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Basket OptionsAnd Monte Carlo Methods

Allissa Cembrook

Slide2Financial 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.

Slide3Financial 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, speculationExamples: forwards, options, swaps, futures

Slide4Role of Derivatives in the Financial Crisis of 2008

Mortgage-backed securitiesLong Term Capital ManagementCredit Default SwapsCollateralized Debt ObligationsBear Stearns, Lehman Brothers, Merrill Lynch

Slide5Definition 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.

Slide6Basket 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.

Slide7Why?

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.

Slide8Correlation 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.

Slide9Initial 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

Slide10Initial 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.

Slide11Next 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.).

## Basket Options

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