By Silvian G.R. Meier, University of Zurich

and Espen G. Haug

Using Monte Carlo simulation to value American or Bermuda style derivatives was considered to be more or less impossible just a few years ago. But the science of Monte Carlo simulation used in finance has been moving fast. In 1997 Broadie and Glasserman published a MC method that can be used to value such derivatives.

Here we demonstrate this powerful Monte Carlo method live on the web, using a JAVA applet. This applet can be used to compare American Monte Carlo with well known numerical methods for American options: binomial, trinomial lattices and finite difference schemes. For comparison we have also included the Black-Scholes-Merton formula (European options only). The example applies to a standard option on a single asset. In this case Monte Carlo models are naturally not preferred. However, to value American/Bermuda style derivatives on multiple assets American Monte Carlo simulation is one of the few methods that can make it. The programming of the Monte Carlo model was done by Silvan G.R. Meier, a quant from the University of Zurich, Switzerland. The remaining models was implemented by Espen G. Haug.

You will need a browser that supports JAVA 2 (Explorer 5.0 or Netscape 4.5). Remember also to enable JAVA.

The applet didn't run on my Mac :-(

• Volatility should be written as 20 for 20%.
• Rate should be written as 10 for 10%

Bermuda options are options with exercise style between European and American. That is a Bermuda style option have a limited number of exercise opportunities during the options life time.

In the Broadie and Glasserman model the computer time grows exponentially with the number of exercise opportunities. If the number of exercise opportunities is set to more than 3 or 4 the calculation will be quite time consuming. In the other numerical models the number of exercise opportunities is equal to the number of time steps.

References:

Broadie, M. and Glasserman, P. 1997: "Pricing American-Style Securities Using Simulation," Journal of Economics Dynamics and Control, 21, 1323-1352