Instructor: Siva Athreya
E-Mail: athreya@isid.ac.in
WWW: http://www.isid.ac.in/~athreya/Teaching/finance
Time: I would prefer one two and half hour session a week with a half hour break in the middle. This is flexible-open to suggestions, will depend on students attending.
Office: 213
Phone: 656 5050 dial 213 at the beep.
Text(s):
Prerequisites: Undergraduate Real Analysis and/or undegraduate probability theory and/or concepts of finance.
Anyone is welcome to attend but must email the instructor as soon as possible, no later than December 15th, 2002. The person attending must be willing to submit weekly assignments.
We will begin with a quick introduction to basic probability concepts- such as random variables, basic distrubition functions, notion of independence, conditional expectation. Then we will device a method on how to price an option when the stock price dynamics is the Binomial model and understand their solutions in probabilistic terms. We will discuss Complete markets, Arbitrage pricing theory and certain well known options (American, Asian, European, Exotic) and at each stage setting up things mathematically.
A study of Random walk and other concepts will be geared towards understanding Brownian motion and Stochastic Calculus, which will be discussed at length. The time spent will be on concepts relevant to finance and applications there in. This will be the significant part of the course ending in the Black-scholes pricing of an option and notions of partial differential equations.
In the unlikely scenario of left over time: We will do either Girsanov Theorem and discuss the risk neutral measure or do some applications in finance.