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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.

The Distribution of the Average of Log-Normal Variables and Exact Pricing of the Arithmetic Asian Options: A Simple, Closed-Form Formula