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minassetbystulz

Determine European rainbow option prices on minimum of two risky assets using Stulz option pricing model

Syntax

Price = minassetbystulz(RateSpec,StockSpec1,StockSpec2,Settle,Maturity,OptSpec,Strike,Corr)

Description

example

Price = minassetbystulz(RateSpec,StockSpec1,StockSpec2,Settle,Maturity,OptSpec,Strike,Corr) computes option prices using the Stulz option pricing model.

Examples

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Consider a European rainbow put option that gives the holder the right to sell either stock A or stock B at a strike of 50.25, whichever has the lower value on the expiration date May 15, 2009. On November 15, 2008, stock A is trading at 49.75 with a continuous annual dividend yield of 4.5% and has a return volatility of 11%. Stock B is trading at 51 with a continuous dividend yield of 5% and has a return volatility of 16%. The risk-free rate is 4.5%. Using this data, if the correlation between the rates of return is -0.5, 0, and 0.5, calculate the price of the minimum of two assets that are European rainbow put options. First, create the RateSpec:

Settle = 'Nov-15-2008';
Maturity = 'May-15-2009';
Rates = 0.045;
Basis = 1;

RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', -1, 'Basis', Basis)
RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: -1
             Disc: 0.9778
            Rates: 0.0450
         EndTimes: 0.5000
       StartTimes: 0
         EndDates: 733908
       StartDates: 733727
    ValuationDate: 733727
            Basis: 1
     EndMonthRule: 1

Create the two StockSpec definitions.

AssetPriceA = 49.75;
AssetPriceB = 51;
SigmaA = 0.11;
SigmaB = 0.16;
DivA = 0.045; 
DivB = 0.05; 

StockSpecA = stockspec(SigmaA, AssetPriceA, 'continuous', DivA)
StockSpecA = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1100
         AssetPrice: 49.7500
       DividendType: {'continuous'}
    DividendAmounts: 0.0450
    ExDividendDates: []

StockSpecB = stockspec(SigmaB, AssetPriceB, 'continuous', DivB)
StockSpecB = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1600
         AssetPrice: 51
       DividendType: {'continuous'}
    DividendAmounts: 0.0500
    ExDividendDates: []

Compute the price of the options for different correlation levels.

Strike = 50.25;
Corr = [-0.5;0;0.5];
OptSpec = 'put';
Price = minassetbystulz(RateSpec, StockSpecA, StockSpecB, Settle,...
Maturity, OptSpec, Strike, Corr)
Price = 3×1

    3.4320
    3.1384
    2.7694

The values 3.43, 3.14, and 2.77 are the price of the European rainbow put options with a correlation level of -0.5, 0, and 0.5 respectively.

Input Arguments

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Annualized, continuously compounded rate term structure, specified using intenvset.

Data Types: structure

Stock specification for asset 1, specified using stockspec.

Data Types: structure

Stock specification for asset 2, specified using stockspec.

Data Types: structure

Settlement or trade dates, specified as an NINST-by-1 vector of numeric dates.

Data Types: double

Maturity dates, specified as an NINST-by-1 vector.

Data Types: double

Option type, specified as an NINST-by-1 cell array of character vectors with a value of 'call' or 'put'.

Data Types: cell

Strike prices, specified as an NINST-by-1 vector.

Data Types: double

Correlation between the underlying asset prices, specified as an NINST-by-1 vector.

Data Types: double

Output Arguments

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Expected option prices, returned as an NINST-by-1 vector.

Introduced in R2009a