Approximating the Sum of Correlated Lognormals: An Implementation

TL;DR

This paper reviews and implements a recent approximation method for the sum of correlated lognormal variables, which are common in engineering and finance, providing a practical C++ solution for applications like financial modeling.

Contribution

It provides a detailed implementation of a modern approximation technique for correlated lognormals, facilitating practical use in engineering and financial applications.

Findings

Effective approximation of correlated lognormal sums

Implementation in C++ enhances usability

Application to financial models demonstrates practical relevance

Abstract

Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form probability distribution exists for such a sum, and it requires approximation. Some approximation methods date back over 80 years and most take one of two approaches, either: 1) an approximate probability distribution is derived mathematically, or 2) the sum is approximated by a single lognormal random variable. In this research, we take the latter approach and review a fairly recent approximation procedure proposed by Mehta, Wu, Molisch, and Zhang (2007), then implement it using C++. The result is applied to a discrete time model commonly encountered within the field of financial economics.