Mathematical Finance

  1. Advanced Derivative Pricing
    1. Exotic Options
      1. Path-Dependent Options
        1. Asian Options
          1. Arithmetic Average
            1. Geometric Average
              1. Pricing Methods
              2. Lookback Options
                1. Fixed Strike Lookback
                  1. Floating Strike Lookback
                    1. Pricing Formulas
                    2. Barrier Options
                      1. Knock-Out Options
                        1. Knock-In Options
                          1. Pricing Methods
                            1. Greeks Calculation
                          2. Multi-Asset Options
                            1. Rainbow Options
                              1. Best-of Options
                                1. Worst-of Options
                                  1. Pricing via Monte Carlo
                                  2. Basket Options
                                    1. Weighted Baskets
                                      1. Correlation Effects
                                        1. Approximation Methods
                                        2. Exchange Options
                                          1. Margrabe Formula
                                        3. Volatility-Dependent Options
                                          1. Variance Swaps
                                            1. Volatility Swaps
                                              1. VIX Options
                                            2. Volatility Modeling
                                              1. Implied Volatility
                                                1. Black-Scholes Implied Volatility
                                                  1. Volatility Surface
                                                    1. Volatility Smile
                                                      1. Volatility Skew
                                                      2. Local Volatility Models
                                                        1. Dupire Model
                                                          1. Local Volatility Surface
                                                            1. Calibration to Market Prices
                                                              1. Forward PDE
                                                              2. Stochastic Volatility Models
                                                                1. Heston Model
                                                                  1. Model Specification
                                                                    1. Characteristic Function
                                                                      1. Option Pricing
                                                                        1. Calibration
                                                                        2. SABR Model
                                                                          1. Model Specification
                                                                            1. Asymptotic Formulas
                                                                              1. Volatility Smile
                                                                            2. Jump-Diffusion Models
                                                                              1. Merton Jump-Diffusion
                                                                                1. Kou Model
                                                                                  1. Variance Gamma Model
                                                                                    1. Option Pricing with Jumps

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                                                                                6. Interest Rate Modeling

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                                                                                8. Credit Risk Modeling