gapbybls - Determine price of gap digital options using Black-Scholes 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 payoff strike price values.
StrikeThreshold	NINST-by-1 vector of strike values that determine if the option pays off.

Description

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.

Examples

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%.

Create the RateSpec:

Settle = 'Jan-1-2008';
Maturity = 'Jul-1-2008';
Compounding = -1; 
Rates = 0.09;
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 =

   -0.0053
    4.4866

See Also

assetbybls | cashbybls | gapsensbybls | supersharebybls

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