Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility

TL;DR

This paper derives short-maturity asymptotics for Asian options in jump-diffusion models with local volatility, providing explicit formulas and an analytical approximation validated by simulations.

Contribution

It extends asymptotic analysis to models with Lévy jumps, including exponential Lévy, and offers a practical approximation method for Asian option pricing.

Findings

Asymptotic formulas match Monte Carlo results for small maturities.

Explicit first-order asymptotics for Merton, double-exponential, and Variance Gamma models.

Proposed approximation satisfies short-maturity constraints and performs well in tests.

Abstract

We present a study of the short maturity asymptotics for Asian options in a jump-diffusion model with a local volatility component, where the jumps are modeled as a compound Poisson process. The analysis for out-of-the-money Asian options is extended to models with L\'evy jumps, including the exponential L\'{e}vy model as a special case. Both fixed and floating strike Asian options are considered. Explicit results are obtained for the first-order asymptotics of the Asian options prices for a few popular models in the literature: the Merton jump-diffusion model, the double-exponential jump model, and the Variance Gamma model. We propose an analytical approximation for Asian option prices which satisfies the constraints from the short-maturity asymptotics, and test it against Monte Carlo simulations. The asymptotic results are in good agreement with numerical simulations for sufficiently small maturity.