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Asymptotics for short maturity Asian options in jump-diffusion models with local volatility

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  • Dan Pirjol
  • Lingjiong Zhu

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 Lévy jumps, including the exponential Lévy 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.

Suggested Citation

  • Dan Pirjol & Lingjiong Zhu, 2024. "Asymptotics for short maturity Asian options in jump-diffusion models with local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 24(3-4), pages 433-449, March.
    • Handle: RePEc:taf:quantf:v:24:y:2024:i:3-4:p:433-449
    DOI: 10.1080/14697688.2024.2326114
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