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maxassetbystulz

Determine European rainbow option price on maximum of two risky assets using Stulz option pricing model

Syntax

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

Arguments

RateSpec

The annualized, continuously compounded rate term structure. For information on the interest rate specification, see intenvset.

StockSpec1

Stock specification for asset 1. See stockspec.

StockSpec2

Stock specification for asset 2. See stockspec.

Settle

NINST-by-1 vector of settlement or trade dates.

Maturity

NINST-by-1 vector of maturity dates.

OptSpec

NINST-by-1 cell array of character vectors 'call' or 'put'.

Strike

NINST-by-1 vector of strike price values.

Corr

NINST-by-1 vector of correlation between the underlying asset prices.

Description

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

Price is a NINST-by-1 vector of expected option prices.

Examples

collapse all

Consider a European rainbow option that gives the holder the right to buy either $100,000 worth of an equity index at a strike price of 1000 (asset 1) or $100,000 of a government bond (asset 2) with a strike price of 100% of face value, whichever is worth more at the end of 12 months. On January 15, 2008, the equity index is trading at 950, pays a dividend of 2% annually and has a return volatility of 22%. Also on January 15, 2008, the government bond is trading at 98, pays a coupon yield of 6%, and has a return volatility of 15%. The risk-free rate is 5%. Using this data, if the correlation between the rates of return is -0.5, 0, and 0.5, calculate the price of the European rainbow option.

Since the asset prices in this example are in different units, it is necessary to work in either index points (asset 1) or in dollars (asset 2). The European rainbow option allows the holder to buy the following: 100 units of the equity index at $1000 each (for a total of $100,000) or 1000 units of the government bonds at $100 each (for a total of $100,000). To convert the bond price (asset 2) to index units (asset 1), you must make the following adjustments:

  • Multiply the strike price and current price of the government bond by 10 (1000/100).

  • Multiply the option price by 100, considering that there are 100 equity index units in the option.

Once these adjustments are introduced, the strike price is the same for both assets ($1000). First, create the RateSpec:

Settle = 'Jan-15-2008';
Maturity = 'Jan-15-2009';
Rates = 0.05;
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: 0.9512
            Rates: 0.0500
         EndTimes: 1
       StartTimes: 0
         EndDates: 733788
       StartDates: 733422
    ValuationDate: 733422
            Basis: 1
     EndMonthRule: 1

Create the two StockSpec definitions.

AssetPrice1 = 950;   % Asset 1 => Equity index
AssetPrice2 = 980;   % Asset 2 => Government bond
Sigma1 = 0.22;
Sigma2 = 0.15;
Div1 = 0.02; 
Div2 = 0.06; 

StockSpec1 = stockspec(Sigma1, AssetPrice1, 'continuous', Div1)
StockSpec1 = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.2200
         AssetPrice: 950
       DividendType: {'continuous'}
    DividendAmounts: 0.0200
    ExDividendDates: []

StockSpec2 = stockspec(Sigma2, AssetPrice2, 'continuous', Div2)
StockSpec2 = struct with fields:
             FinObj: 'StockSpec'
              Sigma: 0.1500
         AssetPrice: 980
       DividendType: {'continuous'}
    DividendAmounts: 0.0600
    ExDividendDates: []

Calculate the price of the options for different correlation levels.

Strike = 1000 ; 
Corr = [-0.5; 0; 0.5];
OptSpec = 'call';

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

  111.6683
  103.7715
   92.4412

These are the prices of one unit. This means that the premium is 11166.83, 10377.15, and 9244.12 (for 100 units).

Introduced in R2009a

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