Description
Book SynopsisLévy processes have found applications in various fields, including physics, chemistry, long-term climate change, telephone communication, and finance. The most famous Lévy process in finance is the Black-Scholes model. This book presents important financial applications of Lévy processes. The Editors consider jump-diffusion and pure non-Gaussian Lévy processes, the multi-dimensional Black-Scholes model, and regime-switching Lévy models. This book is comprised of seven chapters that focus on different approaches to solving applied problems under Lévy processes: Monte Carlo simulations, machine learning, the frame projection method, dynamic programming, the Fourier cosine series expansion, finite difference schemes, and the Wiener-Hopf factorisation. Various numerical examples are carefully presented in tables and figures to illustrate the methods designed in the book.
Table of ContentsPreface; Variance Reduction Applied to Machine Learning for Pricing Bermudan/American Options in High Dimension; A Machine Learning Approach to Option Pricing under Lévy Processes; On Swing Option Pricing Under Lévy Process Dynamics; Fourier-Cosine Expansion Method for Pricing Equity-Indexed Annuities under Lévy Models; The Multilevel Monte Carlo Method for Jump Lévy Models: Central Limit Theorem; Optimal Resource Extraction in Regime Switching Lévy Markets; Numerical Methods for Pricing Options in Lévy Processes: The Approximate Wiener-Hopf Factorization Techniques; Index.
