What's some good literature for Fourier transform methods?

Question

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 1

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 2

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.