On the Estimation of the SABR Model's Beta Parameter: The Role of Hedging in Determining the Beta Parameter

Posted: 2 May 2017 Last revised: 1 Jun 2017

Date Written: September 1, 2016

Abstract

The stochastic-alpha-beta-rho (SABR) model has become the dominant interest rate model used by practitioners. The principal effect of the parameter beta in the model is the effect on the skew, reflecting the belief option traders have about the distribution of the option’s underlying. This paper introduces a new method for estimating the beta parameter. The key to the proposed method is that the option pricing model parameters can not only be estimated by calibrating the model to the cross-sectional data such as the implied volatility smile, but can also be estimated by choosing the set of parameters that minimize the hedging error. The proposed method meets the no-arbitrage condition, delivering better hedging performance than the existing fixed beta style calibration method. The advantage of the proposed method is demonstrated via empirical analysis. The method can be easily generalized so that it can be applied to any option-pricing model and may be preferred in applications where hedging performance is the principal goal for using an interest rate model.

Keywords: interest-rate model, SABR model, fixed-beta calibration method, hedging error, beta estimation, volatility cube, backbone, volatility smile

Suggested Citation

Zhang, Mengfei and Fabozzi, Frank J., On the Estimation of the SABR Model's Beta Parameter: The Role of Hedging in Determining the Beta Parameter (September 1, 2016). Journal of Derivatives, Vol. 24, No. 1, 2016, Available at SSRN: https://ssrn.com/abstract=2961618 or http://dx.doi.org/10.2139/ssrn.2961618

Mengfei Zhang (Contact Author)

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

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