What are fashionable applications of Fourier analysis in trading? I have heard vague ideas of applications in High Frequency Trading but can somebody provide an example, maybe a reference?
Just for clarification: The approach to split up a stock price in its cosines and to apply this for forecasts or anything similar seems theoretically not justified as we can not assume the stock price to be periodic (outside of the period of observation). So I don't really mean such applications.
Put differently: are there useful, theoretically valid applications of Fourier theory in trading? I am curious for any comments, thank you!
EDIT: I am aware of (theoretically $100\%$ valid) applications in option pricing and calculation of risk measures in the context of Lévy processes (see e.g. here p.11 and following and references therein). This is well established, I guess. What I mean are applications in time series analysis. Sorry for any confusions.