Approximating the Sum of Correlated Lognormals: An Implementation

2015/08/30 by Christopher J. Rook, Rook, Christopher J., Mitchell Kerman +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #D.2.4 #FOS: Computer and information sciences #FOS: Economics and business #G.3 #General Finance (q-fin.GN) #J.2 #Mathematical Software (cs.MS) #cs.MS #q-fin.GN #stat.AP

paper · pdf · doi:10.48550/arxiv.1508.07582

Fully documented source code is included

arxiv created 2015/08/30 · arxiv updated 2015/09/01

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.

Related

• Bounds and Approximations for the Distribution of a Sum of Lognormal Random Variables
• Cute but Cunning: Effective Closed-Form Alternatives to the Exact Lognormal Statistics
• On the Efficient Simulation of the Left-Tail of the Sum of Correlated\n Log-normal Variates
• Accurate Computation of the Distribution of Sums of Dependent Log-Normals with Applications to the Black-Scholes Model
• Approximation by the Dickman distribution and quasi-logarithmic combinatorial structures