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


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



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 payoff values or the amount to be paid at expiration.


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.


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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. First, 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)
RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9668
            Rates: 0.0450
         EndTimes: 0.7500
       StartTimes: 0
         EndDates: 733682
       StartDates: 733408
    ValuationDate: 733408
            Basis: 1
     EndMonthRule: 1

Define the StockSpec.

AssetPrice = 110;
Sigma = .25;
DivType = 'Continuous';
DivAmount = Rates;
StockSpec = stockspec(Sigma, AssetPrice, DivType, DivAmount)
StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.2500
         AssetPrice: 110
       DividendType: {'continuous'}
    DividendAmounts: 0.0450
    ExDividendDates: []

Define the call and put options.

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

Calculate the prices.

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


Introduced in R2009a

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