LEARN THE MODEL.
CHALLENGE THE HEDGE.
Choose a track, keep the essential lesson visible, and open derivations or implementation only when you need the depth.
Probability, measures & pricing
A rigorous route from distributions and stochastic calculus through Black–Scholes, conditional expectation, Girsanov and forward-measure pricing.
View all 9 stages
Volatility
A sequenced path through measurement, option-implied coordinates, surface construction, dynamics, calibration and hedge risk.
View all 12 stages
Rates & curves
A sequenced rates path through conventions, overnight compounding, products, curve construction, multi-curve valuation, risk and no-arbitrage dynamics.
View all 13 stages
Numerical finance
Reproducible Monte Carlo, SDE schemes, variance reduction and transform pricing with visible error controls.
Greeks & hedging
Desk-unit Greeks, nonlinear cross-risk and a discrete hedging loop with explicit costs and residuals.
Risk & xVA
Portfolio exposure, counterparty and funding adjustments, tail metrics and the controls that make model outputs defensible.
Explore every concept.
The existing typed catalog remains intact beneath the sequenced flagship curriculum.
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Realized vs Implied Volatility
Compare measured return dispersion with option-implied volatility.
Equity Forward
Lock a future equity purchase price after funding and dividends.
Black-Scholes
Closed-form European option pricing under lognormal diffusion.
Greeks
Local sensitivities that translate model parameters into hedge language.
Implied Volatility
The volatility input that makes a model reproduce a market option price.
Volatility Smile
Strike-dependent implied volatility at a single expiry.
Volatility Surface
Implied volatility across strike and maturity.
Call-Put Parity
Connect European calls, puts, forwards and discounting by no-arbitrage.
Dividend Carry
Separate funding and distributions in equity forward value.
Historical Volatility
Estimate dispersion from a time series of past returns.
Realized Volatility
Measure variance accumulated over an observed period.
Term Structure
Track implied volatility across option maturities.
Local Volatility
Infer state-dependent instantaneous variance from a vanilla surface.
Stochastic Volatility
Model volatility itself as a random process.
Heston
Model variance as a mean-reverting square-root diffusion.
SABR
Model forward and volatility jointly for smile dynamics.
Gamma Scalping
Monetise convexity through repeated delta rebalancing.
Variance Swaps
Trade future realised variance against a fixed strike.
Barrier Options
Activate or extinguish payoff when an underlying crosses a level.
Digital Options
Pay a fixed amount when a terminal condition is met.
American Options
Allow exercise before expiry and introduce an optimal stopping problem.
Early Exercise
Compare continuation value with immediate exercise value.
Volatility Arbitrage
Express relative-value views across implied and realised volatility.