Documentation

# 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 = 3×1 111.6683 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).

collapse all

### Rainbow Option

A rainbow option payoff depends on the relative price performance of two or more assets.

A rainbow option gives the holder the right to buy or sell the best or worst of two securities, or options that pay the best or worst of two assets. Rainbow options are popular because of the lower premium cost of the structure relative to the purchase of two separate options. The lower cost reflects the fact that the payoff is generally lower than the payoff of the two separate options.

Financial Instruments Toolbox™ supports two types of rainbow options:

• Minimum of two assets — The option holder has the right to buy(sell) one of two risky assets, whichever one is worth less.

• Maximum of two assets — The option holder has the right to buy(sell) one of two risky assets, whichever one is worth more.