 Arithmetic stock model with constant volatility

This additive price model has constant absolute volatility and can take negative stock values. With constant cash interest rate $r$, its market price of risk is $(\mu -r{S}_t)/\sigma$. Under an equivalent risk-neutral measure, its drift becomes $r{S}_t$, so its conditional law is Gaussian with mean $e^{r(T-t)}{S}_t$ and variance ${\sigma }^2(e^{2r(T-t)}-1)/(2r)$. It is distinct from a multiplicative Black–Scholes diffusion.