Multi-Asset Options

Diversifying the Underlying

These exotic options have payoffs that depend on the performance of multiple underlying assets. This introduces correlation considerations into their valuation and use.

1. Basket Options:

   • What it is: A basket option has a payoff that depends on the aggregate value of a portfolio (or "basket") of assets.

   • Key Features:

     • Basket Composition: The specific assets included in the basket and their weights.
     • Correlation: The correlation between the assets in the basket is a key factor in determining the option's value.
     • Risk Management Tool: Allows investors to manage risk across a portfolio of assets with a single instrument.

   • Types:

     • Basket Call Option: Pays max(0, Basket Value - K) at expiration.
     • Basket Put Option: Pays max(0, K - Basket Value) at expiration.

     Where K is the strike price.

   • Purpose:

     • Hedging Portfolio Risk: Provides a convenient way to hedge the overall risk of a portfolio.
     • Expressing Views on a Sector or Market: Can be used to bet on the performance of a specific sector or market.

   • Example:

     • A basket call option on a technology index, where the basket value is the weighted average of the prices of the stocks in the index.

   • Payoff Formulas:

     • Basket Call: max(0, Basket Value - K)
     • Basket Put: max(0, K - Basket Value)

2. Options to Exchange One Asset for Another (Exchange Options):

   • What it is: An option that gives the holder the right to exchange one asset (A) for another asset (B) at expiration.

   • Key Features:

     • Two Underlying Assets: The payoff depends on the relative values of the two assets.
     • Correlation: The correlation between the two assets is a crucial factor in the option's value.

   • Purpose:

     • Hedging Commodity Price Risk: Useful for companies that use one commodity to produce another (e.g., an oil refiner).
     • Speculating on Relative Value: Allows traders to bet on the relative performance of two assets.

   • Example:

     • An option to exchange 100 barrels of crude oil for 50 ounces of gold.
     • The payoff is max(0, Value of Gold - Value of Oil)

   • Valuation:

     • The most famous valuation model for an option to exchange one asset for another is Margrabe's formula.
     • Exchange options can be valued using an adaptation of the Black-Scholes model, treating one asset as the "underlying" and the other as the "strike price."

Comparison Table: