The First-Passage Approach to Valuing the American Put Option
University of California-Riverside Working Paper 98-03
Posted: 29 Jun 1998
Date Written: February 1998
We express the American put price as an integral involving first-passage probabilities. This approach allows us an intuitive interpretation to Merton's result for the perpetual put. We also consider the finite-lived case, derive a differential equation for the critical-stock-price function, and develop candidate analytical solutions that satisfy conditions which occur for short and long times to maturity. We present numerical results demonstrating that these solutions for the critical-stock-price functions and numerical integration of the first-passage probability expression to compute accurate prices for American put options.
JEL Classification: G13
Suggested Citation: Suggested Citation