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

Dan Pirjol; Lingjiong Zhu

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arXiv · 2308.15672

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

Dan Pirjol·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.

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Dan Pirjol, Lingjiong Zhu. 2023-08-30. Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility. https://arxiv.org/abs/2308.15672

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