Approximation methods for lognormal characteristic functions

Abstract

The characteristic function of the lognormal distribution is of interest in a number of scientific fields yet an analytic solution remains elusive, making reliable and efficient approximations necessary. In this article, we build on the results of N. C. Beaulieu and A. Saberali in ‘New approximations to the lognormal characteristic function’, by introducing a Taylor- and Bessel function-based partial expansion of the integrand and a Chebyshev quadrature approach. Through computer simulations we show that the Taylor expansion remains accurate and efficient for all commonly computed values, and specify the range of values for which the other two approaches show a significantly stronger performance.