Malliavin Calculus in Finance

Theory and Practice

Elisa Alos (Universitat Pompeu Frabra, Spain), David Garcia Lorite

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English

Chapman & Hall/CRC
23 December 2024

Mathematics & Sciences; Discrete mathematics; Calculus; Probability & statistics; Mathematical modelling; Stochastics

Series: Chapman and Hall/CRC Financial Mathematics Series

Malliavin Calculus in Finance: Theory and Practice, Second Edition introduces the study of stochastic volatility (SV) models via Malliavin Calculus. Originally motivated by the study of the existence of smooth densities of certain random variables, Malliavin calculus has had a profound impact on stochastic analysis. In particular, it has been found to be an effective tool in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks.

This book aims to bridge the gap between theory and practice and demonstrate the practical value of Malliavin calculus. It offers readers the chance to discover an easy-to-apply tool that allows us to recover, unify, and generalize several previous results in the literature on stochastic volatility modeling related to the vanilla, the forward, and the VIX implied volatility surfaces. It can be applied to local, stochastic, and also to rough volatilities (driven by a fractional Brownian motion) leading to simple and explicit results.

Features

Intermediate-advanced level text on quantitative finance, oriented to practitioners with a basic background in stochastic analysis, which could also be useful for researchers and students in quantitative finance Includes examples on concrete models such as the Heston, the SABR and rough volatilities, as well as several numerical experiments and the corresponding Python scripts Covers applications on vanillas, forward start options, and options on the VIX. The book also has a Github repository with the Python library corresponding to the numerical examples in the text. The library has been implemented so that the users can re-use the numerical code for building their examples. The repository can be accessed here: https://bit.ly/2KNex2Y.

New to the Second Edition

Includes a new chapter to study implied volatility within the Bachelier framework. Chapters 7 and 8 have been thoroughly updated to introduce a more detailed discussion on the relationship between implied and local volatilities, according to the new results in the literature.

By: Elisa Alos (Universitat Pompeu Frabra Spain), David Garcia Lorite
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Edition: 2nd edition
Dimensions: Height: 234mm, Width: 156mm,
Weight: 890g
ISBN: 9781032636306
ISBN 10: 1032636300
Series: Chapman and Hall/CRC Financial Mathematics Series
Pages: 368
Publication Date: 23 December 2024
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Format: Hardback
Publisher's Status: Active

Elisa Alòs holds a Ph.D. in Mathematics from the University of Barcelona. She is an Associate Professor in the Department of Economics and Business at Universitat Pompeu Fabra (UPF) and a Barcelona GSE Affiliated Professor. In the last fourteen years, her research focuses on the applications of the Malliavin calculus and the fractional Brownian motion in mathematical finance and volatility modeling. David Garcia Lorite currently works in Caixabank as XVA quantitative analyst and he is doing a Ph.D. at Universidad de Barcelona under the guidance of Elisa Alòs with a focus in Malliavin calculus with application to finance. For the last fourteen years, he has worked in the financial industry in several companies but always working with hybrid derivatives. He has also strong computational skills and he has implemented several quantitative and not quantitative libraries in different languages throughout his career.