Approximating the Sum of Correlated Lognormals: An Implementation

58 Pages Posted: 1 Sep 2015

See all articles by Christopher Rook

Christopher Rook

Stevens Institute of Technology

Mitchell Kerman

Systems Engineering Research Center

Date Written: August 27, 2015

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. The result is applied to a discrete time model commonly encountered within the field of financial economics.

Note: Fully documented source code is included.

Keywords: lognormal distribution, lognormal sum, moment-generating function, numerical quadrature, correlation, approximation techniques, software implementation

JEL Classification: C16, C87

Suggested Citation

Rook, Christopher and Kerman, Mitchell, Approximating the Sum of Correlated Lognormals: An Implementation (August 27, 2015). Available at SSRN: https://ssrn.com/abstract=2653337 or http://dx.doi.org/10.2139/ssrn.2653337

Christopher Rook (Contact Author)

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Mitchell Kerman

Systems Engineering Research Center ( email )

Hoboken, NJ 07030
United States
201-618-4453 (Phone)

HOME PAGE: http://www.sercuarc.org

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