Evaluating the CDF for m weighted sums of n correlated lognormal random variables

Abstract

We show that one can evaluate the cumulative probability density function m weighted sums of n correlated lognormal variables with Monte Carlo simulation rapidly, by deriving its joint probability density function. The adaptive Monte Carlo method allows us to estimate the number of rounds required to achieve a given tolerance. The need for evaluating this function rapidly occurs in many applications, for instance for pricing combinatorial options for bandwidth markets.