Mathematics Achieves Command of Financial Risks

By Roger Lee & Ronnie Sircar

Stock market risk is one of the types of risk which affect financial derivatives.  In particular, equity derivatives are designed to depend on stock market events.

Financial derivatives -- such as options, futures, and swaps -- are instruments which deliver payoffs specified in terms of some underlying risks – such as a stock prices, commodity prices, interest rates, foreign exchange rates, credit events, and weather events.

As of mid-2007, the notional value referenced by financial derivatives totaled more than $613 trillion, and the gross market value of the financial derivatives themselves totaled more than $11 trillion – a value comparable to one year’s GDP of the United States.  The notional value of over-the-counter financial derivatives has more than doubled since 2004 and quintupled since 2001. 

Fueling this explosive growth, applications of mathematics have guided the way for practitioners to understand and to manage the risks driving these instruments, and thereby to allocate each risk -- away from those individuals or firms or governments who don’t want to bear it, and to those who do want to accept it.  Conversely, when misunderstood or mismanaged, these risks may erupt in spectacular disasters.

Click the links to the right to learn more about types of risks involved in financial derivatives, and how mathematical tools give us control over those risks.



About the Authors

Roger Lee, Univeristy of Chicago
Ronnie Sircar, Princeton University