This thesis presents a tailor made method for dimension reduction aimed at approximating the price of basket options in the context of the multivariate lognormal model as well as the PCSV model(introduced by Escobar and Olivares (2012)), a stochastic covariance model that accounts for most stylized facts in prices. The method to approximate the price in a reduced dimensional space is built on principal components. For both models the method is first derived theoretically. In a second step it is illustrated by empirical results.     «

This thesis presents a tailor made method for dimension reduction aimed at approximating the price of basket options in the context of the multivariate lognormal model as well as the PCSV model(introduced by Escobar and Olivares (2012)), a stochastic covariance model that accounts for most stylized facts in prices. The method to approximate the price in a reduced dimensional space is built on principal components. For both models the method is first derived theoretically. In a second step it is...     »