- 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.
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