Fast Calibration of Options on Variance Swaps

Abstract

Using the properties of the Affine and Quadratic models we derive the dynamic of the variance swaps. We then modify the option pricing approximation technique described by Bloch in Fast calibration of the Affine and Quadratic models in order to approximate the price of European options on variance swaps.

Using these results we derive approximations to the equivalent implied volatility surface and compute the Greeks. To conclude, we illustrate our approach in the one-factor Affine and Quadratic models.

Keywords: Option pricing approximation, Variance Swaps, Malliavin calculus, Affine and Quadratic models