### About the Problem

Derivative securities are financial instruments whose value are *derived* from other securities. They are mostly used to help large institutions reduce the risks associated with their portfolios.
There are several ways to compute the expected value of a derivative security. These methods require knowledge of several statistics of the *underlying security*, such as the mean return and the standard deviation of the return (the *volatility*). If these parameters are constant, and if the interest rate is constant, then reasonable formulas exist for determining the value of the derivative. However, if these parameters are not constant, then the simple formulas are not sufficient: price movements of the underlying security as well as the interest rate must be simulated. In general, this *Monte Carlo* simulation is a difficult computational problem, but is well-suited for parallel computation. This applet shows how parallelism can be used to solve the problem of evaluating derivatives.

### How to Use the Derivative Calculator

This Derivative Calculator computes the value of a European put option on an underlying security. The option expires in 1 year. A buyer of the option thinks that the initial price of the underlying will be less than the strike price of the underlying at the end of one year. In the dialog box, you can change
- The initial price of the underlying
- The
*strike price* of the underlying
- An interest rate range (from lower rate to upper rate)
- The number of randomly generated interest rate scenarios (from 1 to 8)

We assume that the volatility of the underlying is 40% per year. The applet generates an interest rate scenario and price scenario based on simulated movements in 100 discrete periods (about every 2 trading days). Change the 5 inputs and watch the scenarios unfold in time in the red slider bars!
This calculator is based on a paper, "Fast-Cost-Effective Computations of Derivatives," published in the *Proceedings of the Third International Conference on Artificial Intelligence Applications on Wall Street*.
Inductive Solutions, Inc. is a New York City corporation that specializes in applying innovative technologies to real-world problems. Drop us a line at
Inductive_Solutions@MCIMail.com.