From the pricing formula to the smile: what the model says, what the Greeks mean, and where the market disagrees.

1. The model and the formula
2. Price an at-the-money call
3. Move the spot and read the explainer
4. The Greeks
5. Watch Gamma peak
6. Hedge it and see the money
7. Back out the volatility
8. The surface
9. What volatility really was

Trees, simulation and finite differences on the same contract: how each works, how fast it converges, and when to use which.

1. Trees
2. A five-step tree, node by node
3. Convergence and the wobble
4. Monte Carlo
5. Simulate and measure the error
6. Finite differences
7. Break the explicit scheme
8. All methods side by side

Three answers to the smile: stochastic volatility, jumps and local volatility. What each explains, and how a desk calibrates.

1. The problem
2. Heston
3. Heston's smile
4. Jumps
5. The short-dated smile
6. Both at once: Bates
7. Local volatility
8. Dupire in pictures
9. Calibrate a market

Strategies, dividends and path-dependent payoffs: the contracts people actually trade and the details that change the price.

1. Spreads and straddles
2. Cash dividends
3. Early exercise before the ex-date
4. Path-dependent payoffs
5. Simulate an Asian
6. Watch the barrier