Heston Model: The Variance Swap Calibration

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.