Mathematical Finance

  1. