within our examples.
Note : These functions are very similar to those contained within the 'CapeTools Storage' category of functions except that the parameter that receives dividend rate, foreign rate or holding costs have been dropped. Internally this value is set to the same value as the 'rate' parameter. This simplifies calling these functions and in effect prices options on futures.
You can commit the trades (portfolio) to disk via the numerous range to XML and XML to range functions present within the 'CapeTools Utils' category of functions.
Once a portfolio has been created, the 'CapeTools Exotic Options Tools' category of functions is responsible for selecting, grouping and pricing these portfolios.
The SubOptionBook() function is responsible for selecting trades via an SQL type criteria and creating a new portfolio object.
The GroupOptionBook() function is responsible for grouping trades via an SQL type criteria and creating a new portfolio object.
The DisplayOptionGroups() function will display the unique columns of the grouped portfolio
The DisplayGRPOptionBook() function will display the trades within the selected group. A list of possible groups can be determined via the said DisplayOptionGroups() function.
The DisplayOptionBook() function will display the trades within a portfolio, sorted on a list of columns.
The PriceOptionBook() function will price the portfolio. This function holds a 'Greek' parameter and this parameter taylors what number are generated.
When priced, you can request the price for the total portfolio, the price of each trade. In addition you can request detailed information for each trade.
All of the functions implemented here have been taken from : 'The Complete Guide To OPTION PRICING FORMULAS' by Espen Gaarder Haug. This book provides an in-depth analysis of every function described here. We have just implemented these functions in C++ and extended their functionality to include risk-numbers.
- CapeTools Exotic Options Tools
General Description
The SubOptionBook() function is responsible for selecting trades via an SQL type criteria and creating a new portfolio object.
The GroupOptionBook() function is responsible for grouping trades via an SQL type criteria and creating a new portfolio object.
The DisplayOptionGroups() function will display the unique columns of the grouped portfolio
The DisplayGRPOptionBook() function will display the trades within the selected group. A list of possible groups can be determined via the said DisplayOptionGroups() function.
The DisplayOptionBook() function will display the trades within a portfolio, sorted on a list of columns.
The PriceOptionBook() function will price the portfolio. This function holds a 'Greek' parameter and this parameter taylors what number are generated.
You can of make use of the following (in-built) case-insensitive Greek values :
- DELTA
- GAMMA
- VEGA
- VOLGA
- THETA
However have have a more advanced interface for requesting Greeks. Assuming that you know before hand the name of the function that you used to create the portfolio originally and the list of the parameter names, you can request Greek values as so :
First order derivative risk numbers can be requested by simply passing in the name of the parameter (preceded by the 'd' character) into the 'Greek' parameter of these functions (ie - dStock).
Second order derivative risk numbers can be requested by simply passing in the name of the parameter (preceded by the 'd' character) ( repeated twice) into the 'Greek' parameter of these functions (ie - dStockdStock).
Cross derivative risk numbers can be requested by simply passing in the name of the parameters (preceded by the 'd' character) into the 'Greek' parameter of these functions (ie - dStockdTime or dTimedStock).
When pricing options composed of two underlyers, we suggest using this notation rather than the 'DELTA' value for requesting the delta value of the first underlyer parameter.
The risk values computed are the mathematical definition of a derivative (via differentiation). Thus if you wish to compute the risk numbers for a given shift (ie - a one basis point change in the parameter), then you simply multiply the risk number by the requested shift.
When priced, you can request the price for the total portfolio, the price of each trade. In addition you can request detailed information for each trade.
All of the functions implemented here have been taken from : 'The Complete Guide To OPTION PRICING FORMULAS' by Espen Gaarder Haug. This book provides an in-depth analysis of every function described here. We have just implemented these functions in C++ and extended their functionality to include risk-numbers.
- CapeTools Exotic Analysis
General Description
Functions that price vanilla and Exotic options using variations of the black-scholes model. These functions do not create objects ***BUT*** take range-valued parameters. Thus these functions are not as fast as those implemented within the 'CapeTools Exotic Options' category of functions, but are perfect for scenario analysis. These functions return risk numbers for every single double valued parameter (first and second derivatives including cross derivatives). Theta is (of course) computed even though it is a date parameter.
In addition, each parameter has a range object (excel range) as an input parameter. You can input a single-valued number in a range and if the function detects that the size of the other input ranges are longer, the function will automatically expand the single range to the same size. Every cell will contain the same constant number. This is used heavily within our examples.
A great usage for these functions is providing a range of numbers for one parameter while providing a constant value for the other parameters. This way you can see the effect of changing values (for any of the Greek values) over the changing values.
Another use is in constructing option strategies. The following strategies can be easily built using this function :
- Bull Call Spread
- Bull Put Spread
- Bear Call Spread
- Bear Put Spread
- Call Back Spread
- Put Back Spread
- Call Ratio Vertical Spread
- Put Ratio Vertical Spread
- Straddle
- Ratio Straddle
- Strangle
- Ratio Strangle
- Butterfly
- Xmas Tree
- Condor
For reference on these strategies, please refer to the excellent book : Option Volatility and Pricing by Sheldon Natenberg. Some of these strategies have been implemented for the regular black formula (see the 'CapeTools Option Strategy' category for stocks and 'CapeTools Exotic Legs' category for interest rate legs. )
First order derivative risk numbers can be requested by simply passing in the name of the parameter (preceded by the 'd' character) into the 'Greek' parameter of these functions (ie - dStock).
Second order derivative risk numbers can be requested by simply passing in the name of the parameter (preceded by the 'd' character) ( repeated twice) into the 'Greek' parameter of these functions (ie - dStockdStock).
Cross derivative risk numbers can be requested by simply passing in the name of the parameters (preceded by the 'd' character) into the 'Greek' parameter of these functions (ie - dStockdTime or dTimedStock).
You can of course make use of the following (in-built) case-insensitive Greek values :
- DELTA
- GAMMA
- VEGA
- VOLGA
- THETA
However when pricing options composed of two underlyers, we suggest using the former notation for the common risk values.
The risk values computed are the mathematical definition of a derivative (via differentiation). Thus if you wish to compute the risk numbers for a given shift (ie - a one basis point change in the parameter), then you simply multiply the risk number by the requested shift.
All of the functions implemented here have been taken from : 'The Complete Guide To OPTION PRICING FORMULAS' by Espen Gaarder Haug. This book provides an in-depth analysis of every function described here. We have just implemented these functions in C++ and extended their functionality to include risk-numbers.
- CapeTools Derivative Matrix
General Description
Functions that price vanilla and Exotic options using variations of the black-scholes model. These functions do not create objects ***BUT*** generate all the second order (including cross) derivatives and displays the results within a matrix.
The risk values computed are the mathematical definition of a derivative (via differentiation). Thus if you wish to compute the risk numbers for a given shift (ie - a one basis point change in the parameter), then you simply multiply the risk number by the requested shift. Thus for gamma risk (second derivative of the underlying price, for a one unit change of the underlying we multiply by (1^2 = 1). For a one basis point change in the underlying we multiply the results by (0.0001^2).
All of the functions implemented here have been taken from : 'The Complete Guide To OPTION PRICING FORMULAS' by Espen Gaarder Haug. This book provides an in-depth analysis of every function described here. We have just implemented these functions in C++ and extended their functionality to include risk-numbers.
- CapeTools Bump Risk
General Description
Functions that price vanilla and Exotic options using variations of the black-scholes model. These functions do not create objects ***BUT*** take range-valued parameters.
These functions are used to compute the changes in option values given a bump map that will be applied to one input parameter. The bump map can be a single value, a vector or a matrix input and will be simply added to the parameter that is to be bumped. The final result will be deducted from the base value. This function is very useful for scenario analysis.
These functions return risk numbers for every single double valued parameter (first and second derivatives including cross derivatives). Theta is (of course) computed even though it is a date parameter.
In addition, each parameter has a range object (excel range) as an input parameter. You can input a single-valued number in a range and if the function detects that the size of the other input ranges are longer, the function will automatically expand the single range to the same size. Every cell will contain the same constant number. This is used heavily within our examples.
First order derivative risk numbers can be requested by simply passing in the name of the parameter (preceded by the 'd' character) into the 'Greek' parameter of these functions (ie - dStock).
Second order derivative risk numbers can be requested by simply passing in the name of the parameter (preceded by the 'd' character) ( repeated twice) into the 'Greek' parameter of these functions (ie - dStockdStock).
Cross derivative risk numbers can be requested by simply passing in the name of the parameters (preceded by the 'd' character) into the 'Greek' parameter of these functions (ie - dStockdTime or dTimedStock).
You can of course make use of the following (in-built) case-insensitive Greek values :
- DELTA
- GAMMA
- VEGA
- VOLGA
- THETA
However when pricing options composed of two underlyers, we suggest using the former notation for the common risk values.
The risk values computed are the mathematical definition of a derivative (via differentiation). Thus if you wish to compute the risk numbers for a given shift (ie - a one basis point change in the parameter), then you simply multiply the risk number by the requested shift.
All of the functions implemented here have been taken from : 'The Complete Guide To OPTION PRICING FORMULAS' by Espen Gaarder Haug. This book provides an in-depth analysis of every function described here. We have just implemented these functions in C++ and extended their functionality to include risk-numbers.
- CapeTools Option Solver
General Description
These functions are used to solve for the value of a single double-valued parameter given the option premium's price. Volatility is often the most sought after parameter and once solved for, the result is called the implied volatility.
All of the functions implemented here have been taken from : 'The Complete Guide To OPTION PRICING FORMULAS' by Espen Gaarder Haug. This book provides an in-depth analysis of every function described here. We have just implemented these functions in C++ and extended their functionality to include risk-numbers.
- CapeTools Option Strategy
General Description
Prices a portfolio of option strategies on equity type underlyers (using the traditional black-scholes model). Possible option strategies are :
- Bull Call Spread
- Bull Put Spread
- Bear Call Spread
- Bear Put Spread
- Call Back Spread
- Put Back Spread
- Call Ratio Vertical Spread
- Put Ratio Vertical Spread
- Straddle
- Ratio Straddle
- Strangle
- Ratio Strangle
- Butterfly
- Xmas Tree
- Condor
Each row within the portfolio represents one strategy and when priced, you can request the price for the total portfolio, the price of each trade. In addition you can request detailed information for each trade.
- CapeTools Bonds
General Description
Functions for constructing a Bond object given a yieldcurve. You can construct FixedCoupon, FloatingRate, MoneyMarket or ZeroCoupon Bond objects.
You can query and price these bond objects via functions present within the 'CapeTools Query Bonds' category of functions.
- CapeTools Bonds (Yield)
General Description
Functions for constructing a Bond object given a yield-to-maturity value (YTM). You can construct FixedCoupon, FloatingRate, MoneyMarket or ZeroCoupon Bond objects.
In addition you can create currency specific FixedCoupon Bond objects. The following currency specific bonds are supported :
- Australian Commonwealth Government Bond (CGB)
- Austrian Federal Government Bond
- Belgian Government Bond (OLO)
- Canadian Treasury Bond (CANADA)
- Czech Government Bond
- Danish Government Bond (DGB)
- Dutch Government Bond (DSL)
- Finnish Government Bond (MARKKAS)
- French Government Bond (BTAN, OAT)
- German Federal Government Bond (BUND)
- Irish Government Bond (IGBS)
- Italian Government Bond (BTP)
- Japanese Government Bond (JGB)
- New Zealand Government Bond (NZG)
- Norwegian Government Bond
- Portuguese Government Bond (OT)
- South African Government Bond (GILT)
- Spanish Government Bond (BONOS)
- Swedish Government Bond (STATSSOBLIGATIONS)
- Swiss Government Bond (SGB)
- UK Government Bond (GILT)
- US Treasury Bond (TREASURY)
These bonds internally are all FixedCoupon Bond objects with a few of the parameters pre-programmed.
You can query and price these bond objects via functions present within the 'CapeTools Query Bonds' category of functions.
- CapeTools Bonds (Price)
General Description
Functions for constructing a Bond object given the Bond's clean price. You can construct FixedCoupon, FloatingRate, MoneyMarket or ZeroCoupon Bond objects.
In addition you can create currency specific FixedCoupon Bond objects. The following currency specific bonds are supported :
- Australian Commonwealth Government Bond (CGB)
- Austrian Federal Government Bond
- Belgian Government Bond (OLO)
- Canadian Treasury Bond (CANADA)
- Czech Government Bond
- Danish Government Bond (DGB)
- Dutch Government Bond (DSL)
- Finnish Government Bond (MARKKAS)
- French Government Bond (BTAN, OAT)
- German Federal Government Bond (BUND)
- Irish Government Bond (IGBS)
- Italian Government Bond (BTP)
- Japanese Government Bond (JGB)
- New Zealand Government Bond (NZG)
- Norwegian Government Bond
- Portuguese Government Bond (OT)
- South African Government Bond (GILT)
- Spanish Government Bond (BONOS)
- Swedish Government Bond (STATSSOBLIGATIONS)
- Swiss Government Bond (SGB)
- UK Government Bond (GILT)
- US Treasury Bond (TREASURY)
These bonds internally are all FixedCoupon Bond objects with a few of the parameters pre-programmed.
You can query and price these bond objects via functions present within the 'CapeTools Query Bonds' category of functions.
- CapeTools Query Bonds
General Description
Given Bond objects created via the 'CapeTools Bonds (Price)', 'CapeTools Bonds (Yield)' or 'CapeTools Bonds' categories of functions, the functions presented here can query for information or price the bond object.
- CapeTools Municipal Bonds
General Description
Functions for constructing a Municipal Bond object. A Municipal Bond object is really a portfolio of bonds with different maturities. However all the bonds use the same BusinessDayConvention, DayCounter and Coupon Frequency.
There are three Municipal Bond object creation functions. One that takes a YieldCurve, one that takes a clean price and finally one that takes a Yield-To-Maturity value.
Functions for querying and pricing these Municipal Bond objects are also present within this category.
- CapeTools Bond Portfolio
General Description
Functions for constructing a Portfolio of Bond objects.
There are three Portfolio Bond object creation functions. One that takes a YieldCurve, one that takes a clean price and finally one that takes a Yield-To-Maturity value.
Functions for querying and pricing these Portfolio Bond objects are also present within this category.
CapeTools Bond Portfolio Description
- CapeTools Forward Bonds
General Description
Functions for constructing Forward Bond Objects
There are two different functions for constructing Forward Bond objects. One that takes a repo curve (see CapeTools Repo Curves) and the other that takes a flat repo rate.
For functions that return derivative values, for example DRepo(), D2Repo(), DPrice() and D2Price(), the derivatives returned are the mathematically defined definition of a derivative. To convert this mathematical definition into a market move, simply multiply the result for the desired shift.
For example a one basis point change in the repo rate would require you to multiply the derivative value obtained from the DRepo() function by 0.00001 and the derivative value obtained from the D2Repo() function by 0.00001*0.00001.
- CapeTools Bond Options
General Description
Functions for constructing Bond Option Objects
There are two different functions for constructing Bond Option objects within this category. One that takes a repo curve (see CapeTools Repo Curves) and the other that takes a flat repo rate.
The functions presented here price European Bond Options. You will not generate accurate results if your underlying Bond object has any of the following features :
- Amortised Notionals
- Step Up/Down Coupon rates
This is because a Cox-Ross-Rubinstein Binomial Tree Engine is used to price the option and only the Bond Price is used from the Bond Object. The pricing algorithm here does not keep track of amortised/coupon values from cashflow to cashflow.
In addition, you cannot use this function if you require Bermudan type option prices.
In order to overcome these limitations, you need to use the Bond Option functions present within the [TOPIC]CapeTools IREngineOptions[TOPIC] category of functions. The Bond Option functions here utilize term-structure models.
- CapeTools FLOAT Legs
General Description
Creates interest rate floating leg objects. Amortised, Quanto, In-Arrear and constant-maturity-swap legs can be constructed.
Amortised legs can be constructed via the amortised versions of the leg objects or you can provide your own amortised notional values. If you are seeking to construct a regular, non amortised leg, simply pass in a single constant notional value to the notional range parameter.
These leg objects can be priced and queried via functions present within the 'CapeTools Query Legs' category of functions.
- CapeTools FIXED Legs
General Description
Creates interest rate FIXED leg objects. Amortised and non-amortised legs can be constructed.
Amortised legs can be constructed via the amortised versions of the leg objects or you can provide your own amortised notional values. If you are seeking to construct a regular, non amortised leg, simply pass in a single constant notional value to the notional range parameter.
These leg objects can be priced and queried via functions present within the 'CapeTools Query Legs' category of functions.
- CapeTools ZeroCoupon FLOAT Legs
General Description
Creates interest rate FIXED RATE leg objects that receive no cashflows until the maturity date of the leg.
These leg objects can be priced and queried via functions present within the 'CapeTools Query Legs' category of functions.
- CapeTools Averaging FLOAT Legs
General Description
Creates interest rate floating rate leg objects which averages a number of fixings within a paying coupon period. Amortised, Quanto, In-Arrear and constant-maturity-swap legs can be constructed.
Amortised legs can be constructed via the amortised versions of the leg objects or you can provide your own amortised notional values. If you are seeking to construct a regular, non amortised leg, simply pass in a single constant notional value to the notional range parameter.
These leg objects can be priced and queried via functions present within the 'CapeTools Query Legs' category of functions.
- CapeTools Compounding FLOAT Legs
General Description
Creates interest rate floating leg objects that receive no cashflows until the maturity date of the leg. Quanto, In-Arrear and constant-maturity-swap legs can be constructed.
These leg objects can be priced and queried via functions present within the 'CapeTools Query Legs' category of functions.
- CapeTools FIXED + FLOAT Legs
General Description
Creates interest rate inverse floater leg objects. Amortised, Quanto, In-Arrear and constant-maturity-swap floater legs can be constructed.
Amortised legs can be constructed via the amortised versions of the leg objects or you can provide your own amortised notional values. If you are seeking to construct a regular, non amortised leg, simply pass in a single constant notional value to the notional range parameter.
The payoff for this leg is in fact the difference of two coupons. The first a FIXED coupon rate, the second FLOAT rate. Thus for each coupon period, the coupon rate computed will be either a FIXED INVERSE FLOATER LEG [X - N*L] or a FLOAT INVERSE FLOATER LEG [N*L - X], where N is a positive integer gearing amount. N represents the 'FixingGearing' parameter within the function call. X is the FIXED coupon rate and L is the floating rate fixing.
These leg objects can be priced and queried via functions present within the 'CapeTools Query Legs' category of functions.
- CapeTools FIXED + AVERAGE FLOAT Legs
General Description
Creates interest rate inverse floater leg objects. Amortised, Quanto, In-Arrear and constant-maturity-swap floater legs can be constructed.
Amortised legs can be constructed via the amortised versions of the leg objects or you can provide your own amortised notional values. If you are seeking to construct a regular, non amortised leg, simply pass in a single constant notional value to the notional range parameter.
The payoff for this leg is in fact the difference of two coupons. The first a FIXED coupon rate, the second averages a number of fixings within the same paying coupon period. Thus for each coupon period, the coupon rate computed will be either a FIXED INVERSE FLOATER LEG [X - N*L] or a FLOAT INVERSE FLOATER LEG [N*L - X], where N is a positive integer gearing amount. N represents the 'FixingGearing' parameter within the function call. X is the FIXED coupon rate and L is the average of a number of fixings within the period.
These leg objects can be priced and queried via functions present within the 'CapeTools Query Legs' category of functions.
- CapeTools FIXED + COMPOUNDING FLOAT Legs
General Description
Creates interest rate inverse floater leg objects. Amortised, Quanto, In-Arrear and constant-maturity-swap floater legs can be constructed.
Amortised legs can be constructed via the amortised versions of the leg objects or you can provide your own amortised notional values. If you are seeking to construct a regular, non amortised leg, simply pass in a single constant notional value to the notional range parameter.
The payoff for this leg is in fact the difference of two coupons. The first a FIXED coupon rate, the second compounds a number of fixings within the same paying coupon period. Thus for each coupon period, the coupon rate computed will be either a FIXED INVERSE FLOATER LEG [X - N*L] or a FLOAT INVERSE FLOATER LEG [N*L - X], where N is a positive integer gearing amount. N represents the 'FixingGearing' parameter within the function call. X is the FIXED coupon rate and L is the result of a number of fixings compounded within the payment period.
These leg objects can be priced and queried via functions present within the 'CapeTools Query Legs' category of functions.
- CapeTools Exotic Legs
General Description
Creates an interest rate option strategy based on an floating interest rate leg (or an inverse floating leg). (using the traditional black model on futures). Possible option strategies are :
- Cap
- Floor
- Cap And Floor
- Bull Call Spread
- Bull Put Spread
- Bear Call Spread
- Bear Put Spread
- Butterfly
- Call Back Spread
- Put Back Spread
- Call Ratio Vertical Spread
- Put Ratio Vertical Spread
- Condor
- Straddle
- Strangle
- Xmas Tree
Each of the strategy above will be applied to each cashflow of the underlying leg.
In-Arrear legs on non-CMS indexes are not currently supported under this framework.
- CapeTools Query Legs
General Description
Functions to query for information given a leg object.
There are functions to query the details of a floating or fixed leg object. The underlying legs must have been created via leg creation functions within the following categories :
There are functions to display various cashflow details from the leg object as well as pricing the leg object.
In addition you can use the CreateStructure function to create a portfolio of leg objects
From this leg portfolio, you can solve for the flat coupon rate or flat margin rate across all the legs.
Furthermore, you can pass the object created from the CreateStructure function to the functions present within the CapeTools IR Risk category of functions in order to run complex interest rate risk analysis.
The CreateStructure function can take in objects created within the following category of functions :
However not all the legs (objects) created from these categories of functions are compatible for solving a flat margin/fixed coupon rate across all the legs (objects). The former list above lists the category of functions that satisfies this criterion.
From either of these lists, you can execute the PrcStructure function in order to see the aggregated PV.
Again interest rate risk can be conducted via the functions present within the CapeTools IR Risk category of functions.
- CapeTools Swaps
General Description
Functions to construct Swap Objects.
The types of swap objects that can be constructed are :
- FIX vs FIX
- FIX vs FLOAT
- FLOAT vs FLOAT
You can use the functions present within the CapeTools Query Swaps category of functions to query for information from these swap objects.
Please note that the SwapFIXFLT2 and SwapFIXFIX2 functions cannot be accessed from the Excel libraries because these functions have more than 21 argument parameters. Excel has a maximum limit of 20 parameters per function.
- CapeTools Query Swaps
General Description
Functions to query for information given a swap object.
The swap objects must have been created via the CapeTools Swaps category of functions.
There are functions to display detailed information regarding any of the legs contained within the swap structure as well as pricing the leg object.
- CapeTools Leg Portfolio
General Description
Functions to construct a portfolio of legs (Floating rate and Fixed rate leg).
In addition you can query for the total PV of the portfolio, the PV for each individual deal, basis point value (BPV) for the total portfolio, and the BPV for each individual deal.
Given an ID of a contract within the portfolio, you can request for more detailed information (a breakdown of the instrument cashflows).
- CapeTools Swap Portfolio
General Description
Functions to construct a portfolio of swaps (same currency).
In addition you can query for the total PV of the portfolio, the PV for each individual deal, basis point value (BPV) for the total portfolio, and the BPV for each individual deal.
Given an ID of a contract within the portfolio, you can request for more detailed information (a breakdown of the instrument cashflows).
- CapeTools Basis Swap Portfolio
General Description
Functions to construct a portfolio of interest rate basis swaps.
In addition you can query for the total PV of the portfolio, the PV for each individual deal, basis point value (BPV) for the total portfolio, and the BPV for each individual deal.
Given an ID of a contract within the portfolio, you can request for more detailed information (a breakdown of the instrument cashflows).
- CapeTools XCcy Swap Portfolio
General Description
Functions to construct a portfolio of cross-currency swaps.
In addition you can query for the total PV of the portfolio, the PV for each individual deal, basis point value (BPV) for the total portfolio, and the BPV for each individual deal.
Given an ID of a contract within the portfolio, you can request for more detailed information (a breakdown of the instrument cashflows).
- CapeTools CDS Swap Portfolio
General Description
Functions to construct a portfolio of regular and binary Credit Default Swap instruments.
In addition you can query for the total PV of the portfolio, the PV for each individual deal, basis point value (BPV) for the total portfolio, and the BPV for each individual deal.
Given an ID of a contract within the portfolio, you can request for more detailed information (a breakdown of the instrument cashflows).
- CapeTools CapFloor Portfolio
General Description
Functions to construct a portfolio of vanilla Cap/Floor instruments.
In addition you can query for the total PV of the portfolio and also the PV for each individual deal.
Given an ID of a contract within the portfolio, you can request for more detailed information.
There is also a function to construct a portfolio of Cap/Floor instruments where the prices are already known. From this one can request for the implied volatility for each Cap/Floor instrument.
- CapeTools Swaption Portfolio
General Description
Functions to construct a portfolio of vanilla swaption instruments.
In addition you can query for the total PV of the portfolio and also the PV for each individual deal.
Given an ID of a contract within the portfolio, you can request for more detailed information.
There is also a function to construct a portfolio of swaption instruments where the prices are already known. From this one can request for the implied volatility for each swaption instrument.
- CapeTools IR Risk
General Description
Functions to compute detailed interest rate risk analysis on a portfolio of deal types.
All of these reports take a Structure object which is created via the CreateStructure function.
A structure object can contain object deals created from the following categories of functions :
The following types of YieldCurve risk reports can be constructed :
The Gamma report contains all the information that the Delta report does.
YieldCurve risk is conducted by first identifying the points within the yieldcurve that all the deals within the structure object are sensitive to.
Then these points are bumped and all the deals repriced. Delta and/or Gamma risk is then computed and stored. Functions within the CapeTools Query IR Risk category of functions are then used to display the generated risk number for either all deals or a user-defined criteria.
The following types of VolCurve risk reports can be constructed :
The Volga report contains all the information that the Vega report does.
VolCurve risk is conducted by first identifying the points within the VolCurve that all the deals within the structure object are sensitive to.
Then these points are bumped and all the deals repriced. Vega and/or Volga (second derivative) risk is then computed and stored. Functions within the CapeTools Query IR Risk category of functions are then used to display the generated risk number for either all deals or a user-defined criteria.
These risk reports can be expensive (in time) especially for large portfolios and so the following functions can be used to read/write the internal state of any of the 5 risk reports above to a file.
These functions are useful for archiving risk reports or to quickly read a risk report in and then apply the same risk analysis one would normally do using the functions present within the CapeTools Query IR Risk category of functions.
The CreateSABRReport() is an very useful report as you can specify any of the three SABR parameters ('ALPHA', 'BETA' and 'RHO').
If the underlying VolCurve that is passed to the VegaRiskReport or VolgaRiskReport is a SABRVolCurve object that you will have realistic movement within the interest rate volatility smile than that of using the ExpiryKVolMatrix or ATMVolMatrix VolCurve objects. Normally when the At-The-Money volatility is bumped by 0.01, for example, the volatility smile does not move by 0.01 at all points. Traditional methods of bumping each point by 0.01 do not give a realistic movement of the volatility smile. The SABRVolCurve object captures this dynamic movement.
- CapeTools Query IR Risk
General Description
Functions to query risk reports produced by functions within the CapeTools IR Risk category of functions. There are four types of query functions within this category of functions.
The first are functions to query the report itself (Report functions). The types of legs, the list of legs and if one were to execute the QueryVCRiskReport() and QueryVCRiskReport() functions, which legs will be selected for the report.
The second category of functions are those that go out and actually produce the risk numbers (Query functions). These functions employ a kind of database SQL method in order to retrieve and aggregate the interest rate reports.
The third type of functions are those that act upon the YieldCurve or VolCurve that are to be manipulated (Curve functions). These functions simply returns a sensitivity curve/matrix of the instruments underlying the curves.
Finally the fourth type of functions are those that do not act upon the report itself, but rather the structure object (Structure functions). These functions simply report which legs within the structure object are sensitive to which curves (Yieldcurve or/and VolCurves).
Report functions are functions that help in determining the types of legs, leg types that are present within the report.
The following (Structure) functions provide a type of heat-map of the points that are to be manipulated during the construction of a riskreport (functions wihin the CapeTools IR Risk category of functions) :
Basically these functions take your structure object (generated via the CreateStructure() function) and the curve that is to be bumped and counts how many times each point within the curve (YieldCurve or VolCurve) are accessed. Thus you can see the points on the curve that have the largest concentration of activity given a structure.
The following (Structure) functions will display the list of legs within a structure object that are sensitive to the given curve (YieldCurve or VolCurve) :
The RiskGetYCVCSenLegs() function is quite interesting as it will return the list of legs that are sensitive to both the given VolCurve and YieldCurve.
The following (Curve) functions will display the sensitivity curve (in the case of a YieldCurve) or sensitivity matrix (in the case of a VolCurve) of the instruments underlying the curve. Thus for the 10Y Tenor within the YieldCurve, this will be the sensitivity (delta) of the 10 year swap rate from spot. For the 5Y into 10Y Volatility point on a SABR VolCurve, this will be the sensitivity (vega) of an At-The-Money 5Y into 10Y Swaption instrument :
The risk reports also store these sensitivity values and they can be extracted via the following functions (given a report object) :
These value are needed in order to output different risk report numbers (notional of the hedge instrument for example.)
The following (Report) functions list the leg names that are stored within the report :
These legs should correspond to the list of legs passed to the CreateStructure() function.
Each leg within a report is assigned a leg type. For example all legs created via functions contained within the 'CapeTools FLOAT Legs' category of functions are given a type of 'FLOAT'. When querying the risk reports you can supply a list of leg names, leg types or both.
Thus it is important to remember that a Leg-Name is an identifier for a single deal.
A Leg-Type however is a group of Leg-Names and thus is an identifier for a group of deals.
The following list provides the leg type assigned to the functions stored within the given function categories or functions :
The following (Report) functions will display the leg types given a risk report :
The following (Report) functions go further and display a two column range of LegName and the type associated with it :
The following (Report) functions will display a list of Leg-Name, given a Leg-Type. Thus if you pass in the type 'FLOAT', all objects created from the CapeTools FLOAT Legs category of functions and that have been processed by the risk report will be displayed :
From a combination of using the following functions above, you may have decided on a list of Leg-Names and/or Leg-Types that you wish to view a report from. You may also wish to see the whole list, but exclude certain Leg-Names and/or Leg-Types. Which legs will actually be selected given all the possible combinations?
The following list of (Report) functions allows you to view the resulting legs given Leg-Names and/or Leg-Types combinations with an exclusion criteria :
A powerful parameter to note is the 'Operation' parameter. Basically These functions take three lists :
- List of Leg-Names to view
- List of Leg-Types to view
- List of Leg-Names to exclude
How does the function, given this list, decide which legs to accept from the report and which legs to exclude?
This is where the 'Operation' parameter comes into play and takes on the following values, "And", "Or" and "Diff".
If the 'Operation' parameter is set to "And" then all the legs present in **BOTH** the Leg-Names (LimitToLegs parameter) **AND** Leg-Types (LimitToTypes parameter) are taken. Then the legs that are not wanted are excluded (ExcludeLegs parameter).
If the 'Operation' parameter is set to "Or" then all the legs present in **EITHER** the Leg-Names (LimitToLegs parameter) **OR** Leg-Types (LimitToTypes parameter) are taken. Then the legs that are not wanted are excluded (ExcludeLegs parameter).
If the 'Operation' parameter is set to "Diff" then basically we select all the legs within the report, apply the **AND** operator to generate a sub-list, throw away this sub-list and select whatever is left. Then the legs that are not wanted are excluded (ExcludeLegs parameter).
Executing the QueryLegsYCRiskReport or QueryLegsVCRiskReport will help you to ensure that you are using the correct logic when trying to compose a list of legs to base your report on.
Finally the following (Query) functions will apply a selection criteria to the generated report and list the risk numbers that you are requesting :
The parameters are similar to that of the QueryLegsYCRiskReport and QueryLegsVCRiskReport functions except that you also provide how you would like to see your risk numbers.
In the case of a Gamma or Volga Report, you can also request for Delta and Vega results as these are computed as well.
- CapeTools Simple Processes
General Description
Functions to construct various Equity, Future, FX or Commodity type process objects. A process object simulates an asset value (or a correlated set of asset values) over time.
The following asset functions can be used :
- GBSProcess() -Generalized BlackScholes Process.
- BS73Process() - Black-Scholes (1973) stochastic process.
- BlackProcess() - Black (1976) stochastic process.
- GKProcess() - Garman-Kohlhagen (1983) stochastic process.
- Merton76Process() - Merton (1976) Process.
Some basic stochastic process objects that can be constructed are :
- GBMProcess() - Geometric Brownian Motion Process.
- OUProcess() - OrnsteinUhlenbeck Process.
- SQRTProcess() - Square Root Process.
- SQRTProcess() - Square Root Process.
Finally you can group a collection of stochastic process objects along with a correlation matrix via the following function :
- CorrArrayProcesses() - Creates an array of correlated one dimensional stochastic processes.
All of these objects can be passed to various pricing functions (see the CapeTools EngineOptions category of functions).
You can set up your own simulation of these processes by using the functions contained within the CapeTools (Full) Process Simulation or CapeTools (Compact) Process Simulation category of functions.
Additionally you can carry out your own generic pricing via the GenericMCPricer, GenericTreePricer or GenericPDEPricer functions.
- CapeTools LMM Processes
General Description
Functions to construct Libor Market Model simulation process objects.
Given Libor Libor Market Model volatility and correlation specification objects (see CapeTools EngineOptions), creates a Libor Forward Market Simulation Process object to be used within the CapeTools LMM Process Simulation or CapeTools Generic IR LMM MonteCarlo Pricer category of functions.
Volatility and correlation specification objects can be produced via a call to any of the appropriate functions within the CapeTools LMM Volatility/Correlation Models category of functions.
Within the LMMSimProcess function, you can set the number of simulations to zero (0). In this case no simulations will be generated, but you can request a new simulation path from this object by executing the LMMNextPath function. This will return a 2 column array of rates and discount factors. You can also perform generic montecarlo pricing via the GenericLMM_MCPricer function.
- CapeTools IR Processes
General Description
Functions to construct short-rate model simulation process objects.
Currently, we only have one model defined and that is a single-factor Hull-White (extended Vasicek) Forward short-rate Model process object. Defined as : dr_t = (theta(t) - alpha*r_t)dt + sigma*dW_t, where alpha and sigma are constants
You can set up your own simulation of these processes by using the functions contained within the CapeTools (Full) IR Process Simulation or CapeTools (Compact) IR Process Simulation category of functions.
- CapeTools (Full) Process Simulation
General Description
Functions to construct and simulate Equity, Future, FX or Commodity type stochastic processes.
The (Full) indicates that if one wishes to conduct 50000 simulations, all 50000 simulations will be simulated in one shot, via the ProcessViewer function.
All further functions that refers to the object constructed by the ProcessViewer function simply reads data from the object. No further simulation takes place.
The benefit of this method is that enough information is returned for you to conduct your own customised monte-carlo pricing within your own environment (you can additionally use the functions present within the CapeTools Generic MonteCarlo Pricer category of functions.). Because all the paths are retained, with a little more work, you can compute the risk parameters of your product (not present within the CapeTools Generic MonteCarlo Pricer category of functions.)
Unfortunately, this object will utilize a lot of memory if you specify a huge amount of paths to be simulated.
You may want to use the DeleteObject() function to remove the simulation object from memory once you have priced you product.
Alternatively, you may want to use the functions present within the CapeTools (Compact) Process Simulation category of functions. Here each time you execute the MCNextStep function from a constructed StepMonteCarlo object a new path is generated and the previous path destroyed.
This uses less memory, but makes it difficult for you to compute risk numbers using the original paths.
- CapeTools (Compact) Process Simulation
General Description
Functions to construct and simulate Equity, Future, FX or Commodity type stochastic processes.
The (Compact) indicates that a single path will be simulated each time you call the MCNextStep function from a constructed StepMonteCarlo object.
The benefit of this method is that enough information is returned for you to conduct your own customised monte-carlo pricing within your own environment.
However it would be difficult to compute risk numbers as the original path would have been wiped from memory (if generating risk via perturbation).
Alternatively, you may want to use the functions present within the CapeTools (Full) Process Simulation category of functions. Under this scenario, if one wishes to conduct 50000 simulations, all 50000 simulations will be simulated in one shot, via the ProcessViewer function and all the paths are stored.
However you may want to use the DeleteObject() function to remove the simulation object from memory once you have priced you product.
- CapeTools (Full) IR Process Simulation
General Description
Functions to construct and simulate interest rate type stochastic processes.
The (Full) indicates that if one wishes to conduct 50000 simulations, all 50000 simulations of LIBOR paths will be simulated in one shot, via the IRProcessViewer function.
All further functions that refers to the object constructed by the IRProcessViewer function simply reads data from the object. No further simulation takes place.
The benefit of this method is that enough information is returned for you to conduct your own customised monte-carlo pricing within your own environment. Because all the paths are retained, with a little more work, you can compute the risk parameters of your product.
Unfortunately, this object will utilize a lot of memory if you specify a huge amount of paths to be simulated.
You may want to use the DeleteObject() function to remove the simulation object from memory once you have priced you product.
Alternatively, you may want to use the functions present within the CapeTools (Compact) IR Process Simulation category of functions. Here each time you execute the IRMCNextStep function from a constructed IRStepMonteCarlo object a new LIBOR path is generated and the previous path destroyed.
This uses less memory, but makes it difficult for you to compute risk numbers using the original paths.
- CapeTools (Compact) IR Process Simulation
General Description
Functions to construct and simulate interest rate type stochastic processes.
The (Compact) indicates that a single LIBOR path will be simulated each time you call the IRMCNextStep function from a constructed IRStepMonteCarlo object.
The benefit of this method is that enough information is returned for you to conduct your own customised monte-carlo pricing within your own environment.
However it would be difficult to compute risk numbers as the original path would have been wiped from memory (if generating risk via perturbation).
Alternatively, you may want to use the functions present within the CapeTools (Full) IR Process Simulation category of functions. Under this scenario, if one wishes to conduct 50000 simulations, all 50000 simulations of LIBOR paths will be simulated in one shot, via the IRProcessViewer function and all the paths are stored.
However you may want to use the DeleteObject() function to remove the simulation object from memory once you have priced you product.
- CapeTools LMM Process Simulation
General Description
Functions to construct and simulate interest rate type stochastic processes under the LMM model.
A single LIBOR path will be simulated each time you call the LMMNextPath function from a constructed LMMSimProcess object.
The benefit of this method is that enough information is returned for you to conduct your own customised monte-carlo pricing within your own environment.
However it would be difficult to compute risk numbers as the original path would have been wiped from memory (if generating risk via perturbation).
Alternatively, if you specified a number for the 'NoOfSims' parameter within the LMMSimProcess function, then under this scenario, if one wishes to conduct 50000 simulations, all 50000 simulations of LIBOR paths will be simulated in one shot and stored.
You then use a series of functions to extract information from the stored paths ( ie - LMMDisplayPath, LMMDisplayStep etc...).
However you may want to use the DeleteObject() function to remove the simulation object from memory once you have priced you product.
- CapeTools Generic PDE Pricer
General Description
Functions to price generic Equity/FX/Commodity structures under a PDE framework. If your product's payoff does not refer to asset prices in the past (ie - Asian options) you can use this framework. This framework can also handle bermudan callable structures
Here are some general rules to keep in mind regarding how the payoff grid will be processed :
- Rows are time points. As you read down the grid you are moving forward in time.
- Columns represent your payoff formulas. You can create as many columns as you like. Columns are there to help you split up your payoff, or for a payoff function within a cell to refer to other cells within the grid.
- For the PDE pricer, the pricing starts at the final timestep and prices from left to right.
- Formula expressions within a cell cannot refer to formula cells to the right of itself.
- Formula expressions within a cell cannot refer to formula cells above itself (past time points).
If you bear the 5 points in mind, this should aid you in constructing payoff grids.
Below is an example of a payoff table. This deal prices a callable structure (The Step column is not required).
| Step | EventDate | Repeat? | PayOff Col | PayOff Col | PayOff Col | PayOff Col | PayOff Col |
|---|
| 1 | #19/07/2005# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 2 | #19/01/2006# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 3 | #19/07/2006# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 4 | #19/01/2007# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 5 | #19/07/2007# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 6 | #19/01/2008# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 7 | #19/07/2008# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 8 | #19/01/2009# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 9 | #19/07/2009# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 10 | #19/01/2010# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 11 | #19/07/2010# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
| 12 | #19/01/2011# | FALSE | Asset(cRow) + 10pct | Interp1D(1,cRow) | GridRowSum(cRow, cCol-2, cCol-1) | max(Cell(cRow, cCol-1) - _var1, 0.0) | max(Cell(cRow, cCol-1), PVCol(cCol)) |
The 'Repeat' column indicates that the instruction at the current step will be repeated for all the timesteps between this and the next.
Even though there are only 12 timesteps above, you can instruct the function to insert additional steps between each step.
Financial variables (case sensitive) :
- cRow - refers to the current Row with the payoff table. Within all the Financial functions listed below, we recommend that you always use this variable (with perhaps offset values, ie - cRow, cRow-1, cRow+2 etc...) instead of a fixed value (ie - 1, 2 etc...). This is important especially if you enable American type handling from one timestep to another. Using static integer values will generate incorrect results.
- cCol - refers to the current Column with the payoff table. Within all the financial functions listed below, we recommend that you always use this variable (with perhaps offset values, ie - cCol, cCol-1, cCol+2 etc...).
- pct - When an integer value is placed in front of this expression (no spaces), the function will interp the whole expression as a percent. (ie - 5pct => 0.05)
- bp - When an integer value is placed in front of this expression (no spaces), the function will interp the whole expression as basis points. (ie - 5bp => 0.0005)
- _XXX - Constant variables can be defined by filling in the 'ConstParams' parameter of the GenericPDEPricer() function. All variables must be defined with a leading underscore character ( ie - _XXX = 0.5)
Financial functions (case sensitive) :
- Asset(row) - Returns the asset value at the integer row indicated. Starts at 1. You may refer to future values of the asset's price because the PDE methodology prices backwards in time (from the last expiry date). The expression 'Asset(cRow)' retrieves the asset price for the current timestep. The expression 'Asset(cRow+1)' retrieves the asset price for the next timestep (in the future).
- Cell(row, col) - Retrieves a computed value within the PayOff Table. You can only refer to rows and columns below and to the left of the current cell location. You can also refer to the current cell location. This is because the PDE pricer prices backwards in time and thus past payoff values have not been computed as yet. The expression 'Cell(cRow, cCol-1)' retrieves the payoff value for the current timestep but at the previous column.
- GridRowMin(Row, startCol, endCol) - Retrieves the minimum value across the columns of the PayOff table (given a 'TimeStep' or row value). For the 'startCol' and 'endCol' parameters you can only refer to columns to the left or equal to the current cell location.
