The COS method for pricing European options

Abstract

The COS method exploits the relation between the characteristic function of a random variable and the series coefficients of the Fourier-cosine expansion of the density function. After the mathematical introduction and the derivation of the Black-Scholes formula, we introduce with all the details the COS method. We compare, in terms of absolute error and in CPU time, its performance when pricing European options with a Monte Carlo scheme and with the Black-Scholes value of the derivative. An error analysis of COS method is also provided. Numerical experiments confirm the fast convergence and the precision of the COS method.