Fourier methods in finance - Nevrla, Matěj (2015)
This thesis aims to provide an insight into Fourier transform based techniques utilized in the field of derivative pricing. We discuss mathematical background of Fourier transform techniques and concept of characteristic functions within the probability theory. We analyze three methods for pricing European-style derivatives, namely FFT method, COS method, and CONV method. These methods are examined in cases when the underlying asset price follows geometric Brownian motion, Heston stochastic volatility model, and variance gamma process. Then, we present generalization of COS and CONV method for pricing path-dependent derivatives. In the appendix we also provide introduction to complex analysis.