optstocksensbybls - Determine option prices and sensitivities using Black-Scholes option pricing model

Syntax

Arguments

RateSpec	The annualized continuously compounded rate term structure. For information on the interest rate specification, see intenvset.
StockSpec	Stock specification. See stockspec.
Settle	NINST-by-1 vector of settlement or trade dates.
Maturity	NINST-by-1 vector of maturity dates.
OptSpec	NINST-by-1 cell array of strings 'call' or 'put'.
Strike	NINST-by-1 vector of strike price values.
OutSpec	(Optional) All optional inputs are specified as matching parameter name/value pairs. The parameter name is specified as a character string, followed by the corresponding parameter value. Parameter name/value pairs may be specified in any order; names are case-insensitive and partial string matches are allowed provided no ambiguities exist. Valid parameter names are: NOUT-by-1 or 1-by-NOUT cell array of strings indicating the nature and order of the outputs for the function. Possible values are: 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', or 'All'. For example, OutSpec = {'Price'; 'Lamba'; 'Rho'} specifies that the output should be Price, Lambda, and Rho, in that order. To invoke from a function: [Price, Lambda, Rho] = optstocksensbybls(..., 'OutSpec', {'Price', 'Lamba', 'Rho'}) OutSpec = {'All'} specifies that the output should be Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec as OutSpec = {'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', 'Price'};. Default is OutSpec = {'Price'}.

Description

PriceSens = optstocksensbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike, 'Name1', Value1...) computes option prices and sensitivities using the Black-Scholes option pricing model.

PriceSens is a NINST-by-1 vector of expected prices or sensitivities values.

Note   When using StockSpec with optstocksensbybls, you can modify StockSpec to handle other types of underliers when pricing instruments that use the Black-Scholes model. When pricing Futures (Black model), enter the following in StockSpec: DivType = 'Continuous'; DivAmount = RateSpec.Rates; When pricing Foreign Currencies (Garman-Kohlhagen model), enter the following in StockSpec: DivType = 'Continuous'; DivAmount = ForeignRate; where ForeignRate is the continuously compounded, annualized risk free interest rate in the foreign country.

Examples

Consider a European call and put options with an exercise price of $30 that expires on June 1, 2008. The underlying stock is trading at $30 on January 1, 2008 and has a volatility of 30% per annum. The annualized continuously compounded risk-free rate is 5% per annum. Using this data, compute the delta, gamma, and price of the options using the Black-Scholes model.

AssetPrice = 30;
Strike = 30;
Sigma = .30;
Rates = 0.05;
Settle = 'January-01-2008';
Maturity = 'June -01-2008';

Define RateSpec and StockSpec :

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates',...
Maturity, 'Rates', Rates, 'Compounding',-1, 'Basis', 1);

StockSpec = stockspec(Sigma, AssetPrice);

Define the options:

OptSpec = {'call', 'put'};

Compute delta, gamma, and price for the European options:

OutSpec = {'Delta','Gamma','Price'};
[Delta, Gamma, Price] = optstocksensbybls(RateSpec, StockSpec, Settle,...
Maturity, OptSpec, Strike,'OutSpec', OutSpec)

Delta =

    0.5810
   -0.4190


Gamma =

    0.0673
    0.0673


Price =

    2.6126
    1.9941

See Also

impvbybls | intenvset | optstockbybls | stockspec

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