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


PriceSens = assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike)
PriceSens = assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OutSpec)



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.


(Optional) All optional inputs are specified as matching parameter name-value pairs. The parameter name is specified as a character vector, followed by the corresponding parameter value. You can specify parameter name-value pairs in any order. Names are case-insensitive and partial matches are allowed provided no ambiguities exist. Valid parameter names are:

  • NOUT-by-1 or 1-by-NOUT cell array of character vectors indicating the nature and order of the outputs for the function. Possible values are 'Price', 'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', or 'All'.

    For example, OutSpec = {'Price'; 'Lambda'; 'Rho'} specifies that the output should be Price, Lambda, and Rho, in that order.

    To invoke from a function: [Price, Lambda, Rho] = assetsensbybls(..., 'OutSpec', {'Price', 'Lambda', 'Rho'})

    OutSpec = {'All'} specifies that the output should be Delta, Gamma, Vega, Lambda, Rho, Theta, and Price, in that order. This is the same as specifying OutSpec as OutSpec = {'Delta', 'Gamma', 'Vega', 'Lambda', 'Rho', 'Theta', 'Price'};.

  • Default is OutSpec = {'Price'}.


PriceSens = assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike) computes asset-or-nothing option prices using the Black-Scholes option pricing model.

PriceSens = assetsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OutSpec) includes the parameter/value pairs defined for OutSpec, and computes asset-or-nothing option prices or sensitivities using the Black-Scholes option pricing model.

PriceSens is a NINST-by-1 vector of expected option prices or sensitivities.


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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 and sensitivity 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 delta, price, and gamma.

OutSpec = { 'delta';'price';'gamma'};
[Delta, Price, Gamma] = assetsensbybls(RateSpec, StockSpec, Settle,...
Maturity, OptSpec, Strike, 'OutSpec', OutSpec)
Delta = 


Price = 


Gamma = 


Introduced in R2009a

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