Workgroup Financial Mathematics

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Pricing multidimensional derivate under stochastic correlation and jumps (Pablo Olivares)


We study the pricing of Spread, Quanto and Mountain Range Options under models with stochastic correlation and jumps. In order to describe the covariance process we consider a stochastic dynamic in their eigenvalues and a correlation following certain S.D.E. on (-1;1). Furthermore, we add jumps to the dynamic of the assets, driven by a Merton jump-diffusion processes and a Levy process with random time changed via a sub- ordinator. We provide approximate closed-form expressions for the pricing based on first- and second-order Taylor expansions as in Hull and White (1986). In some cases, we give bounds of the errors in the approximation and compare them with Monte Carlo simulation. Sensitivities to the parameters in the model are also discussed.