Heston Model: The Variance Swap Calibration

15 Pages Posted: 24 Apr 2013

See all articles by Florence Guillaume

Florence Guillaume

Independent

Wim Schoutens

KU Leuven - Department of Mathematics

Date Written: April 23, 2013

Abstract

This paper features a market implied methodology to infer adequate starting values for the spot and long run variances and for the mean reversion rate of a calibration exercise under the Heston model. More particularly, these initial parameters are obtained by matching the term structure of the future expected total variance, inferred from the volatility surface, with the model's term structure. In the numerical study, we compare the goodness of fit and the parameter stability of the Heston model calibrated by using either plausible random or market implied starting values for a one-year sample period including the recent credit crunch. In particular, we show that the proposed methodology avoids getting stuck in one "bad"' local minimum and stabilizes the calibrated parameters through time.

Keywords: Heston model, Starting values, Variance term structure matching

Suggested Citation

Guillaume, Florence and Schoutens, Wim, Heston Model: The Variance Swap Calibration (April 23, 2013). Available at SSRN: https://ssrn.com/abstract=2255550 or http://dx.doi.org/10.2139/ssrn.2255550

Wim Schoutens

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

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