Malliavin Calculus in Finance: Theory and Practice

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.

《金融中的Malliavin微分法：理論與實踐》旨在通過Malliavin微分法介紹隨機波動率（SV）模型的研究。

Malliavin微分法對隨機分析產生了深遠的影響。最初是為了研究某些隨機變量的平滑密度的存在性而提出的，它在許多其他問題中被證明是一個有用的工具。特別是在量化金融中，它被應用於對沖策略的計算或希臘值的高效估計等方面。

本書的目標是提供理論與實踐之間的橋樑。它展示了Malliavin微分法是一個易於應用的工具，可以使我們恢復、統一和概括文獻中與香草期權、遠期期權和VIX隱含波動率曲面相關的隨機波動率建模的幾個先前結果。它可以應用於局部、隨機和粗糙波動率（由分數布朗運動驅動），從而得到簡單明確的結果。

特點：
- 中高級量化金融文本，面向具有隨機分析基礎的從業人員，也對量化金融研究人員和學生有用。
- 包括Heston模型、SABR模型和粗糙波動率等具體模型的示例，以及多個數值實驗和相應的Python腳本。
- 涵蓋香草期權、遠期起始期權和VIX期權的應用。
- 本書還有一個Github存儲庫，其中包含與文本中數值示例相對應的Python庫。該庫已經實現，以便用戶可以重用數值代碼來構建自己的示例。存儲庫可以在此處訪問：https://bit.ly/2KNex2Y。

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.

Elisa Alòs擁有巴塞隆納大學的數學博士學位。她是巴塞隆納龐培法布拉大學（UPF）經濟與商業學系的副教授，也是巴塞隆納經濟學研究中心（Barcelona GSE）的聯合教授。在過去的十四年中，她的研究專注於Malliavin微積分和分數布朗運動在數學金融和波動率建模中的應用。

David Garcia Lorite目前在Caixabank擔任XVA量化分析師，並在巴塞隆納大學攻讀博士學位，由Elisa Alòs指導，專注於Malliavin微積分在金融中的應用。在過去的十四年中，他在多家金融公司工作，一直從事混合衍生品的工作。他還具有強大的計算能力，在職業生涯中實現了多種定量和非定量庫，使用不同的語言。