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Determine price of gap digital options using Black-Scholes model


Price = gapbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold)



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 payoff strike price values.


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


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

Price is a NINST-by-1 vector of expected option prices.


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This example shows how to compute gap option prices 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 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;
% calculate 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;
% calculate the price
Pgap = gapbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec,...
Strike, StrikeThreshold)
Pgap = 


Introduced in R2009a

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