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.
⌘K Search by concept, model, instrument or tag.
Random Variables
Map uncertain outcomes to measurable numerical values.
Brownian Motion
The continuous-time noise behind classical diffusion models.
Risk-Neutral Pricing
Value discounted payoffs under a measure that removes risk premia.
Bid Ask and Mid
Separate executable sides from the midpoint used for analysis.
Market Price vs Model Price
Keep observed quotes separate from calculated fair values.
Streaming Quotes and Staleness
Treat market data as a timed state, not a timeless number.
Reference vs Real-Time Data
Distinguish official observations, delayed feeds and executable streams.
Prediction Market Probabilities
Interpret binary contract prices without treating them as certainty.
Prediction Event Market Outcome and Token
Keep event, market, outcome and CLOB token identifiers distinct.
Prediction Market Order Books
Read bid, ask, midpoint, spread, depth and imbalance for outcome tokens.
Prediction Market Resolution and Negative Risk
Connect settlement rules, oracle resolution and linked mutually exclusive markets.
Prediction Market Liquidity Open Interest and Volume
Separate trading activity, outstanding exposure and available book depth.
Conditional Expectation
Update expected values using the information currently available.
Martingales
Processes whose conditional future value equals their current value.
Change of Measure
Reweight probabilities to move between pricing numeraires.
Itô Calculus
Differential calculus for stochastic processes with quadratic variation.
Monte Carlo
Estimate prices and risk by simulating many model paths.
Variance Reduction
Improve simulation precision without merely adding paths.
Finite Differences
Approximate derivatives and solve pricing PDEs on a grid.
PDE Methods
Translate no-arbitrage dynamics into boundary-value problems.
Calibration Basics
Choose parameters that reconcile a model with observed instruments.
Interpolation Basics
Estimate values between liquid market pillars without inventing arbitrage.
Numerical Stability
Keep computed outputs reliable under finite precision and difficult inputs.