BASKET OPTIONSAND MONTE CARLO

METHODSAllissa Cembrook

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.

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

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

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.

Basket OptionsA 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.

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.

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.

Initial Steps in R

Set up parameters for the optionStarting Stock PriceRiskless Interest RateDrift (sigma)Time to expiry

Set up empty matrices for two stocks Define number of random walks needed Set up an empty payoff vector

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 payoffThe difference between the average of the

final stock price and the strike or nothing if the difference is negative.

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.).