Gaussian process regression approach to pricing multi-asset American options

This dissertation explores the problem of pricing American options in high dimensions using machine learning. In particular, the Gaussian Process Regression Monte Carlo (GPR-MC) algorithm developed by Goudenege et al (2019). is explored, and ` its performance, i.e., its accuracy and efficiency, is benchmarked against the Least Squares Regression Method (LSM) developed by Carriere (1996) and popularised by Longstaff and Schwartz (2001). In this dissertation, American options are approximated by Bermudan options due to limited computing power. To test the performance of GPR-MC, an American geometric mean basket put option, an American arithmetic mean basket put option and an American maximum call option are priced under the multi-asset Black-Scholes and Heston models, using both GPRMC and LSM. The algorithms are run a 100 times to obtain mean option values, 95% confidence intervals about the means, and average computational times. Numerical results show that the efficiency of GPR-MC is independent of the number of underlying assets, in contrast to the LSM method which is not. At 10 underlying assets, GPR-MC is shown to be more efficient than LSM. Moreover, GPR-MC is reasonably accurate, producing relative errors that are within reasonable bounds