Textbok:Gaussian Process Models for Quantitative Finance

Author(s): Mike Ludkovski, Jimmy Risk


Our exposition begins with Chaps. 1 and 2 that form the bedrock of GP theory.
The introductory Sect. 1.1 sets the context for GP models within computational finance, highlighting the convergence of machine learning and financial analysis and acquainting the reader with examples that are tackled in later chapters. The rest of Chap. 1 is dedicated to the core methodologies, equipping the reader with thetheoretical framework for GP modeling. Chapter 2 goes into details of GP kernels
(covariance functions), drawing connections to other mathematical sub-fields, such as reproducing kernel Hilbert spaces and stochastic differential equations. Chapter 3
pivots toward more specialized GP approaches, sampling among non-Gaussian likelihoods, multi-output modeling, and heteroskedastic modeling. This chapter's relevance shifts depending on the specific applications the reader pursues.
The remaining four chapters can be explored independently of one another, each delving into a distinct application of GPs in the financial realm. Specifically, Chapter 4 discusses the application of GPs in option pricing and sensitivity analysis.
Chapter 5 examines Regression Monte Carlo methods, illustrating the use of GPs as functional surrogates for the continuation value in optimal stopping problems.
Chapter 6 presents the use of GPs for non-parametric modeling of financial objects, such as yield curves, implied volatility surfaces and mortality rate surfaces.
Chapter 7 addresses the application of GP surrogates in stochastic control.
The brief Appendix offers a review on prerequisite mathematics, like the theory of multivariate Gaussian distributions, linear algebra, and function spaces.