1 Department of Business Studies, Aarhus School of Business, Aarhus BSS, Aarhus University2 Finance Research Group, Aarhus School of Business, Aarhus BSS, Aarhus University3 Columbia University4 Department of Economics and Business Economics, Aarhus BSS, Aarhus University5 Department of Economics and Business Economics, Aarhus BSS, Aarhus University
In this paper a model for the joint dynamics of forward variance swap prices and the underlying stock index is proposed. It is shown how options on forward variance swaps, along with options on the underlying can be priced consistently. The calibration of the model is done step-wise, first by fitting VIX option prices and then options on the underlying making the model implementable from a calibration perspective. Finally, the model is implemented and it is shown how it fits VIX index option prices along with European options on S&P 500 for various maturities.