This thesis deals with derivatives pricing under a multidimensional stochastic volatility model for the asset prices. The considered principal component framework is characterized by the widely observed phenomena of volatility clustering and asymmetric fat-tailed stock return distributions. We assume stochastic eigenvalues exhibiting a mean-reverting character in order to incorporate stochastic volatility as well as stochastic correlation between assets. Furthermore, the considered model allows for correlation between the volatility driving processes and the stock price processes. An empirical study is conducted to motivate the presence of both a slow and a fast mean-reverting component for each eigenvalue. By applying perturbation theory we derive price approximations for endpoint and path-dependent derivatives. The convergence of the approximation is proved analytically and illustrated at some numerical examples.      «

This thesis deals with derivatives pricing under a multidimensional stochastic volatility model for the asset prices. The considered principal component framework is characterized by the widely observed phenomena of volatility clustering and asymmetric fat-tailed stock return distributions. We assume stochastic eigenvalues exhibiting a mean-reverting character in order to incorporate stochastic volatility as well as stochastic correlation between assets. Furthermore, the considered model allows...     »