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  1. 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.


  2. 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.


  3. 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.


  4. 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.


  5. 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.


  6. 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.

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