Fourier Transform Methods in Finance (The Wiley Finance Series)

In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes.Fourier Transform Methods in Finance is a practical and accessible guide to pricing financial instruments using Fourier transform. Written by an experienced team of practitioners and academics, it covers Fourier pricing methods; the dynamics of asset prices; non stationary market dynamics; arbitrage free pricing; generalized functions and the Fourier transform method.Readers will learn how tocompute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) techniquecharacterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumpsapply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniquesperform a change of measure on the characteristic function in order to make the price process a martingalerecover a general representation of the pricing kernel