Abstract
We consider the pricing of options written on the quadratic variation of a given stock price process. Using the Laplace transform approach, we determine semi-explicit formulas in general affine models allowing for jumps, stochastic volatility, and the leverage effect. Moreover, we show that the joint dynamics of the underlying stock and a corresponding variance swap again are of affine form. Finally, we present a numerical example for the Barndorff-Nielsen and Shephard model with leverage. In particular, we study the effect of approximating the quadratic variation with its predictable compensator.
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