Gaussian process regression for pricing option with stochastic votality and interest rate

Abstract

In this thesis, I attempt to apply a capable method of Machine Learning technique that permits of quickly eval- uation of European option value considering the stochas- tics votality and the interest rate. Based on the idea of Spiegeleer et al. , I use Gaussian Process Regression to compute the price of the European option. As a normal regression model, the algorithm conclude two main part, the training step and the test step or the evaluation step. In mainly, when working with Gaussian Process Regre- sion, the part of training step is semmed to be required a lot of demanding cause of the high accuracy of prediction, but fortunately, it will be performed at only once time. In contrast to the training step, time to evaluate the test step is so fast. Additionally, I also take into considera- tion of the complexity models Black-Scholes to compute the European option price based on the Implied Votality and the Interest Rate. In the last chapter of this thesis, the numerical experiments illustrate that the accuracy of Gaussian Process Regression is nearly high, whereas the time of computing the algorithm does not waste as some old approaches (PDE method). Brie y, Gaussian Process Regression can be carried out for European op- tion product and it can be suitable for other nancial products. Keywords: Gaussian Process Regression, European op- tion, Implied Votality, Interest Rate