A New Formula for Lognormal Characteristic Functions

Numerical computation of lognormal characteristic functions is a challenging problem because the defining integral formulas are not well suited to the more common numerical integration techniques. In this paper, a simple change-of-contour argument is used to convert the integral into one in which the oscillatory nature of the new integrand does not depend on the argument of the characteristic function. Hence, efficient numerical computation of the characteristic function is possible for an extremely large range of its argument. The method generalizes to allow the computation of the moment-generating function when the argument has a negative real part. A simple program for computing the new integral using Gaussian quadrature and another program for generating the quadrature nodes and weights are given.