Projection of Functionals and Fast Pricing of Exotic Options

We investigate the approximation of path functionals. In particular, we advocate the use of the Karhunen-Loève expansion, the continuous analogue of Principal Component Analysis, to extract relevant information from the image of a functional. Having accurate estimate of functionals is of paramount importance in the context of exotic derivatives pricing, as presented in the practical applications. Specifically, we show how a simulation-based procedure, which we call the Karhunen-Loève Monte Carlo...