Simulation and the Early Exercise Option Problem

Abstract

This article uses Monte Carlo simulation to identify optimal early-exercise condition(s) for options. Thus, Monte Carlo simulation can value American style options for which there is no closed form solution and which may be too complex for other numerical methods. We first illustrate the procedure and demonstrate its accuracy by valuing an option with a known solution, the American put on an asset price that follows a pure diffusion stochastic process. We then demonstrate the flexibility of the method, and its capacity to value options that other methods cannot, by valuing an American put on an asset price that follows a jump diffusion stochastic process.