  On April 22, 2020, the CME Group switched to Bachelier pricing for a group of
oil futures options. The Bachelier model, or more generally the arithmetic
Brownian motion (ABM), is not so widely used in finance, though. This paper
provides the first comprehensive survey of options pricing under ABM. Using the
risk-neutral valuation, we derive formulas for European options for three
underlying types, namely an underlying that does not pay dividends, an
underlying that pays a continuous dividend yield, and futures. Further, we
derive Black-Scholes-Merton-like partial differential equations, which can in
principle be utilized to price American options numerically via finite
difference.
