1 Department of Economics and Business - Business Studies, Department of Economics and Business Economics, Aarhus BSS, Aarhus University2 Department of Business Studies, Aarhus School of Business, Aarhus BSS, Aarhus University3 Finance Research Group, Aarhus School of Business, Aarhus BSS, Aarhus University4 Department of Economics and Business Economics, Aarhus BSS, Aarhus University5 Department of Economics and Business Economics, Aarhus BSS, Aarhus University
We propose a flexible modeling framework for the joint dynamics of an index and a set of forward variance swap rates written on this index. Our model reproduces various empirically observed properties of variance swap dynamics and enables volatility derivatives and options on the underlying index to be priced consistently, while allowing for jumps in volatility and returns. An affine specification using Lévy processes as building blocks leads to analytically tractable pricing formulas for volatility derivatives, such as VIX options, as well as efficient numerical methods for pricing of European options on the underlying asset. The model has the convenient feature of decoupling the vanilla skews from spot/volatility correlations and allowing for different conditional correlations in large and small spot/volatility moves. We show that our model can simultaneously fit prices of European options on S&P 500 across strikes and maturities as well as options on the VIX volatility index.