Regularization effect on model calibration

Mesias Alfeus; Xin-Jiang He; Song-Ping Zhu

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This paper considers the regularization effect on model calibration
It compares two methods to calibrate two popular models that are widely used for stochastic volatility modeling, i.e., the SABR and Heston models, with the time series of options written on Nasdaq 100 index
It performs empirical studies to examines the regularization effect on the out-of-sample pricing accuracy.
Overall results agree with the calibration literature that adding an extra penalty to an objective function for calibration raises in-sample pricing errors to a higher level, while on a long-time horizon, parameters obtained from a regularized calibration yield better out-of-sample performance
The paper concludes that regularized calibration is only to be recommended when considering out-of-sample pricing for a long-time horizon.

Abstract

As is well known, the centerpiece of model calibration is regularization, which plays an important role in transforming an ill-posed calibration problem into a stable and well-formulated one. This realm of research has not been explored empirically in much detail in the literature. The goal of this paper is to understand and give an answer to a question concerning pricing accuracy using the parameters resulting from a correctly posed calibration problem in comparison with those inferred from a relaxed calibration. Our empirical findings indicate that regularized calibration is only to be recommended when considering out-of-sample pricing for a long time horizon.

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