Basket Options with monte carlo applications

Allissa 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
 Derivatives are based on some underlying
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,
Examples: forwards, options,
swaps, futures
Role of Derivatives in the
Financial Crisis of 2008
 Long Term Capital
 Credit Default Swaps
 Collateralized Debt
 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
 Basket options are usually cash settled.
 Also called a Multifactor Option, whose
payoff depends on the performance of
two or more underliers.
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
Some examples of basket
options include Options on a
Portfolio and Index options.
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
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
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
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
 Evaluate the payoff
 The 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.).