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Malliavin Calculus in Finance: Theory and Practice, 2nd Edition
Author(s): Elisa Alòs, David Garcia Lorite
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 generalise several previous results in the literature on stochastic volatility modelling related to the vanil-la, 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 practitio-
ners 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.
Malliavin Calculus in Finance_ Theory and Practice (2025).pdf
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