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optstocksensbyblk

Determine option prices and sensitivities on futures using Black pricing model

Syntax

PriceSens = optstocksensbyblk(RateSpec, StockSpec, Settle,
Maturity, OptSpec, Strike, 'Name1', Value1...)

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'; 'Lambda'; 'Rho'} specifies that the output should be Price, Lambda, and Rho, in that order.

    To invoke from a function: [Price, Lambda, Rho] = optstocksensbyblk(..., 'OutSpec', {'Price', 'Lambda', '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 = optstocksensbyblk(RateSpec, StockSpec, Settle,
Maturity, OptSpec, Strike, 'Name1', Value1...)
computes option prices and sensitivities on futures using the Black pricing model.

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

Examples

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Compute Option Prices and Sensitivities on Futures Using the Black Pricing Model

This example shows how to compute option prices and sensitivities on futures using the Black pricing model. Consider a European put option on a futures contract with an exercise price of $60 that expires on June 30, 2008. On April 1, 2008 the underlying stock is trading at $58 and has a volatility of 9.5% per annum. The annualized continuously compounded risk-free rate is 5% per annum. Using this data, compute delta, gamma, and the price of the put option.

AssetPrice = 58;
Strike = 60;
Sigma = .095;
Rates = 0.05;
Settle = 'April-01-08';
Maturity = 'June-30-08';

% define the 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 = {'put'};

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

   -0.7469


Gamma =

    0.1130


Price =

    2.3569

See Also

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