Fourier Transform Methods in Finance
Fourier Transform Methods in Finance
by Umberto Cherubini, Giovanni Della Lunga, Sabrina Mulinacci, Pietro Rossi
English | EPUB | 10.6 MB
by Umberto Cherubini, Giovanni Della Lunga, Sabrina Mulinacci, Pietro Rossi
English | EPUB | 10.6 MB
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 to:
- compute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) technique
- characterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumps
- apply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniques
- perform a change of measure on the characteristic function in order to make the price process a martingale
- recover a general representation of the pricing kernel of the economy in terms of Hilbert transform using the theory of generalised functions
- apply the pricing formula to the most famous pricing models, with stochastic volatility and jumps.