Brownian Motion
The continuous-time noise behind classical diffusion models.
Build the mental model first.
Brownian motion accumulates independent, normally distributed shocks. Paths are continuous but nowhere differentiable.
The continuous-time noise behind classical diffusion models.
Now make it exact.
Notation and units
Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.
Every model has a price.
Educational conventions are stated explicitly and may simplify market quotation or settlement details.
Rates are continuously compounded unless the section says otherwise.
Inputs are deterministic in the base model.
“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
Why a quant cares.
It drives Black-Scholes diffusions and remains a baseline building block for stochastic models.
The hedge has opinions.
Start with the quote convention, then ask which Foundations risk survives the hedge. A number without its convention is merely well-dressed ambiguity.
Ask Bateman about this model →