The Distribution of the Sum of Log-normal Variables and Exact Pricing of the Arithmetic Asian Options: A Simple, Explicit Formula

11 Pages Posted: 25 Sep 2019 Last revised: 13 Jul 2020

See all articles by Moawia Alghalith

Moawia Alghalith

University of the West Indies (UWI)

Date Written: September 16, 2019

Abstract

We overcome a long-standing obstacle in statistics. In doing so, we show that the distribution of the sum of log-normal variables is log-normal. Furthermore, we offer a breakthrough result in finance. In doing so, we introduce a simple, exact and explicit formula for pricing the arithmetic Asian options. The pricing formula is as simple as the classical Black-Scholes formula.

Keywords: Distribution of the sum of log-normals, Arithmetic Asian option, Black-Scholes formula

JEL Classification: C5, C0, G0

Suggested Citation

Alghalith, Moawia, The Distribution of the Sum of Log-normal Variables and Exact Pricing of the Arithmetic Asian Options: A Simple, Explicit Formula (September 16, 2019). Available at SSRN: https://ssrn.com/abstract=3454650 or http://dx.doi.org/10.2139/ssrn.3454650

Moawia Alghalith (Contact Author)

University of the West Indies (UWI) ( email )

Trinidad and Tobago

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