Bachelier’s arithmetic Brownian motion assumed Gaussian-symmetric price moves

Evidence

Bachelier’s model was an “arithmetic” Brownian motion: it had the symmetry of the Gaussian or normal distribution. If the price of a bond was, for example, 100 francs, the probability on Bachelier’s model of a one-franc upward movement was the same as that of a one-franc downward movement. Given the pervasiveness of the normal distribution, employing such a model was a natural step for someone with a background in mathematics or physics. — Donald MacKenzie, An Engine, Not a Camera, 285

Categorization

• DEFINE: Defines ‘arithmetic’ Brownian motion and its Gaussian-symmetry assumption, foundational for later geometric-Brownian-motion contrasts.
• XREF: connects to: Stock price changes are modeled with thin-tailed lognormal distributions, not fat-tailed ones — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 138; The bell-curve shape of Gaussian distributions is what banks’ risk models assume; Under a Gaussian distribution extreme tail events become effectively impossible — Mark Blyth, Austerity: The History of a Dangerous…, 106

Broader Connections

• Stock price changes are modeled with thin-tailed lognormal distributions, not fat-tailed ones #complicates (0.80) — Donald MacKenzie, An Engine, Not a Camera, 138
• Under a Gaussian distribution extreme tail events become effectively impossible #expands (0.80) — Mark Blyth, Austerity, 106
• The bell-curve shape of Gaussian distributions is what banks’ risk models assume #expands (0.75)