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Most-Likely-Path In Asian Option Pricing Under Local Volatility Models

Author

Listed:
  • LOUIS-PIERRE ARGUIN

    (Department of Mathematics, Baruch College, CUNY, 1 Bernard Baruch Way, New York, NY 10010, USA)

  • NIEN-LIN LIU

    (BKC Research Organization of Social Sciences, Ritsumeikan University, Noji-higashi 1-1-1, Kusatsu, Shiga 525-8577, Japan)

  • TAI-HO WANG

    (Department of Mathematics, Baruch College, CUNY, 1 Bernard Baruch Way, New York, NY 10010, USA)

Abstract

This paper addresses the problem of approximating the price of options on discrete and continuous arithmetic averages of the underlying, i.e. discretely and continuously monitored Asian options, in local volatility models. A “path-integral”-type expression for option prices is obtained using a Brownian bridge representation for the transition density between consecutive sampling times and a Laplace asymptotic formula. In the limit where the sampling time window approaches zero, the option price is found to be approximated by a constrained variational problem on paths in time-price space. We refer to the optimizing path as the most-likely path (MLP). An approximation for the implied normal volatility follows accordingly. The small-time asymptotics and the existence of the MLP are also rigorously recovered using large deviation theory.

Suggested Citation

  • Louis-Pierre Arguin & Nien-Lin Liu & Tai-Ho Wang, 2018. "Most-Likely-Path In Asian Option Pricing Under Local Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(05), pages 1-32, August.
    • Handle: RePEc:wsi:ijtafx:v:21:y:2018:i:05:n:s0219024918500292
    DOI: 10.1142/S0219024918500292
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    References listed on IDEAS

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    Cited by:

    1. Dan Pirjol, 2020. "Asymptotic expansion for the Hartman-Watson distribution," Papers 2001.09579, arXiv.org, revised Feb 2021.
    2. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    3. Dan Pirjol, 2024. "Subleading correction to the Asian options volatility in the Black-Scholes model," Papers 2407.05142, arXiv.org, revised Aug 2024.
    4. Dan Pirjol & Lingjiong Zhu, 2024. "Short-maturity Asian options in local-stochastic volatility models," Papers 2409.08377, arXiv.org.
    5. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility," Papers 2308.15672, arXiv.org, revised Feb 2024.

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