Today’s Focus

Short, daily concepts with quiz + applied notebook.

Conditional Expectation as an L² Projection

Medium • 12 min

Open
ProbabilityHilbert SpacesConditional Expectation

Brownian Motion and Quadratic Variation

Medium • 18 min

Open
Stochastic CalculusBrownian MotionQuadratic Variation

Itô's Lemma: Derivation and Applications

Hard • 22 min

Open
Stochastic CalculusItô's LemmaStochastic Differential Equations

Girsanov's Theorem and Equivalent Martingale Measures

Hard • 25 min

Open
Stochastic CalculusGirsanov's TheoremRisk-Neutral PricingChange of Measure

Feynman-Kac and the Connection to PDEs

Hard • 20 min

Open
Stochastic CalculusFeynman-KacPDEsBlack-Scholes

Black-Scholes: Derivation, Greeks, Limitations

Medium • 22 min

Open
Derivatives PricingBlack-ScholesGreeksPDE Methods

Analytical Greeks for European Options

Medium • 22 min

Open
Risk & GreeksBlack-ScholesGreeksP&L Decomposition

Implied Vol Surfaces and Smile Dynamics

Hard • 25 min

Open
Derivatives PricingImplied VolatilityLocal VolatilitySABRVol Surface

Heston Model: Calibration and Simulation

Hard • 28 min

Open
Derivatives PricingStochastic VolatilityHeston ModelFourier PricingCalibration

Hull-White and the LMM Framework

Hard • 25 min

Open
Derivatives PricingInterest Rate ModelsHull-WhiteLibor Market ModelTerm Structure

Monte Carlo: Antithetic Variates, Control Variates, Quasi-MC

Medium • 22 min

Open
Numerical MethodsMonte CarloVariance ReductionQuasi-Monte Carlo

Finite Difference Schemes and Convergence Analysis

Hard • 25 min

Open
Numerical MethodsFinite DifferencesBlack-Scholes PDEConvergence Analysis

PSOR for American Options

Hard • 22 min

Open
Numerical MethodsAmerican OptionsPSORLinear ComplementarityFree Boundary

FFT and Carr-Madan Pricing

Hard • 23 min

Open
Numerical MethodsFFTCharacteristic FunctionsCarr-MadanFourier Pricing

Numerical Differentiation and Bump-Reval

Medium • 18 min

Open
Risk & GreeksNumerical MethodsBump-RevalComplex-Step Differentiation

Portfolio Greeks Aggregation

Hard • 22 min

Open
Risk & GreeksPortfolio RiskVega LadderVannaVolga

Stressed Scenarios and Model Risk

Hard • 25 min

Open
Risk & GreeksScenario AnalysisModel RiskP&L AttributionVaR

Newton-Raphson and Brent for Implied Volatility

Hard • 22 min

Open
CalibrationImplied VolatilityRoot-FindingBlack-Scholes

Levenberg-Marquardt for Model Calibration

Hard • 25 min

Open
CalibrationNumerical OptimisationHeston ModelImplied Volatility

SVI Parametrisation

Hard • 27 min

Open
CalibrationImplied VolatilityVol SurfaceSVIArbitrage-Free Conditions

Regularisation and Stability in Calibration

Hard • 25 min

Open
CalibrationRegularisationTikhonovInverse ProblemsNumerical Stability

Factor Models: CAPM, APT, and Fama-French

Medium • 22 min

Open
Statistical / ML for QuantsFactor ModelsCAPMFama-FrenchRisk Premia

Time Series for Quants: ARIMA and GARCH

Medium • 22 min

Open
Statistical / ML for QuantsTime SeriesARIMAGARCHVolatility Forecasting

ML in Signal Generation

Hard • 25 min

Open
Statistical / ML for QuantsMachine LearningAlpha SignalsRegularisationCross-Validation

Backtesting and Statistical Testing

Hard • 22 min

Open
Statistical / ML for QuantsBacktestingSharpe RatioMultiple Hypothesis TestingOverfitting

Limit Order Book Mechanics

Medium • 20 min

Open
Market MicrostructureLimit Order BookMarket MakingAdverse Selection

Market Impact Estimation

Hard • 23 min

Open
Market MicrostructureMarket ImpactKyle ModelPrice ImpactEmpirical Methods

Adverse Selection and Inventory Models

Hard • 28 min

Open
Market MicrostructureMarket MakingAdverse SelectionStochastic ControlAvellaneda-Stoikov

Almgren-Chriss Optimal Execution

Hard • 25 min

Open
Market MicrostructureOptimal ExecutionMarket ImpactStochastic ControlAlmgren-Chriss