📘 Derivatives
→ Forwards and Futures
→ Options (Call & Put)
→ Call & Put Options Payoffs
→ European vs American Options
→ Put-Call Parity
→ Option Greeks (Delta, Gamma, Vega, Theta, Rho)
→ Black-Scholes Model
→ Binomial/Trinomial Trees
→ Monte Carlo Pricing
→ Volatility Smile & Surface
→ Exotic Options: Barrier, Asian, Lookback, Binary
→ Swaps: Interest Rate & Equity Swaps
→ Implied Volatility
→ Hedging Strategies & Real-world Use Cases
💵 Fixed Income
→ Bond Pricing, YTM, Spot/Forward Rates
→ Duration, Modified Duration, Convexity
→ Bootstrapping Yield Curve
→ Term Structure Models (Nelson-Siegel, Svensson)
→ Interpolation (Linear, Cubic Spline, Monotone Convex)
→ Interest Rate Derivatives (Caps, Floors, Swaptions)
→ Z-Spread, Option-Adjusted Spread (OAS) → Mortgage-Backed Securities (MBS), ABS → Prepayment Risk (CPR, PSA, SMM) → Repo, Reverse Repo
→ Key Rate Duration
→ Interest Rate Models: Vasicek, CIR, Hull-White, BGM
📉 Market Risk
→ Value at Risk (VaR): Historical, Parametric, Monte Carlo
→ Expected Shortfall (CVaR)
→ Volatility Modeling: EWMA, GARCH
→ Risk Sensitivities: Greeks, DV01, PV01
→ Full Revaluation vs Delta-Normal VaR
→ Stress Testing & Scenario Analysis
→ Marginal & Incremental VaR
→ P&L Attribution
→ Backtesting VaR
→ Capital Models (Basel, FRTB)
→ Liquidity Risk and Market Data Mapping
→ Sensitivity Analysis (IR, FX, Credit, Equity)
🔢 Stochastic Calculus
→ Brownian Motion
→ Ito’s Lemma
→ Geometric Brownian Motion
→ Stochastic Differential Equations (SDEs)
→ Martingales
→ Risk-Neutral Valuation & Girsanov’s Theorem
→ Black-Scholes Derivation from SDE
→ Jump Diffusion Models (Merton)
→ Heston Model
→ SABR Model
→ Numerical Methods: Euler, Milstein
→ Feynman-Kac Theorem
→ Applications to Derivatives & Interest Rate Modeling
⏱️ Time Series Analysis
→ Stationarity and Unit Root Tests → Autocorrelation, Partial Autocorrelation (ACF, PACF)
→ Autocorrelation, Partial Autocorrelation (ACF, PACF) → AR, MA, ARMA, ARIMA, SARIMA
→ ARCH, GARCH, EGARCH, TGARCH
→ Volatility Clustering
→ Rolling Mean & Rolling Volatility
→ Seasonality & Trend Detection
→ Forecast Accuracy: MAPE, RMSE
→ Cointegration and Error Correction Models
→ Kalman Filter
→ VAR Models
→ Application: Forecasting asset returns, volatility, macro variables
🤖 Machine Learning in Quant Finance
→ Supervised vs Unsupervised Learning
→ Feature Engineering for Financial Data
→ Regression Models (Linear, Lasso, Ridge)
→ Classification Models (Logistic, Decision Tree, SVM)
→ Ensemble Methods (Random Forest, XGBoost)
→ Time Series ML (Lag features, Rolling stats)
→ Clustering: K-Means, DBSCAN
→ Dimensionality Reduction: PCA, t-SNE
→ Cross-Validation Techniques (K-Fold, TimeSeriesSplit)
→ Model Evaluation: AUC-ROC, Precision, Recall, F1
→ Overfitting/Underfitting, Regularization
→ Use Cases: Credit Risk Modeling, Algo Trading, Fraud Detection, Price Prediction