Malliavin Calculus in Finance: Theory and Practice

Malliavin Calculus in Finance: Theory and Practice provides an introduction to stochastic volatility (SV) models using Malliavin Calculus, highlighting its applications in quantitative finance and offering a bridge between theory and practice. It includes examples on concrete models, numerical experiments, and a Python library for re-using the numerical code.

Format: Hardback
Length: 328 pages
Publication date: 02 July 2021
Publisher: Taylor & Francis Ltd

Malliavin Calculus in Finance: Theory and Practice is a comprehensive guide that aims to introduce the study of stochastic volatility (SV) models through the lens of Malliavin Calculus. This mathematical framework has had a profound impact on stochastic analysis, initially driven by the quest to establish the existence of smooth densities for certain random variables. However, its applications have expanded far beyond this initial motivation, making it a valuable tool in various fields, particularly quantitative finance.

In the realm of quantitative finance, Malliavin calculus finds its applications in computing hedging strategies and efficiently estimating the Greeks, which are crucial parameters in pricing options and derivatives. The objective of this book is to provide a seamless bridge between theory and practice. It demonstrates that Malliavin calculus is a user-friendly tool that enables us to recover, unify, and generalize numerous previous results in the literature on stochastic volatility modeling related to vanilla, forward, and VIX implied volatility surfaces. This applies to local, stochastic, and even rough volatilities driven by fractional Brownian motion, resulting in simple and explicit solutions.

The book is designed for practitioners with a basic background in stochastic analysis, making it accessible to researchers and students in quantitative finance as well. It includes examples on concrete models such as the Heston model, SABR model, and rough volatilities, along with numerical experiments and corresponding Python scripts. These examples allow readers to apply the theoretical concepts directly and gain hands-on experience with the modeling techniques.

Furthermore, the book boasts a Github repository that accompanies the text. The repository contains a Python library that implements the numerical examples discussed in the book. This library has been designed to be reusable, enabling users to build their own examples and further explore the applications of Malliavin Calculus in finance. The repository can be accessed at the following link: https://bit.ly/2KNex2.

In summary, Malliavin Calculus in Finance: Theory and Practice is a valuable resource for anyone interested in advancing their understanding of stochastic volatility modeling and its applications in quantitative finance. With its clear explanations, practical examples, and accompanying Python library, this book provides a comprehensive guide to leveraging Malliavin Calculus for effective risk management and investment strategies.

Weight: 668g
Dimension: 160 x 241 x 26 (mm)
ISBN-13: 9780367893446