# Cos Method in Finance / Practice

A lot of my professors advised me on doing an undergrad thesis that has something to do with the "relatively new" cosine method (~10 years). What applications are there in Finance of the FFT/Cosine Method beside of option Pricing? What are common uses of the resulting density in practice?

• The main application of COS method is pricing and calibration. Not sure what other potential methods you had in mind? – ilovevolatility Nov 20 '19 at 16:34
• My professor was talking about how it is slowly becoming popular in risk management, but for me it was hard to understand in what context (I'm only an undergrad). I think he meant that the approximated density function by the cosine expansion could be used for calculating risk measures such as VaR. – MikeHeimlich Nov 20 '19 at 20:42
• COS can be used for efficient density recovery in VaR/CVaR applications too – James Spencer-Lavan Nov 21 '19 at 2:04
• @JamesSpencer-Lavan Do you know if this is something very common, or rather something used only by very quantitative-driven (hedge) funds / institutions? – MikeHeimlich Nov 21 '19 at 10:15
• I use it at an investment bank, but it is not a common technique as the lazy option of monte carlo is too appealing. – James Spencer-Lavan Nov 22 '19 at 0:11

Leitao et al. (2018) develop a model-free approach which does not require an analytically known characteristic function. Instead, the coefficients $$A_n$$ representing the distribution of the terminal stock price are estimated based on historical values. Thus, they name this approach data driven cosine (ddCOS) method.