Fourier‐Based Option Pricing

Fourier‐based option pricing approach allows the use of semi‐analytic valuation formulas for European options whenever the characteristic function of the stochastic process representing the underlying is known. This chapter focuses on European call options since these are in general the instruments of choice for the calibration of financial models. It reformulates the risk‐neutral pricing problem and shows how Fourier‐based option pricing can help in solving it. It also presents the two popular pricing approaches as developed by Lewis and Carr‐Madan. The chapter treats Fourier series and the Fast Fourier Transform algorithm as numerical methods for function approximation and option valuation. The focus lies on the application to the binomial model of Cox‐Ross‐Rubinstein which allows a closer look into the inner workings of Fourier pricing and allows a first assessment of the accuracy and speed of the approach.