On approximating deep in‐the‐money Asian options under exponential Lévy processes

This note proposes a new approach of valuing deep in‐the‐money fixed strike and discretely monitoring arithmetic Asian options. This new approach prices Asian options whose underlying asset price evolves according to the exponential of a Lévy process as a weighted sum of European options. Numerical results from experimenting on three different types of Lévy processes—a diffusion process, a jump diffusion process, and a pure jump process—illustrate the accuracy of the approach. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark