Oct 12

3:30 pm

## An Introduction to Option Pricing: Black-Scholes, Biniomial Trees and Other Comments

### R. Douglas Martin

Seminar

University of Washington

In 1997 the Nobel Prize for Economics was awarded to Myron Scholes and Robert Merton for their work on the Black-Scholes option pricing model. It was only unfortunate that Fisher Black had died in an untimely fashion and was unable to share in the award. The collective pioneering work of Black, Scholes and Merton has had a tremendous influence on both traders and researchers in the area of option and derivative product price models. In effect their work has helped spawn a new discipline sometimes called "financial engineering." There are several components to this tutorial talk. First I will sketch the derivation of the Black-Scholes option pricing model for European calls and puts. The result is based on a geometric Brownian motion model for stock prices, the notion of an Ito process and Ito's Lemma, and uses notions of "no arbitrage," "risk free interest rates" and "risk neutral" worlds. Then I will sketch the use of binomial tree models as an alternative flexible approach for pricing derivative products that works in situations not covered by the Black-Scholes theory. I will also point to related statistical problems of interest because of the, e.g., modeling and forecasting volatility.

With regard to the "Other Comments": Option Pricing is just one of the many interesting problems in modern finance that have a probability and statistical aspects - there are many other interesting problem areas in finance where I believe application of modern statistical theory and methods can result in significant advances. This has motivated me to put effort into an initiative to create a new interdisciplinary Master's Degree program in "Quantitative and Computational Finance" at the University of Washington. I will briefly describe the motivation for such a program and it's general nature, and will describe one or two examples of new programs of this type at other universities (e.g., the Carnegie-Mellon program).