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assetbybls

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

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Syntax

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

Description

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

Note

Alternatively, you can use the Binary object to price digital options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

example

Examples

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Open Live Script

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 = datetime(2008,11,3);
Maturity = datetime(2009,1,30);
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

   33.7666
   26.9662

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 using a datetime array, string array, or date character vectors.

To support existing code, assetbybls also accepts serial date numbers as inputs, but they are not recommended.

Maturity date for the basket option, specified as an NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, assetbybls also accepts serial date numbers as inputs, but they are not recommended.

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.

Version History

Introduced in R2009a

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See Also

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