Efficient Pricing and Reliable Calibration in the Heston Model

40 Pages Posted: 4 Jan 2012

Date Written: January 4, 2012

Abstract

We suggest a general scheme for improvement of FT-pricing formulas for European option and give efficient recommendations for the choice of the parameters of the numerical scheme, which allow for very accurate and fast calculations. The efficiency of the method stems from the properties of functions analytical in a strip, which were introduced to finance by Feng and Lintesky (2008). We demonstrate that an indiscriminate choice of parameters of a numerical scheme leads to an inaccurate pricing and calibration. As applications, we consider the Heston model and its generalization. For many parameter sets documented in empirical studies of financial markets, relative accuracy better than 0.01% can be achieved by summation of less than 10-20 terms even in the situations in which the standard approach requires more than 200. In some cases, the one-term formula produces an error of several percent, and the summation of two terms — less than 0.5%. Typically, 10 terms and fewer suffice to achieve the error tolerance of several percent and smaller.

Keywords: Heston model, Fourier transform, European options, calibration

JEL Classification: C63

Suggested Citation

Levendorskii, Sergei Z., Efficient Pricing and Reliable Calibration in the Heston Model (January 4, 2012). Available at SSRN: https://ssrn.com/abstract=1979225 or http://dx.doi.org/10.2139/ssrn.1979225

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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