Gaussian Process Regression for Option Pricing and Hedging

Recent literature in the field of quantitative finance has employed machine learning methods to speed up typical numerical calculations including derivative pricing, fitting Greek profiles, constructing volatility surfaces and modelling counterparty credit risk, to name a few. This dissertation aims to investigate the accuracy and efficiency of Gaussian process regression (GPR) compared to traditional quantitative pricing algorithms. The GPR algorithm is applied to pricing a down-and-out barrier call option. Notably, Crepey and Dixon ´ (2019) propose an alternative method for computing the Gaussian process Greeks by directly differentiating the GPR option pricing model. Based on their approach, the GPR algorithm is further extended to compute the delta and vega of the option. Numerical experiments display that option pricing accuracy scores are within a tolerable range and demonstrate increased speed of considerable magnitudes with speed-up factors in the 1 000s. Computing the Greeks convey favourable computational properties; however, the GPR model struggles to obtain accurate predictions for the delta and vega. The trade-off between accuracy and speed is further investigated, where the inclusion of additional GPR input parameters hinder performance metrics whilst a larger training data set improves model accuracy.

Grantor

Department of Finance and Tax

Year dc:date.issued

2022

Author dc:creator

• Patel, Ishani

Advisor dc:contributor.advisor

• Ouwehand, Peter

• Mathematical Finance

Handle dc:identifier.uri

http://hdl.handle.net/11427/37735

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/37735