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


Price = assetbyls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)



Price = assetbyls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike) computes asset-or-nothing European digital options using the Black-Scholes option pricing model.


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Consider two asset-or-nothing put options on a nondividend paying stock with a strike of 95 and 93 and expiring on January 30, 2009. On November 3, 2008 the stock is trading at 97.50. Using this data, calculate the price of the asset-or-nothing put options if the risk-free rate is 4.5% and the volatility is 22%. First, create the RateSpec.

Settle = 'Nov-3-2008';
Maturity = 'Jan-30-2009';
Rates = 0.045;
Compounding = -1;
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding)
RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9893
            Rates: 0.0450
         EndTimes: 0.2391
       StartTimes: 0
         EndDates: 733803
       StartDates: 733715
    ValuationDate: 733715
            Basis: 0
     EndMonthRule: 1

Define the StockSpec.

AssetPrice = 97.50;
Sigma = .22;
StockSpec = stockspec(Sigma, AssetPrice)
StockSpec = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.2200
         AssetPrice: 97.5000
       DividendType: []
    DividendAmounts: 0
    ExDividendDates: []

Define the put options.

OptSpec = {'put'};
Strike = [95;93];

Calculate the price.

Paon = assetbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike)
Paon = 2×1


Input Arguments

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Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

Stock specification for the underlying asset. For information on the stock specification, see stockspec.

stockspec handles several types of underlying assets. For example, for physical commodities the price is StockSpec.Asset, the volatility is StockSpec.Sigma, and the convenience yield is StockSpec.DividendAmounts.

Data Types: struct

Settlement or trade date for the basket option, specified as an NINST-by-1 vector of serial date numbers or date character vectors.

Data Types: double | char | cell

Maturity date for the basket option, specified as an NINST-by-1 vector of serial date numbers or date character vectors.

Data Types: double | char | cell

Definition of the option as 'call' or 'put', specified as an NINST-by-1 vector.

Data Types: char | cell

Pay-off strike value, specified as an NINST-by-1 vector.

Data Types: double

Output Arguments

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Expected prices for asset-or-nothing option, returned as a NINST-by-1 vector.

Introduced in R2009a