Pricing American Options for Jump Diffusions by Iterating Optimal Stopping Problems for Diffusions

TL;DR

This paper introduces an iterative numerical method for approximating American put option prices under jump diffusion models, leveraging optimal stopping problems for Brownian motion and finite difference techniques.

Contribution

It presents a novel iterative scheme that converges rapidly to the true option price, combining jump diffusion modeling with classical numerical methods.

Findings

Convergence is uniform and exponentially fast.

Method accurately approximates American put prices under jump diffusions.

Numerical examples demonstrate the scheme's effectiveness.

Abstract

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically computed using the classical finite difference methods. We prove the convergence of this numerical scheme and present examples to illustrate its performance.