Four guided paths through the app, from Black-Scholes in an hour to calibrating Heston, each step a page with its inputs set and the lecturer's notes alongside.

Closed-form pricing for European options with every first- and second-order Greek, plus charts of value and sensitivities against spot and time.

Sell an option and hedge it path by path. See the profit of selling volatility above what is realised, the noise of hedging discretely, and what costs do to both.

Discrete-time pricing with early exercise. Read every node of a small tree and watch four parameterisations converge to the closed form.

Cash dividends on dates instead of a yield. Escrowed-dividend pricing, an American tree that shows exactly when a call should be exercised early, and the yield that would give the same price.

Simulate thousands of price paths and price by averaging discounted payoffs, with confidence intervals, variance reduction and Longstaff-Schwartz early exercise.

Solve the Black-Scholes partial differential equation on a grid with explicit, implicit or Crank-Nicolson schemes, and see the whole value surface.

Combine calls, puts and the underlying into spreads, straddles, butterflies and condors. See the payoff, the cost, the breakevens and the net Greeks.

Price one contract with every method side by side: values, Greeks, error and speed, with a CSV export.

Back out the volatility the market is pricing from an observed option price, watch Newton's method converge, and build a smile.

Let the variance mean-revert, fluctuate and correlate with the spot. Semi-analytic pricing, a simulator, and the smile the model implies at every maturity.

Heston plus jumps: the model that fits both ends of the term structure. Semi-analytic pricing through a shared characteristic-function engine, and Bates and Heston smiles side by side.

Add Poisson-timed jumps to Black-Scholes. A fast series price, a simulator that shows the gaps, and the steep short-dated smile that jumps explain.

Asian, lookback and barrier options priced by simulation, with closed-form checks, a control variate that cuts the error tenfold, and the discrete-monitoring bias made visible.

The rates and FX smile model: four parameters per maturity and a closed-form implied volatility. Draw the smile, then fit it to a market slice in milliseconds.

Dupire's formula turns an implied surface into the one deterministic volatility function that reproduces it. Heatmaps of both, the two-times rule, and a simulation that closes the loop.

Paste or generate a price history and measure the volatility it delivered: rolling windows, fat tails, drawdowns, and a direct comparison with the implied volatility.

A hidden market, five sliders and a score. Fit Heston to the smile by hand, then let Nelder-Mead finish the job and reveal the answer.

Price pure volatility with a model-free strip of options, see which strikes carry the value, check the strip against Heston's exact expectation, and read the payoff against realised volatility.

Generate a market with a skew, a smile or a sloped term structure, edit the quotes, and solve the whole grid back into implied volatilities.

Closed forms for digital, barrier and geometric Asian options beside the vanilla, with live parity checks and charts against spot and barrier level.

Sixteen short chapters with the formulas and the intuition behind each method, from the pricing equation to the smile, each ending in a short quiz.

Over a hundred terms defined in a sentence or two, most linked to the page where they are put to work.