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Implied Stochastic Volatility Models
[Testing continuous-time models of the spot interest rate]

Author

Listed:
  • Yacine Aït-Sahalia
  • Chenxu Li
  • Chen Xu Li

Abstract

This paper proposes “implied stochastic volatility models” designed to fit option-implied volatility data and implements a new estimation method for such models. The method is based on explicitly linking observed shape characteristics of the implied volatility surface to the coefficient functions that define the stochastic volatility model. The method can be applied to estimate a fully flexible nonparametric model, or to estimate by the generalized method of moments any arbitrary parametric stochastic volatility model, affine or not. Empirical evidence based on S&P 500 index options data show that the method is stable and performs well out of sample.

Suggested Citation

  • Yacine Aït-Sahalia & Chenxu Li & Chen Xu Li, 2021. "Implied Stochastic Volatility Models [Testing continuous-time models of the spot interest rate]," The Review of Financial Studies, Society for Financial Studies, vol. 34(1), pages 394-450.
    • Handle: RePEc:oup:rfinst:v:34:y:2021:i:1:p:394-450.
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    File URL: http://hdl.handle.net/10.1093/rfs/hhaa041
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    Citations

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    Cited by:

    1. Liexin Cheng & Xue Cheng, 2024. "Decomposing Smiles: A Time Change Approach," Papers 2401.03776, arXiv.org, revised Jan 2024.
    2. Jo-Hui & Chen & Sabbor Hussain, 2022. "Jump Dynamics and Leverage Effect: Evidences from Energy Exchange Traded Fund (ETFs)," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 12(6), pages 1-7.
    3. 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.
    4. Christian Keller & Michael C. Tseng, 2023. "Arrow-Debreu Meets Kyle: Price Discovery for Derivatives," Papers 2302.13426, arXiv.org, revised Mar 2024.
    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. Shuzhen Yang & Wenqing Zhang, 2023. "Fixed-point iterative algorithm for SVI model," Papers 2301.07830, arXiv.org.
    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.

    More about this item

    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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