Malliavin Calculus in Finance: Theory and Practice
暫譯: 金融中的馬利亞文微積分：理論與實踐

Alos, Elisa, Lorite, David Garcia

Malliavin Calculus in Finance: Theory and Practice
  • 出版商: CRC
  • 出版日期: 2023-07-24
  • 售價: $2,400
  • 貴賓價: 9.5 折 $2,280
  • 語言: 英文
  • 頁數: 328
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 0367863251
  • ISBN-13: 9780367863258
  • 相關分類: 微積分 Calculus

    • 海外代購書籍(需單獨結帳)

商品描述

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.

商品描述(中文翻譯)

《Malliavin Calculus in Finance: Theory and Practice》旨在通過Malliavin微積分介紹隨機波動率（SV）模型的研究。

Malliavin微積分對隨機分析產生了深遠的影響。最初是受到某些隨機變數平滑密度存在性研究的啟發，它已被證明在許多其他問題中都是一個有用的工具。特別是，它在量化金融中找到了應用，例如對沖策略的計算或希臘字母的有效估計。

本書的目標是提供理論與實踐之間的橋樑。它顯示Malliavin微積分是一個易於應用的工具，允許我們恢復、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幾個先前結果。它可以應用於局部、隨機以及由分數布朗運動驅動的粗糙波動率，從而導致簡單且明確的結果。

特色


  • 中高級量化金融文本，面向具有基本隨機分析背景的從業者，對於量化金融的研究者和學生也可能有用。

  • 包括Heston模型、SABR模型和粗糙波動率等具體模型的例子，以及幾個數值實驗和相應的Python腳本。

  • 涵蓋香草期權、遠期開始期權和VIX期權的應用。

  • 本書還有一個Github倉庫，包含與文本中數值例子相對應的Python庫。該庫已實現，以便用戶可以重用數值代碼來構建他們的例子。倉庫可以在此訪問：https://bit.ly/2KNex2Y。

作者簡介

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.

作者簡介(中文翻譯)

Elisa Alòs 擁有巴塞隆納大學的數學博士學位。她是巴賽隆納庞培法布拉大學 (Universitat Pompeu Fabra, UPF) 經濟與商業系的副教授，並且是巴塞隆納GSE的附屬教授。在過去的十四年中，她的研究專注於 Malliavin 微積分及分數布朗運動在數學金融和波動性建模中的應用。

David Garcia Lorite 目前在 Caixabank 擔任 XVA 量化分析師，並在巴塞隆納大學 (Universidad de Barcelona) 進行博士研究，指導教授為 Elisa Alòs，研究重點為 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，但始終專注於混合衍生品。他還具備強大的計算技能，並在職業生涯中使用不同語言實現了多個量化和非量化的庫。

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