Options and Volatility: Pricing Without Forecasting

An option's value at expiry is arithmetic. Before expiry it looks like it needs a forecast of the underlying, and the central result of the subject is that it does not. This path builds put-call parity, which needs no model at all, then the replication argument that cancels direction and leaves volatility as the only thing being traded. The greeks decompose what a hedged position still carries, and the volatility surface turns out to be the market correcting the model in the model's own units.