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

10 Pages Posted: 25 Sep 2019 Last revised: 24 May 2021

See all articles by Moawia Alghalith

Moawia Alghalith

University of the West Indies (UWI)

Date Written: September 16, 2019

Abstract

We overcome an obstacle in statistics and finance. In doing
so, we show that the distribution of the arithmetic, continuous average of lognormal 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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