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

Dan Pirjol, Lingjiong Zhu

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)433-449
Number of pages17
JournalQuantitative Finance
Volume24
Issue number3-4
DOIs
StatePublished - 2024

Keywords

  • Asian options
  • Local volatility
  • Lévy jumps
  • Short maturity

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