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MA 490-02: The Mathematics of Option and Derivative Pricing

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Kurt Bryan, Winter 2007-08

Most people are familiar with traditional investments like stocks,
bonds, and commodities. However, in the past few decades a huge
market has arisen in the trading of "options" and other "financial
derivatives", contracts in which payment is based on the value of
some benchmark, e.g., the price of a given stock on a certain
date. In short, the value of the contract is derived from the
price of some underlying asset (hence the term "derivative').

As an example, suppose a contract is written in which I give you
the option (but not the obligation) to buy from me one share of
Microsoft stock for a guaranteed price of $25 on March 1, 2008
(today, September 28, 2007, it's selling for about $29). This is an example of
a European Call Option, in which you have the right to buy some
asset at a guaranteed price sometime in the future. How much
should you pay to enter into such an agreement? Surprisingly,
there is a very quantitative strategy for determining the value of
this option contract.

In this class we'll examine the problem of option
pricing. We'll start by looking at various types of options, and at
probabilistic models for random fluctuations in asset prices. We'll also
derive the celebrated Black-Scholes partial differential equation
which shows how one can rationally determine option prices. This
is the work for which Robert Merton and Myron Scholes won the 1997
Nobel Prize in economics.

A variety of different mathematics will appear in the course, including simple probability,
differential equations, and some numerical techniques. We'll learn what we need as
we need it. The only prerequisites are the first year calculus and second year differential equations
sequence. The grading in this course will be based on homework assignments,
in-class work, and a couple take-home exams.

Go check out this link for more information!