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Some asymptotics for short maturity Asian options

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  • Humayra Shoshi
  • Indranil SenGupta

Abstract

Most of the existing methods for pricing Asian options are less efficient in the limit of small maturities and small volatilities. In this paper, we use the large deviations theory for the analysis of short-maturity Asian options. We present a local volatility model for the underlying market that incorporates a jump term in addition to the drift and diffusion terms. We estimate the asymptotics for the out-of-the-money, in-the-money, and at-the-money short-maturity Asian call and put options. Under appropriate assumptions, we show that the asymptotics for out-of-the-money Asian call and put options are governed by rare events. For the at-the-money Asian options, the result is more involved and in that case, we find the upper and lower bounds of the asymptotics of the Asian option price.

Suggested Citation

  • Humayra Shoshi & Indranil SenGupta, 2023. "Some asymptotics for short maturity Asian options," Papers 2302.05421, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2302.05421
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    References listed on IDEAS

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    1. Victor Nistor & Wen Cheng & Nick Costanzino & John Liechty & Anna L. Mazzucato, 2011. "Closed-form asymptotics and numerical approximations of 1{D} parabolic equations with applications to option pricing," Post-Print hal-01284880, HAL.
    2. Humayra Shoshi & Erik Hanson & William Nganje & Indranil SenGupta, 2021. "Stochastic Analysis and Neural Network-Based Yield Prediction with Precision Agriculture," JRFM, MDPI, vol. 14(9), pages 1-17, August.
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    7. Humayra Shoshi & Indranil SenGupta, 2020. "Hedging and machine learning driven crude oil data analysis using a refined Barndorff-Nielsen and Shephard model," Papers 2004.14862, arXiv.org, revised Feb 2021.
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