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Sequential Itô–Taylor expansions and characteristic functions of stochastic volatility models

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  • Kailin Ding
  • Zhenyu Cui
  • Yanchu Liu

Abstract

This study proposes a new approach to derive the characteristic function of a general stochastic volatility model by sequentially utilizing the Itô–Taylor expansions. In particular, our method applies to non‐affine stochastic volatility models with jumps, for which the corresponding characteristic functions do not have closed‐form expressions. Numerically inverting these characteristic functions can yield accurate probability density functions of stochastic volatility models to serve for various pricing and hedging purposes in quantitative finance. The proposed sequential Itô–Taylor expansion allows us to handle derivatives with medium to long maturities. Numerical experiments illustrate the accuracy and effectiveness of our approach.

Suggested Citation

  • Kailin Ding & Zhenyu Cui & Yanchu Liu, 2023. "Sequential Itô–Taylor expansions and characteristic functions of stochastic volatility models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(12), pages 1750-1769, December.
    • Handle: RePEc:wly:jfutmk:v:43:y:2023:i:12:p:1750-1769
    DOI: 10.1002/fut.22455
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    References listed on IDEAS

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    1. Jan Baldeaux & Alexander Badran, 2014. "Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(4), pages 299-312, September.
    2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    3. Wan, Xiangwei & Yang, Nian, 2021. "Hermite expansion of transition densities and European option prices for multivariate diffusions with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 125(C).
    4. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Xiu, Dacheng, 2014. "Hermite polynomial based expansion of European option prices," Journal of Econometrics, Elsevier, vol. 179(2), pages 158-177.
    7. Jan Baldeaux & Alexander Badran, 2012. "Consistent Modeling of VIX and Equity Derivatives Using a 3/2 Plus Jumps Model," Research Paper Series 306, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Martino Grasselli, 2017. "The 4/2 Stochastic Volatility Model: A Unified Approach For The Heston And The 3/2 Model," Mathematical Finance, Wiley Blackwell, vol. 27(4), pages 1013-1034, October.
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