Fourier Transform Methods in Finance
暫譯: 金融中的傅立葉變換方法
Cherubini, Umberto, Della Lunga, Giovanni, Mulinacci, Sabrina
相關主題
商品描述
Fourier Transform Methods in Finance is a practical and accessible guide to pricing financial instruments using Fourier transform. Written by an experienced team of practitioners and academics, it covers Fourier pricing methods; the dynamics of asset prices; non stationary market dynamics; arbitrage free pricing; generalized functions and the Fourier transform method.
Readers will learn how to:
- compute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) technique
- characterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumps
- apply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniques
- perform a change of measure on the characteristic function in order to make the price process a martingale
- recover a general representation of the pricing kernel of the economy in terms of Hilbert transform using the theory of generalised functions
- apply the pricing formula to the most famous pricing models, with stochastic volatility and jumps.
Junior and senior practitioners alike will benefit from this quick reference guide to state of the art models and market calibration techniques. Not only will it enable them to write an algorithm for option pricing using the most advanced models, calibrate a pricing model on options data, and extract the implied probability distribution in market data, they will also understand the most advanced models and techniques and discover how these techniques have been adjusted for applications in finance.
ISBN 978-0-470-99400-9
商品描述(中文翻譯)
近年來，傅立葉變換方法已成為評估衍生合約的主要方法之一，這主要是因為需要在擴展現有定價模型（超越傳統的 Black-Scholes 設定）與一致評估市場報價之間取得平衡。
金融中的傅立葉變換方法 是一本實用且易於理解的指南，介紹如何使用傅立葉變換對金融工具進行定價。這本書由一支經驗豐富的實務工作者和學者團隊撰寫，涵蓋了傅立葉定價方法、資產價格的動態、非平穩市場動態、無套利定價、廣義函數及傅立葉變換方法。
讀者將學會如何：
- 在快速傅立葉變換（Fast Fourier Transform, FFT）技術下計算定價核的希爾伯特變換
- 根據特徵函數描述市場上的價格動態，考慮擴散過程和跳躍
- 將特徵函數的概念應用於非平穩過程，特別是在隨機波動性存在的情況下，以及更一般的時間變換技術
- 對特徵函數進行測度變換，以使價格過程成為鞅
- 利用廣義函數理論恢復經濟定價核的一般表示形式，通過希爾伯特變換
- 將定價公式應用於最著名的定價模型，包括隨機波動性和跳躍。
初級和高級實務工作者都將從這本快速參考指南中受益，該指南涵蓋了最先進的模型和市場校準技術。這不僅使他們能夠使用最先進的模型編寫期權定價算法，還能在期權數據上校準定價模型，並從市場數據中提取隱含的概率分佈，他們還將理解最先進的模型和技術，並發現這些技術如何調整以應用於金融領域。
ISBN 978-0-470-99400-9
作者簡介
GIOVANNI DELLA LUNGA is a quantitative analyst at Prometeia Consulting. Prior to this he was head of Market Risk Methodologies at Prometeia and acted as Principal at Polyhedron Computational Finance, a Florence-based consulting company in mathematical models for financial firms and software companies. He also lectures at the University of Bologna in computational finance for undergraduates and runs courses in computational finance at the Bank of Italy. Giovanni is a member of the scientific committee of Abiformazione, the educational branch of the Italian Banking Association and manages the charge of screen-based educational program. His research background covers physics, chemistry and finance, and he co-authored Structured Finance: The Object Oriented Approach, John Wiley & Sons, 2007.
SABRINA MULINACCI is a Professor of Mathematical Methods for Economics and Finance at the University of Bologna, Italy. Prior to this Sabrina was Associate Professor of Mathematical Methods for Economics and Actuarial Sciences at the Catholic University of Milan. She has a PhD in Mathematics from the University of Pisa and has published a number of research papers in international journals in probability and mathematical finance.
PIETRO ROSSI is a Senior Financial Analyst within the Market Risk Group at Prometeira Consulting, specializing in the development of analytical tractable approximations for exotic options. Prior to this, he worked as senior scientist at ENEA in the high performance computing division and was also Director of the Parallel Computing Group at the Center for Advanced Studies, Research and Development in Sardinia (CRS4), working on high performance computing and large scale computational problems for companies such as FIAT. He has a PhD in physics from NYU and his scientific activity has been mainly in theoretical physics and computer science.
作者簡介(中文翻譯)
翁貝托·切魯比尼是博洛尼亞大學金融數學的副教授。他是華威大學金融計量經濟學研究中心（FERC）及意大利銀行的恩特·艾納烏迪的研究員，並且是意大利銀行協會（ABI）風險管理教育計畫的科學委員會成員。他在國際經濟與金融期刊上發表過多篇論文，並且是書籍《金融中的聯結方法》（Copula Methods in Finance，約翰·威利與兒子出版社，2004年）和《結構性金融：面向物件的方法》（Structured Finance: The Object Oriented Approach，約翰·威利與兒子出版社，2007年）的共同作者。
喬凡尼·德拉·倫加是Prometeia Consulting的量化分析師。在此之前，他曾擔任Prometeia的市場風險方法學部門負責人，並在位於佛羅倫斯的Polyhedron Computational Finance擔任首席顧問，該公司專注於金融公司和軟體公司的數學模型。他還在博洛尼亞大學教授本科生的計算金融課程，並在意大利銀行開設計算金融課程。喬凡尼是意大利銀行協會教育分支機構Abiformazione的科學委員會成員，負責管理基於螢幕的教育計畫。他的研究背景涵蓋物理學、化學和金融，並共同撰寫了《結構性金融：面向物件的方法》（Structured Finance: The Object Oriented Approach，約翰·威利與兒子出版社，2007年）。
薇薇安娜·穆利納奇是意大利博洛尼亞大學經濟與金融數學方法的教授。在此之前，薇薇安娜曾擔任米蘭天主教大學經濟學與精算科學的副教授。她擁有比薩大學的數學博士學位，並在國際期刊上發表了多篇有關概率和數學金融的研究論文。
皮耶特羅·羅西是Prometeia Consulting市場風險小組的高級金融分析師，專注於開發可分析的異國選擇權近似解。在此之前，他曾在ENEA的高效能計算部門擔任高級科學家，並且是撒丁島高級研究、開發中心（CRS4）平行計算小組的主任，專注於高效能計算和大型計算問題，為FIAT等公司工作。他擁有紐約大學的物理學博士學位，並且他的科學活動主要集中在理論物理學和計算機科學領域。
