Sparse Gaussian Processes in the Longstaff-Schwartz algorithm

Abstract

In financial applications it is often necessary to determine conditional expectations in Monte Carlo type of simulations. The industry standard at the moment relies on linear regression, which is characterized by the inconvenient problem of having to choose the type and number of basis functions used to build the model, task which is made harder by the frequent impossibility to use an alternative numerical method to evaluate the "ground truth". In this thesis Gaussian Process Regression is investigated as potential substitute for linear regression, as it is a flexible Bayesian non-parametric regression model, which requires little tuning to be used. Its downfall is the computational complexity related to its "training" phase, namely cubic, which requires the use of algorithmic approximations. The most prominent approximations are reviewed and tested in different scenarios requiring the approximation
of conditional expectation by regression, among which the Longstaff-Schwartz algorithm for the pricing of Bermudan options. This thesis was carried out in cooperation with ABN-AMRO bank.