derivatives
4 free lessons tagged derivatives across Business. Each one is a short sequence of focused steps with narration and a five-question quiz at the end — take them in any order, no signup required.
The Volatility Surface: Reading the Model's Own Errors
If the pricing model were right, implied volatility would be one number per underlying. It is not: it varies by strike and by maturity, in a persistent shape. This lesson treats that shape as data rather than as a defect, shows what it reveals about the market's distribution, and separates forecast from risk premium.
The Greeks: What a Hedged Position Is Still Exposed To
Delta-hedging removes the obvious risk and leaves the interesting ones. The greeks name each remaining exposure separately, which is what lets a trader hold some and neutralise others. This lesson covers what each one measures, why gamma and theta are two sides of one trade, and where the numbers stop behaving.
The Hedging Argument: Pricing Without Forecasting
The Black-Scholes contribution is usually remembered as a formula. It is really an argument: an option can be manufactured from the underlying and cash, so its price is the cost of manufacturing it. This lesson builds that replication argument, shows why the asset's expected return cancels out, and locates each assumption where it fails.
Payoffs, and the One Relation That Needs No Model
An option's value at expiry is trivial arithmetic. Its value before expiry is a hard modelling problem. Between those two facts sits put-call parity, which pins calls and puts to each other using no model at all, only the impossibility of free money. This lesson builds the contracts and that relation.