Options on Realized Variance by Transform Methods : A Non-Affine Stochastic Volatility Model

In this paper we study the pricing and hedging of options on realized variance in the 3/2 non-affine stochastic volatility model, by developing efficient transform based pricing methods. This non-affine model gives prices of options on realized variance which allow upward sloping implied volatility of variance smiles. Heston's (1993) model, the benchmark affine stochastic volatility model, leads to downward sloping volatility of variance smiles - in disagreement with variance markets in practice. We show a robust method, using control variates, to express the Laplace transform of the variance call function in terms of the Laplace transform of realized variance. The proposed method works in any model where the Laplace transform of realized variance is available in closed form. Additionally, we apply a new numerical Laplace inversion algorithm which gives fast and accurate prices for options on realized variance, simultaneously at a sequence of variance strikes. The method is also used to derive hedge ratios for options on variance with respect to variance swaps