Quantitative Finance

  1. Derivatives Modeling and Pricing
    1. Introduction to Derivatives
      1. Forward and Futures Contracts
        1. Contract Specifications
          1. Pricing Models
            1. Valuation Methods
              1. Hedging Applications
              2. Swap Contracts
                1. Interest Rate Swaps
                  1. Currency Swaps
                    1. Valuation Techniques
                      1. Market Applications
                      2. Options Contracts
                        1. Call Options
                          1. Put Options
                            1. Payoff Diagrams
                              1. Moneyness Concepts
                            2. Option Pricing Theory
                              1. Binomial Tree Models
                                1. One-Step Binomial Model
                                  1. Risk-Neutral Valuation
                                    1. Replicating Portfolio
                                      1. Multi-Step Trees
                                        1. Lattice Construction
                                          1. Convergence to Black-Scholes
                                          2. Trinomial Tree Models
                                            1. Model Construction
                                              1. Pricing Applications
                                              2. Black-Scholes-Merton Model
                                                1. Model Assumptions
                                                  1. Market Assumptions
                                                    1. Asset Price Assumptions
                                                      1. Model Limitations
                                                        1. Black-Scholes PDE
                                                          1. Derivation Methods
                                                            1. Solution Techniques
                                                              1. European Option Pricing Formula
                                                                1. Call Option Formula
                                                                  1. Put Option Formula
                                                                2. Greeks and Dynamic Hedging
                                                                  1. Delta
                                                                    1. Definition and Interpretation
                                                                      1. Delta Hedging Strategies
                                                                        1. Dynamic Rebalancing
                                                                        2. Gamma
                                                                          1. Definition and Interpretation
                                                                            1. Gamma Hedging
                                                                              1. Convexity Effects
                                                                              2. Vega
                                                                                1. Volatility Sensitivity
                                                                                  1. Vega Hedging
                                                                                  2. Theta
                                                                                    1. Time Decay
                                                                                      1. Theta Management
                                                                                      2. Rho
                                                                                        1. Interest Rate Sensitivity
                                                                                          1. Rho Hedging
                                                                                          2. Dynamic Hedging Strategies
                                                                                            1. Portfolio Rebalancing
                                                                                              1. Practical Considerations
                                                                                                1. Transaction Costs
                                                                                              2. Volatility Modeling
                                                                                                1. Historical Volatility
                                                                                                  1. Calculation Methods
                                                                                                    1. Estimation Techniques
                                                                                                      1. Uses and Limitations
                                                                                                      2. Implied Volatility
                                                                                                        1. Extraction from Market Prices
                                                                                                          1. Volatility Smile
                                                                                                            1. Volatility Skew
                                                                                                              1. Volatility Surface
                                                                                                              2. Local Volatility Models
                                                                                                                1. Dupire's Model
                                                                                                                  1. Calibration Techniques
                                                                                                                    1. Implementation Methods
                                                                                                                    2. Stochastic Volatility Models
                                                                                                                      1. Heston Model
                                                                                                                        1. Model Specification
                                                                                                                          1. Solution Methods
                                                                                                                            1. SABR Model
                                                                                                                              1. Interest Rate Applications
                                                                                                                              2. GARCH Models
                                                                                                                                1. GARCH(1,1) Model
                                                                                                                                  1. EGARCH Model
                                                                                                                                    1. TGARCH Model
                                                                                                                                      1. Estimation Methods
                                                                                                                                        1. Forecasting Applications
                                                                                                                                      2. Exotic Options
                                                                                                                                        1. Path-Dependent Options
                                                                                                                                          1. Asian Options
                                                                                                                                            1. Average Price Options
                                                                                                                                              1. Average Strike Options
                                                                                                                                                1. Lookback Options
                                                                                                                                                  1. Maximum Price Features
                                                                                                                                                    1. Minimum Price Features
                                                                                                                                                      1. Barrier Options
                                                                                                                                                        1. Knock-In Options
                                                                                                                                                          1. Knock-Out Options
                                                                                                                                                          2. Other Exotic Options
                                                                                                                                                            1. Binary Options
                                                                                                                                                              1. Digital Options
                                                                                                                                                                1. Cash-or-Nothing Options
                                                                                                                                                                  1. Asset-or-Nothing Options
                                                                                                                                                                    1. Compound Options
                                                                                                                                                                      1. Options on Options
                                                                                                                                                                    2. Interest Rate Derivatives and Models
                                                                                                                                                                      1. Term Structure of Interest Rates
                                                                                                                                                                        1. Yield Curve Construction
                                                                                                                                                                          1. Bootstrapping Methods
                                                                                                                                                                            1. Interpolation Techniques
                                                                                                                                                                              1. Spot Rates
                                                                                                                                                                                1. Forward Rates
                                                                                                                                                                                  1. Rate Calculations
                                                                                                                                                                                  2. Short-Rate Models
                                                                                                                                                                                    1. Vasicek Model
                                                                                                                                                                                      1. Mean Reversion
                                                                                                                                                                                        1. Analytical Solutions
                                                                                                                                                                                          1. Cox-Ingersoll-Ross Model
                                                                                                                                                                                            1. Non-Negativity Constraints
                                                                                                                                                                                              1. Model Calibration
                                                                                                                                                                                                1. Hull-White Model
                                                                                                                                                                                                  1. Time-Dependent Parameters
                                                                                                                                                                                                    1. Yield Curve Fitting
                                                                                                                                                                                                    2. Forward Rate Models
                                                                                                                                                                                                      1. Heath-Jarrow-Morton Framework
                                                                                                                                                                                                        1. Model Specification
                                                                                                                                                                                                          1. Bond Pricing Applications
                                                                                                                                                                                                          2. Market Models
                                                                                                                                                                                                            1. LIBOR Market Model
                                                                                                                                                                                                              1. Model Structure
                                                                                                                                                                                                                1. Swaption Pricing Applications
                                                                                                                                                                                                                2. Interest Rate Derivatives Pricing
                                                                                                                                                                                                                  1. Bond Pricing
                                                                                                                                                                                                                    1. Forward Rate Agreement Pricing
                                                                                                                                                                                                                      1. Caps and Floors
                                                                                                                                                                                                                        1. Payoff Structures
                                                                                                                                                                                                                          1. Valuation Methods
                                                                                                                                                                                                                            1. Interest Rate Collars
                                                                                                                                                                                                                              1. Swaptions
                                                                                                                                                                                                                                1. Types and Payoffs
                                                                                                                                                                                                                                  1. Pricing Approaches

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                                                                                                                                                                                                                              5. Numerical Methods in Finance