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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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    2. Amine Ouazad, 2022. "Do Investors Hedge Against Green Swans? Option-Implied Risk Aversion to Wildfires," Papers 2208.06930, arXiv.org.
    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. Leunga Njike, Charles Guy & Hainaut, Donatien, 2024. "Affine Heston model style with self-exciting jumps and long memory," LIDAM Discussion Papers ISBA 2024001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. 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).
    6. 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).
    7. 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.
    8. Charles Guy Njike Leunga & Donatien Hainaut, 2024. "Affine Heston model style with self-exciting jumps and long memory," Annals of Finance, Springer, vol. 20(1), pages 1-43, March.
    9. 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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