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Determine price or sensitivities of gap digital options using Black-Scholes model


PriceSens = gapsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold)
PriceSens = gapsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold,OutSpec)



The annualized, continuously compounded rate term structure. For information on the interest rate specification, see intenvset.


Stock specification. See stockspec.


NINST-by-1 vector of settlement or trade dates.


NINST-by-1 vector of maturity dates.


NINST-by-1 cell array of character vectors with values of 'call' or 'put'.


NINST-by-1 vector of strike price values.


NINST-by-1 vector of strike values that determine if the option pays off.


(Optional) All optional inputs are specified as matching parameter name-value pairs. The parameter name is specified as a character vector, followed by the corresponding parameter value. You can specify parameter name-value pairs may in any order. Names are case-insensitive and partial matches are allowed provided no ambiguities exist. Valid parameter names are:

  • NOUT-by-1 or 1-by-NOUT cell array of character vectors 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] = gapsensbybls(..., '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'}.


PriceSens = gapsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold) computes gap option prices using the Black-Scholes option pricing model.

PriceSens = gapsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold,OutSpec) includes an OutSpec argument defined as parameter/value pairs, and computes gap option prices or sensitivities using the Black-Scholes option pricing model.

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


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This example shows how to compute gap option prices and sensitivities using the Black-Scholes option pricing model. Consider a gap call and put options on a nondividend paying stock with a strike of 57 and expiring on January 1, 2008. On July 1, 2008 the stock is trading at 50. Using this data, compute the price and sensitivity of the option if the risk-free rate is 9%, the strike threshold is 50, and the volatility is 20%.

Settle = 'Jan-1-2008';
Maturity = 'Jul-1-2008';
Compounding = -1; 
Rates = 0.09;
%create the RateSpec
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', 1);
% define the StockSpec
AssetPrice = 50;
Sigma = .2;
StockSpec = stockspec(Sigma, AssetPrice);
% define the call and put options
OptSpec = {'call'; 'put'};
Strike = 57;
StrikeThreshold = 50;
% compute the price
Pgap = gapbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec,...
Strike, StrikeThreshold)
Pgap = 


% compute the gamma and delta
OutSpec = {'gamma'; 'delta'};
[Gamma ,Delta] = gapsensbybls(RateSpec, StockSpec, Settle, Maturity,... 
OptSpec, Strike, StrikeThreshold, 'OutSpec', OutSpec)
Gamma = 


Delta = 


Introduced in R2009a

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