Fourier Transform Methods in Finance (The Wiley Finance Series) [Hardcover]

Umberto Cherubini (Author), Giovanni Della Lunga (Author), Sabrina Mulinacci (Author), Pietro Rossi (Author)

Book Description

Publication Date: February 3, 2010 | ISBN-10: 0470994002 | ISBN-13: 978-0470994009 | Edition: 1

In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes.

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

Editorial Reviews

From the Inside Flap

Fourier transform methods in finance

“Fourier Transform Methods in Finance is rigorous, instructive, and loaded with useful examples. The authors have synthesized everything from the necessary underlying elements of complex analysis up through methods for derivative pricing. Almost anyone doing research or business applications in this area will want their own copy.”

—Professor Darrell Duffie, Dean Witter Distinguished Professor of Finance at The Graduate School of Business, Stanford University

“This excellent book is a selection of ready-to-use Fourier transform methods applied to option pricing and calibration, a technique that is indispensable today across different asset classes in a non Gaussian world.”

—Hélyette Geman, Professor of Finance, Birkbeck College, University of London & ESCP Europe

About the Author

UMBERTO CHERUBINI is Associate Professor of Financial Mathematics at the University of Bologna. He is fellow of the Financial Econometrics Research Center, FERC, University of Warwick and Ente Einaudi, Bank of Italy, and member of the Scientific Committee of the Risk Management Education program of the Italian Banking Association (ABI). He has published in international journals in economics and finance, and he is co-author of the books Copula Methods in Finance, John Wiley & Sons, 2004, and Structured Finance: The Object Oriented Approach, John Wiley & Sons, 2007.

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.

Product Details

• Hardcover: 256 pages
• Publisher: Wiley; 1 edition (February 3, 2010)
• Language: English
• ISBN-10: 0470994002
• ISBN-13: 978-0470994009
• Product Dimensions: 9.6 x 6.7 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 2.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,613,736 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

3.0 out of 5 stars Too little mathematics, too much old stuff., June 17, 2011

By 

pierre (Germany) - See all my reviews

This review is from: Fourier Transform Methods in Finance (The Wiley Finance Series) (Kindle Edition)

Well, to be honest it unpleasant to read. Everything is presented in an extremely non-rigorous form. Some statements are even questionable. This book really needs to be revised. The approach of generalized functions is promising and works. But please - this is not trivial. You must take some care about convergence and the like. They thought so much about writing for practitioners so they forgot: Practitioners are also mathematicians who want to be convinced.
Besides: Only 1/4 of this book is new and worth reading. The rest is known stuff you can find in other books, which is well known and not worth writing yet another finance book. I think a neat and clean paper would have been the better choice.

4 of 7 people found the following review helpful:

1.0 out of 5 stars For Those with Graduate Degrees in Math Science Only, February 2, 2011

By 

TechCharter - See all my reviews

This review is from: Fourier Transform Methods in Finance (The Wiley Finance Series) (Hardcover)

This book is extremely difficult to read and understand for this individual with a graduate degree in Electrical Engineering in Signal processing. The authors propose probabilistic models and incorporate Fourier Transforms. Had the authors performed a Fourier transform to any market traded, they would have quickly determined the market is NOT random. The authors do not show how their portfolios performed over time using their model. AVOID THIS BOOK.