T. R. (Tom) Hurd

Professor of Mathematics

Financial Mathematics: what's it all about?

Modern financial mathematics has grown enormously in tandem with the importance of derivative securities, ever since the revolutionary work of Black--Scholes--Merton in 1973. Derivatives of the financial variety are essentially contracts whose value becomes determined by the performance of an underlying security or collection of securities. The basic examples are simple put and call options: a put option gives the purchaser the option to sell a security at a specified price at a specified time; likewise, a call option is the option to buy.

While the popular perception of derivatives as dangerous instruments used to speculate wildly on stocks, their pragmatic use in industry is the exact opposite. By purchasing the right combination of derivatives, market participants can reduce or eliminate their natural exposure to risk. For example, the canny hog farmer may choose to buy a number of put options on pork bellies which mature around the date he intends to put his produce on the market. This way he protects himself against a sharp decline in the market value of his livestock. Of course, he'll have to pay a price to offset his risk: puts can be expensive.

The problem with derivatives is that while straightforward to use, they are difficult to price. It was the brilliance of Black, Scholes and Merton which led to the development of arbitrage pricing theory for derivatives. However, the pricing of derivatives is only as good as the stochastic modeling of the underlying securities, which may be any of a multitude of different varieties: stocks, bonds, FX rates, commodities, etc.

This is where math really starts: adequate modeling of any of these problems will require at minimum graduate level mathematics, probability and statistics, plus a very strong capacity for computation. This explains why the financial industry continues to cry out for graduates in mathematics or physics: Ph.D. level preparation is a minimum requirement for many of the most attractive careers in the financial industry.

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last updated  2/06/04