cashbybls - Determine price of cash-or-nothing digital options using Black-Scholes model

Syntax

Price = cashbybls(RateSpec, StockSpec, Settle, Maturity,
OptSpec, Strike, Payoff)

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.
Payoff	NINST-by-1 vector of payoff values or the amount to be paid at expiration.

Description

Price = cashbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike, Payoff) computes cash-or-nothing option prices using the Black-Scholes option pricing model.

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

Examples

Consider a European call and put cash-or-nothing options on a futures contract with and exercise strike price of $90, a fixed payoff of $10 that expires on October 1, 2008. Assume that on January 1, 2008, the contract trades at $110, and has a volatility of 25% per annum and the risk-free rate is 4.5% per annum. Using this data, calculate the price of the call and put cash-or-nothing options on the futures contract.

Create the RateSpec:

Settle = 'Jan-1-2008';
Maturity = 'Oct-1-2008';
Rates = 0.045;
Compounding = -1;  
Basis = 1;
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis);

Define the StockSpec:

AssetPrice = 110;
Sigma = .25;
DivType = 'Continuous';
DivAmount = Rates;
StockSpec = stockspec(Sigma, AssetPrice, DivType, DivAmount);

Define the call and put options:

OptSpec = {'call'; 'put'};
Strike = 90;
Payoff = 10;

Calculate the price:

Pcon = cashbybls(RateSpec, StockSpec, Settle,...
Maturity, OptSpec, Strike, Payoff)

Pcon =

    7.6716
    1.9965

See Also

assetbybls | cashsensbybls | gapbybls | supersharebybls

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