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
Date Written: September 16, 2019
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: Suggested Citation