- GridRowMax(Row, startCol, endCol) - Retrieves the maximum value across the columns of the PayOff table (given a 'TimeStep' or row value). For the 'startCol' and 'endCol' parameters you can only refer to columns to the left or equal to the current cell location.
- GridRowAvg(Row, startCol, endCol) - Retrieves the average value across the columns of the PayOff table (given a 'TimeStep' or row value). For the 'startCol' and 'endCol' parameters you can only refer to columns to the left or equal to the current cell location.
- GridRowSum(Row, startCol, endCol) - Retrieves the sum across the columns of the PayOff table (given a 'TimeStep' or row value). For the 'startCol' and 'endCol' parameters you can only refer to columns to the left or equal to the current cell location.
- Interp1D(nIndex, XValue ) - If any 1D interpolation objects have been passed into GenericPDEPricer() function (a maximum of 2 objects can be defined), then you can execute this function within your payoff grid. The 'nIndex' parameter refers to the intepolation object (1-based). 'XValue' is the value where the interpolation is to be performed. The interpolation object will not extrapolate values.
- Interp2D(nIndex, XValue, YValue) - If any 2D interpolation objects have been passed into GenericPDEPricer() function (a maximum of 2 objects can be defined), then you can execute this function within your payoff grid. The 'nIndex' parameter refers to the intepolation object (1-based). 'XValue' and 'YValue' are the values where the interpolation is to be performed. The interpolation object will not extrapolate values.
- iff(condition, a, b) - Tests for the condition and returns the value of 'a' if true or 'b' if false.
- PVCol(Column) - Requests the PV value of the indicated column up to the current step (cRow). This function must be used when pricing Bermudan / American type products.
Predefined functions (case sensitive) :
- sin(x) ( sine function )
- cos(x) ( cosine function )
- tan(x) ( tangens function )
- asin(x) ( arcus sine function )
- acos(x) ( arcus cosine function )
- atan(x) ( arcus tangens function )
- sinh(x) ( hyperbolic sine function )
- cosh(x) ( hyperbolic cosine function )
- tanh(x) ( hyperbolic tangens function )
- asinh(x) ( hyperbolic arcus sine function )
- acosh(x) ( hyperbolic arcus cosine function )
- atanh(x) ( hyperbolic arcur tangens function )
- log2(x) ( logarithm to the base 2 )
- log10(x) ( logarithm to the base 10 )
- log(x) ( logarithm to the base 10 )
- ln(x) ( logarithm to the base e (2.71828...)
- exp(x) ( e raised to the power of x )
- sqrt(x) ( square root of a value )
- sign(x) ( sign function ) -1=(if x<0), 1=(if x>0 )
- rint(x) ( round to nearest integer )
- abs(x) ( absolute value )
- min(a,b,c,d,e,...) ( min of all arguments ie - min(-2,1,5,-6) )
- max(a,b,c,d,e,...) ( max of all arguments ie - max(-2,1,5,-6) )
- sum(a,b,c,d,e,...) ( sum of all arguments ie - sum(-2,1,5,-6) )
- avg(a,b,c,d,e,...) ( mean value of all arguments ie - avg(-2,1,5,-6) )
- ite(x,y,z) ( if ... then ... else ... : ie - ite(a<b, 5.0, -3.0) )
Predefined operators :
- + ( addition )
- - ( subtraction )
- * ( multiplication )
- / ( division )
- ^ ( raise x to the power of y )
Predefined operators that can be used within the first parameter of the ite() or iff() function :
- and ( logical and )
- or ( logical or )
- <= ( less or equal )
- >= ( greater or equal )
- != ( not equal )
- == ( equal to )
- > ( greater than )
- < ( less than )
- Brackets, '(' and ')', can also be used to simplify expressions.
Some possible examples of what is possible now follow (Today = 19/07/2005):
Vanilla Option. (The Step column is not required).
| Step | EventDate | Repeat? | PayOff Col | |
|---|
| 1 | #19/07/2006# | FALSE | max(Asset(cRow) - 10, 0) | |
Sum of two Vanilla Options (Call and Put). (The Step column is not required).
| Step | EventDate | Repeat? | PayOff Col | |
|---|
| 1 | #19/07/2006# | FALSE | 100 | max(Asset(cRow) - Cell(cRow, cCol-1), 0) + PVCol(cCol) |
| 2 | #19/07/2007# | FALSE | 90 | max(Cell(cRow, cCol-1) - Asset(cRow), 0) |
American Option (Repeat column and PVCol() function are used differently). (The Step column is not required).
| Step | EventDate | Repeat? | PayOff Col | |
|---|
| 1 | #19/07/2005# | TRUE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 1 | #19/07/2006# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
Delayed start American Option (starts at 19/10/2005, today is 19/07/2005). (The Step column is not required).
| Step | EventDate | Repeat? | PayOff Col | |
|---|
| 1 | #19/10/2005# | TRUE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 1 | #19/10/2006# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
Bermudan Option. (The Step column is not required).
| Step | EventDate | Repeat? | PayOff Col | |
|---|
| 1 | #19/07/2005# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 2 | #19/01/2006# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 3 | #19/07/2006# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 4 | #19/01/2007# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 5 | #19/07/2007# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 6 | #19/01/2008# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 7 | #19/07/2008# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 8 | #19/01/2009# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 9 | #19/07/2009# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
Starts as American then becomes Bermudan Option. (The Step column is not required).
| Step | EventDate | Repeat? | PayOff Col | |
|---|
| 1 | #19/07/2005# | TRUE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 2 | #19/01/2006# | TRUE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 3 | #19/07/2006# | TRUE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 4 | #19/01/2007# | TRUE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 5 | #19/07/2007# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 6 | #19/01/2008# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 7 | #19/07/2008# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 8 | #19/01/2009# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
| 9 | #19/07/2009# | FALSE | max(Asset(cRow) - 10, PVCol(cCol)) | |
Chooser Option. (The Step column is not required).
| Step | EventDate | Repeat? | PayOff Col | PayOff Col | |
|---|
| 1 | #19/07/2005# | FALSE | | max(PVCol(cCol-1), PVCol(cCol)) | |
| 2 | #19/07/2006# | FALSE | max(Asset(cRow) - 10, 0) | max(10 - Asset(cRow), 0) | |
Compound Option (european on european). (The Step column is not required).
