In recent years, Fourier transform methods have emerged as one ofthe major methodologies for the evaluation of derivative contracts,largely due to the need to strike a balance between the extensionof existing pricing models beyond the traditionalBlack-Scholes setting and a need to evaluate pricesconsistently with the market quotes.
Fourier Transform Methods in Finance is a practical andaccessible guide to pricing financial instruments using Fouriertransform. Written by an experienced team of practitioners andacademics, it covers Fourier pricing methods; the dynamics of assetprices; 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 aFast Fourier Transform (FFT) technique
* characterise the price dynamics on a market in terms of thecharacteristic function, allowing for both diffusive processes andjumps
* apply the concept of characteristic function to non-stationaryprocesses, in particular in the presence of stochastic volatilityand more generally time change techniques
* perform a change of measure on the characteristic function inorder to make the price process a martingale
* recover a general representation of the pricing kernel of theeconomy in terms of Hilbert transform using the theory ofgeneralised functions
* apply the pricing formula to the most famous pricing models,with stochastic volatility and jumps.
Junior and senior practitioners alike will benefit from thisquick reference guide to state of the art models and marketcalibration techniques. Not only will it enable them to write analgorithm for option pricing using the most advanced models,calibrate a pricing model on options data, and extract the impliedprobability distribution in market data, they will also understandthe most advanced models and techniques and discover how thesetechniques have been adjusted for applications in finance.
ISBN 978-0-470-99400-9