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The Bachelier model is a model of an asset price under Brownian motion presented by Louis Bachelier on his PhD thesis The Theory of Speculation, published 1900. It is also called the normal model equivalently. One early criticism of the Bachelier model is that the probability distribution which he chose to use to describe stock prices allowed for negative prices. The (much) later Black–Scholes–(Merton) model addresses that issue by positing stock prices as following a log-normal distribution which does not allow negative values. This in turn, implies that returns follow a normal distribution.
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