Malliavin Calculus in Finance

Theory and Practice

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

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English

Chapman & Hall/CRC
14 July 2021

Calculus; Applied mathematics; Stochastics

Series: Chapman and Hall/CRC Financial Mathematics Series

Malliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic volatility (SV) models via Malliavin Calculus.

Malliavin calculus has had a profound impact on stochastic analysis. Originally motivated by the study of the existence of smooth densities of certain random variables, it has proved to be a useful tool in many other problems. In particular, it has found applications in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks.

The objective of this book is to offer a bridge between theory and practice. It shows that Malliavin calculus is 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.

By: Elisa Alos (Universitat Pompeu Frabra Spain), David Garcia Lorite, Dariusz Gatarek
Imprint: Chapman & Hall/CRC
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm,
Weight: 612g
ISBN: 9780367893446
ISBN 10: 0367893444
Series: Chapman and Hall/CRC Financial Mathematics Series
Pages: 350
Publication Date: 14 July 2021
Audience: Professional and scholarly , College/higher education , Undergraduate , Further / Higher Education
Replaced By: 9781032636306
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.

Reviews for Malliavin Calculus in Finance: Theory and Practice

Malliavin calculus, alongside Ito calculus, is emerging as a vital tool for researchers in the area of financial engineering. This book provides an unprecedented and balanced account, taking the reader from theoretical foundations to practical applications, including state-of-the-art research topics like rough volatility and VIX option skew. - Colin Turfus