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Calibration of a nonlinear feedback option pricing model

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  • Simona Sanfelici

Abstract

We consider the option pricing model proposed by Mancino and Ogawa, where the implementation of dynamic hedging strategies has a feedback impact on the price process of the underlying asset. We present numerical results showing that the smile and skewness patterns of implied volatility can actually be reproduced as a consequence of dynamical hedging. The simulations are performed using a suitable semi-implicit finite difference method. Moreover, we perform a calibration of the nonlinear model to market data and we compare it with more popular models, such as the Black-Scholes formula, the Jump-Diffusion model and Heston's model. In judging the alternative models, we consider the following issues: (i) the consistency of the implied structural parameters with the times-series data; (ii) out-of-sample pricing; and (iii) parameter uniformity across different moneyness and maturity classes. Overall, nonlinear feedback due to hedging strategies can, at least in part, contribute to the explanation from a theoretical and quantitative point of view of the strong pricing biases of the Black-Scholes formula, although stochastic volatility effects are more important in this regard.

Suggested Citation

  • Simona Sanfelici, 2007. "Calibration of a nonlinear feedback option pricing model," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 95-110.
    • Handle: RePEc:taf:quantf:v:7:y:2007:i:1:p:95-110
    DOI: 10.1080/14697680601019522
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    References listed on IDEAS

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    1. 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.
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    7. Maria Elvira Mancino & Shigeyoshi Ogawa, 2004. "Non Linear Feedback Effects by Hedging Strategies," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 12, pages 255-269, World Scientific Publishing Co. Pte. Ltd..
    8. Bates, David S, 1991. "The Crash of '87: Was It Expected? The Evidence from Options Markets," Journal of Finance, American Finance Association, vol. 46(3), pages 1009-1044, July.
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    1. Romuald Kenmoe & Simona Sanfelici, 2014. "An application of nonparametric volatility estimators to option pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 37(2), pages 393-412, October.

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