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Closed-form implied volatility surfaces for stochastic volatility models with jumps

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  • Aït-Sahalia, Yacine
  • Li, Chenxu
  • Li, Chen Xu

Abstract

We develop a closed-form bivariate expansion of the shape characteristics of the implied volatility surface generated by a stochastic volatility model with jumps in returns. We use the expansion to analyse the impact on the shape of the implied volatility surface of the various features of the stochastic volatility model and to determine which stochastic volatility models are capable of reproducing the observed characteristics of the implied volatility market data.

Suggested Citation

  • Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
  • Handle: RePEc:eee:econom:v:222:y:2021:i:1:p:364-392
    DOI: 10.1016/j.jeconom.2020.07.006
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    3. Ballotta, Laura & Rayée, Grégory, 2022. "Smiles & smirks: Volatility and leverage by jumps," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1145-1161.
    4. Kirkby, J.L. & Nguyen, Dang H. & Nguyen, Duy & Nguyen, Nhu N., 2022. "Maximum likelihood estimation of diffusions by continuous time Markov chain," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    5. Chen, Ding & Guo, Biao & Zhou, Guofu, 2023. "Firm fundamentals and the cross-section of implied volatility shapes," Journal of Financial Markets, Elsevier, vol. 63(C).
    6. Kevin W. Lu & Phillip J. Paine & Simon P. Preston & Andrew T. A. Wood, 2022. "Approximate maximum likelihood estimation for one‐dimensional diffusions observed on a fine grid," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1085-1114, September.
    7. Danial Saef & Yuanrong Wang & Tomaso Aste, 2022. "Regime-based Implied Stochastic Volatility Model for Crypto Option Pricing," Papers 2208.12614, arXiv.org, revised Sep 2022.

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    More about this item

    Keywords

    Implied volatility surface; Stochastic volatility; Jumps; Option pricing; Closed-form expansion; Model selection;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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