Pricing Extendible Options Using the Fast Fourier Transform

Abstract

This paper applies the fast Fourier transform (FFT) approach, within the Black-Scholes framework, to the valuation of options whose time to maturity can be extended to a future date (extendible options). We determine the valuation of the extendible options as sums of expectations of indicator functions, leading to a semianalytic expression for the value of the options over a range of strikes. Compared to Monte Carlo simulation, numerical examples demonstrate that the FFT is both computationally more efficient and higher in accuracy.