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.
General
Imprint: |
Crc Press
|
Country of origin: |
United Kingdom |
Series: |
Chapman and Hall/CRC Financial Mathematics Series |
Release date: |
July 2023 |
First published: |
2022 |
Authors: |
Elisa Alos
• David Garcia Lorite
|
Dimensions: |
234 x 156mm (L x W) |
Pages: |
328 |
ISBN-13: |
978-0-367-86325-8 |
Categories: |
Books
|
LSN: |
0-367-86325-1 |
Barcode: |
9780367863258 |
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