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

Dan Pirjol and Lingjiong Zhu

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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.

Date: 2023-08, Revised 2024-02
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Published in Quantitative Finance 2024, Vol. 24, Nos. 3-4, 433-449

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