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In this paper, we investigate the applicability of the comonotonicity approach in the context of various benchmark models for equities and commodities. Instead of classical Lévy models as in Albrecher et al. we focus on the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and Schwartz' 1997 stochastic convenience yield model. We show how the technical difficulties of inverting the distribution function of the sum of the comonotonic random vector can be overcome and that the method delivers rather tight upper bounds for the prices of Asian Options in these models, at least for strikes which are not too large. As a by-product the method delivers super-hedging strategies which can be easily implemented.

We discuss the application of gradient methods to calibrate mean reverting stochastic volatility models. For this we use formulas based on Girsanov transformations as well as a modification of the Bismut-Elworthy formula to compute the derivatives of certain option prices with respect to the parameters of the model by applying Monte Carlo methods. The article presents an extension of the ideas to apply Malliavin calculus methods in the computation of Greek's.