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A chaos expansion approach under hybrid volatility models

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  • Hideharu Funahashi

Abstract

In this paper, we propose an approximation method based on the Wiener-Ito chaos expansion for the pricing of European contingent claims. Our method is applicable to widely used option pricing models such as local volatility models, stochastic volatility models and their combinations. This method is useful in practice since the resulting approximation formula is not computationally expensive, hence it is suitable for calibration purposes. We will show through some numerical examples that our approximation remains quite good even for the long maturity and/or the high volatility cases, which is a desired feature. As an example, we propose a hybrid volatility model and apply our approximation formula to the JPY/USD currency option market obtaining very accurate results.

Suggested Citation

  • Hideharu Funahashi, 2014. "A chaos expansion approach under hybrid volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1923-1936, November.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:11:p:1923-1936
    DOI: 10.1080/14697688.2013.872283
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    Cited by:

    1. Hideharu Funahashi & Tomohide Higuchi, 2018. "An analytical approximation for single barrier options under stochastic volatility models," Annals of Operations Research, Springer, vol. 266(1), pages 129-157, July.
    2. Hideharu Funahashi & Masaaki Kijima, 2017. "Does the Hurst index matter for option prices under fractional volatility?," Annals of Finance, Springer, vol. 13(1), pages 55-74, February.
    3. Hideharu Funahashi & Masaaki Kijima, 2017. "A unified approach for the pricing of options relating to averages," Review of Derivatives Research, Springer, vol. 20(3), pages 203-229, October.

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