Fourier Transform Methods in Finance

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.

Junior and senior practitioners alike will benefit from this
quick reference guide to state of the art models and market
calibration techniques. Not only will it enable them to write an
algorithm for option pricing using the most advanced models,
calibrate a pricing model on options data, and extract the implied
probability distribution in market data, they will also understand
the most advanced models and techniques and discover how these
techniques have been adjusted for applications in finance.

ISBN 978-0-470-99400-9