Basket Options And Monte Carlo Methods

1. Allissa Cembrook Basket OptionsAnd Monte Carlo Methods

2. Financial Basics • Investors purchase shares in the hopes that the company does well and will pay dividends to its shareholders. • Financial derivatives are contracts between a writer (seller) and a holder (buyer). • Derivatives are based on some underlying equity.

3. Financial Derivatives • Financial derivatives are contracts that are based on the expected future price of an asset (i.e. currencies, commodities, securities). • They are considered to be extremely profitable but also can be extremely risky. • Used for hedging, arbitrage, speculation • Examples: forwards, options, swaps, futures

4. Role of Derivatives in the Financial Crisis of 2008 • Mortgage-backed securities • Long Term Capital Management • Credit Default Swaps • Collateralized Debt Obligations • Bear Stearns, Lehman Brothers, Merrill Lynch

5. Definition of a Basket Option • A basket option is a type of financial derivative whose underlying asset is a “basket” of commodities, securites, and currencies. • Basket options are usually cash settled. • Also called a Multifactor Option, whose payoff depends on the performance of two or more underliers.

6. Basket Options A basket option is a form of a financial derivative. This option is based on two or more underlying assets. The payoff of this option is a function of a weighted average of these underlying assets. Some examples of basket options include Options on a Portfolio and Index options.

7. Why? • Basket options are typically used by large corporations to hedge their risk in the foreign exchange markets. • By using a basket option, the corporation can hedge their risk on multiple currencies at once instead of purchasing options on each individual currency.

8. Correlation between Underliers • From the perspective of this project, I will be investigating the changes in the price of an option when the correlation between the assets in the basket is constant and when it is variable. • Basket options are typically a weighted average of the underlying equities. First, I will look at the pricing of basket options when the correlation factor, rho, is constant.

9. Initial Steps in R • Set up parameters for the option • Starting Stock Price • Riskless Interest Rate • Drift (sigma) • Time to expiry • Set up empty matrices for two stocks • Define number of random walks needed • Set up an empty payoff vector

10. Initial Steps in R (cont’d) • Create random variables Z1 and Z2 such that the following is true: • Z1=sigma1*N(0,sqrt(dt)) • Z2=rho*Z1+(1-rho^2)*sigma2*N(0,sqrt(dt)) • Create loops that generate the random walks • Evaluate the payoff • The difference between the average of the final stock price and the strike or nothing if the difference is negative.

11. Next Steps for the Project • Correlation factor that is variable • How does this variation affect the price of the option? • Investigate the implications of adding a third asset to the basket. • How does the code in R change? • How does the pricing change? • Apply a basket option to a set of actual underliers (i.e. Google, Apple, etc.).