Literature Survey Paths for Fourier Methods in Quantitative Finance
Summary
The document recommends starting with a survey of Fourier transform applications in quantitative finance, then moving to specialized references. It presents the survey as an accessible entry point for readers seeking an overview of pricing methods based on Fourier techniques and characteristic functions, rather than assuming that one book will cover every approach in depth.
The replies identify further material on general Fourier pricing methods, applications to the Heston model, broader model families, implementation, and numerical analysis. They also flag that one survey contains errors in its discussion of a particular approach, while noting that the original paper is accessible. This is a curated reading path rather than a technical tutorial: it describes sources and their focus, but provides no derivations, comparisons of accuracy, or guidance on selecting a numerical method for a specific model.
Key ideas
- Begin with a survey to gain an overview of Fourier pricing applications in finance.
- Follow the overview with specialized work on characteristic functions and particular pricing approaches.
- Some references focus on Heston model applications, while others cover broader models or numerical implementation.
- The suggested survey may contain errors in its treatment of one method, so consult original papers when needed.
- The document recommends a reading route rather than comparing methods or explaining their algorithms.
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Full text
# What's some good literature for Fourier transform methods? # What's some good literature for Fourier transform methods? I am looking for literature on Fourier methods in Quantitative Finance. I've been googling and found the book "Fourier Transform Methods in Finance" (Wiley), but the book seems poorly reviewed. Are there any others? If not a book, then any other sort of literature review? I know that most papers refer back to the work of Carr and Madan, but that's 20 years ago. It would be nice to know of a book or note that provides an overview of the progression over the past two decades when it comes to Fourier methods applied to the models we use in Quant Finance. ## Answer by user34971 (score 3) https://quant.stackexchange.com/a/46510 No need to buy a book for a first introduction of applications to finance. Here is a good review to start with. After reading the review you can then move on to more specialized texts. https://pfadintegral.com/docs/Schmelzle2010%20Fourier%20Pricing.pdf ## Answer by Kevin (score 0) https://quant.stackexchange.com/a/46633 I agree with iLoveVolatility that Schmelzle's survey paper is a good way to start but it does contain some errors in the section to the Lewis (2001) approach. So be aware there. Lewis' original paper is however quite accessible. Zhu (2010) contains in chapter 2 and 4 an introduction of various Fourier methods in finance. More specific to the Heston model is Rouah (2013) in Chapters 3,4,5 but his ideas are easy to be generalised to different models. Kienitz Wetterau (2013) Chapter 5 and 6 are super surveys as well. The book furthermore introduces many relevant more complicated model which are ideal for FT techniques. Similarly, Chapter 2 in Hirsa (2013) also presents different Fourier techniques but focusses more on the implementation and numerical analysis of the methods. You see, perhaps you are not looking for one book which is completely devoted to characteristic functions but a book that describes all the different approaches. Then, you can still specialise into one area. But first, you ought to obtain an overview about the different possibilities there are.
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