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An efficient estimate and forecast of the implied volatility surface: A nonlinear Kalman filter approach

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  • Chen, Si
  • Zhou, Zhen
  • Li, Shenghong

Abstract

As suggested by numerous studies, while the implied volatility surface changes over time, its shape tends to pervade. This motivates us to construct a dynamic model for implied volatility surface, which not only captures cross-sectional information of implied volatilities with different strikes and maturities, but also describes how the implied volatility surface evolves over time. In this paper, we use nonlinear parametric function to capture single implied volatility surface, and model the dynamics of implied volatility surface by modeling the dynamics of function coefficients. We introduce unscented Kalman filter to propagate the nonlinear system, which is constructed by the nonlinear parametric function and the dynamics of its coefficients. A dynamic approach is proposed to provide optimal estimation of model parameters and efficient forecast of future implied volatility surface. It shows that our model has a better description of implied volatility surface dynamics than other similar models, and can be used to do volatility surface forecast.

Suggested Citation

  • Chen, Si & Zhou, Zhen & Li, Shenghong, 2016. "An efficient estimate and forecast of the implied volatility surface: A nonlinear Kalman filter approach," Economic Modelling, Elsevier, vol. 58(C), pages 655-664.
  • Handle: RePEc:eee:ecmode:v:58:y:2016:i:c:p:655-664
    DOI: 10.1016/j.econmod.2016.06.003
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    References listed on IDEAS

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    1. Zhang, Li-Hua & Zhang, Wei-Guo & Xu, Wei-Jun & Xiao, Wei-Lin, 2012. "The double exponential jump diffusion model for pricing European options under fuzzy environments," Economic Modelling, Elsevier, vol. 29(3), pages 780-786.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Rama Cont & Jose da Fonseca, 2002. "Dynamics of implied volatility surfaces," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 45-60.
    4. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. "Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-2049, December.
    5. Matthias Fengler & Wolfgang Härdle & Christophe Villa, 2003. "The Dynamics of Implied Volatilities: A Common Principal Components Approach," Review of Derivatives Research, Springer, vol. 6(3), pages 179-202, October.
    6. Li, Junye, 2013. "An unscented Kalman smoother for volatility extraction: Evidence from stock prices and options," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 15-26.
    7. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    8. 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.
    9. Bakshi, Gurdip & Carr, Peter & Wu, Liuren, 2008. "Stochastic risk premiums, stochastic skewness in currency options, and stochastic discount factors in international economies," Journal of Financial Economics, Elsevier, vol. 87(1), pages 132-156, January.
    10. Sílvia Gonçalves & Massimo Guidolin, 2006. "Predictable Dynamics in the S&P 500 Index Options Implied Volatility Surface," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1591-1636, May.
    11. 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.
    12. George Skiadopoulos & Stewart Hodges & Les Clewlow, 2000. "The Dynamics of the S&P 500 Implied Volatility Surface," Review of Derivatives Research, Springer, vol. 3(3), pages 263-282, October.
    13. Bedendo, Mascia & Hodges, Stewart D., 2009. "The dynamics of the volatility skew: A Kalman filter approach," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1156-1165, June.
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    3. Pattnaik, Debidutta & Kumar, Satish & Burton, Bruce & Lim, Weng Marc, 2022. "Economic Modelling at thirty-five: A retrospective bibliometric survey," Economic Modelling, Elsevier, vol. 107(C).
    4. Guidolin, Massimo & Wang, Kai, 2023. "The empirical performance of option implied volatility surface-driven optimal portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    5. Ulze, Markus & Stadler, Johannes & Rathgeber, Andreas W., 2021. "No country for old distributions? On the comparison of implied option parameters between the Brownian motion and variance gamma process," The Quarterly Review of Economics and Finance, Elsevier, vol. 82(C), pages 163-184.

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