Calibration of a nonlinear feedback option pricing model

Simona Sanfelici

Quantitative Finance, 2007, vol. 7, issue 1, 95-110

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.

Keywords: Option pricing; Numerical methods for option pricing; Partial differential equations; Implied volatilities; Option pricing via simulation; Parameter estimation techniques; Quantitative finance (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1080/14697680601019522

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