Black-Scholes
Closed-form European option pricing under lognormal diffusion.
Build the mental model first.
A continuously rebalanced hedge removes the diffusion shock, leaving a price pinned by no-arbitrage.
Closed-form European option pricing under lognormal diffusion.
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.
Still the quoting and risk lingua franca even where richer models price exotics.
The hedge has opinions.
Start with the quote convention, then ask which EQ risk survives the hedge. A number without its convention is merely well-dressed ambiguity.
Ask Bateman about this model →