Just-in-Time Monte Carlo for Path Dependent American Options

Abstract

We establish simple analytical and numerical methods for propagating stochastic price processes backwards in time, step by step, to the initial value while satisfying all cross-sectional and serial requirements. This proves useful in dealing with complex path-dependent options with American triggers, where storing the history of the underlying can become computationally onerous. Examples involving the Wiener, Ornstein-Uhlenbeck, Clark, and Cox-Ingersoll-Ross processes illustrate our techniques. Our "just-in-time" method, which can be thought of as stochastic involution, extends the reach and accuracy of Monte Carlo pricing techniques beyond what has hitherto been possible.

Keywords: American options, least squares Monte Carlo, stochastic involution

JEL Classification: C15, G12, G13