We consider an 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; (iii) parameter uniformity across different moneyness and maturity classes. Overall, nonlinear feedback due to hedging strategies can, at least in part, contribute to explain from a theoretical and quantitative point of view the strong pricing biases of the Black-Scholes formula, although stochastic volatility effects are more important in this regard.

Calibration of a nonlinear feedback option pricing model / Sanfelici, Simona. - In: QUANTITATIVE FINANCE. - ISSN 1469-7688. - 7:(2007), pp. 95-110. [10.1080/14697680601019522]

Calibration of a nonlinear feedback option pricing model

SANFELICI, Simona
2007-01-01

Abstract

We consider an 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; (iii) parameter uniformity across different moneyness and maturity classes. Overall, nonlinear feedback due to hedging strategies can, at least in part, contribute to explain from a theoretical and quantitative point of view the strong pricing biases of the Black-Scholes formula, although stochastic volatility effects are more important in this regard.
Calibration of a nonlinear feedback option pricing model / Sanfelici, Simona. - In: QUANTITATIVE FINANCE. - ISSN 1469-7688. - 7:(2007), pp. 95-110. [10.1080/14697680601019522]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/1653001
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