Continuous Time Processes for Finance: Switching, Self-exciting, Fractional and other Recent Dynamics

This book discusses recent topics in quantitative finance with an emphasis on applications and calibration to time-series, including switching regime processes, self-excited processes, stochastic volatility models, fractional Brownian motion, and Gaussian fields. It is designed for undergraduate students and practitioners in risk management.

Format: Hardback
Length: 345 pages
Publication date: 26 August 2022
Publisher: Springer International Publishing AG

This comprehensive book delves into the latest developments in quantitative finance, placing a strong emphasis on practical applications and the calibration of models to time-series data. While the existing mathematical finance literature often overlooks the importance of considering time-series dynamics in risk management, this book addresses this critical aspect.

The first part of the book explores switching regime processes, which are used to model economic cycles
cycles in financial markets. After presenting the mathematical features and applications of these processes to stocks and interest rates, the estimation techniques using the Hamilton filter and Markov Chain Monte-Carlo algorithm (MCMC) are detailed.

A second part of the book focuses on self-excited processes, which are used to model the clustering of shocks in financial markets. These processes have gained significant attention from researchers in recent years, and this book provides a comprehensive exploration of their econometric estimation and simulation. A dedicated chapter is devoted to the estimation of stochastic volatility models, which are crucial for capturing the dynamic behavior of financial prices.

Two chapters are dedicated to the fractional Brownian motion and Gaussian fields, which are important tools for modeling complex financial phenomena. After summarizing their features, the book presents applications for stock and interest rate modeling, showcasing the practical relevance of these models in risk management and investment analysis.

Two chapters also focus on sub-diffusions, which are used to replicate illiquidity in financial markets. By understanding the dynamics of sub-diffusions, researchers and practitioners can develop more accurate models for pricing and trading illiquid assets.

This book is designed for undergraduate students who have completed a first course in stochastic finance and for practitioners working as quantitative analysts or actuaries in risk management. It provides a comprehensive and up-to-date introduction to the latest quantitative finance techniques, with a focus on their practical applications and calibration to time-series data.

Weight: 798g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031063602
Edition number: 1st ed. 2022