Pricing Asian Options for Jump Diffusions

TL;DR

This paper develops a fast numerical method for pricing Asian options on stocks with jump diffusion dynamics, using a sequence of PDE solutions that converge rapidly to the true option price.

Contribution

It introduces a sequence of PDE-based approximations that efficiently compute Asian option prices under jump diffusion models, avoiding complex integro-differential equations.

Findings

The approximation converges uniformly and exponentially fast.

The method provides controllable accuracy and speed.

Numerical examples demonstrate effective performance.

Abstract

We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. Each of the element in this sequence solves a parabolic partial differen- tial equation (not an integro-differential equation). As a result we obtain a fast numerical approximation scheme whose accuracy versus speed characteristics can be controlled. We analyze the performance of our numerical algorithm on several examples.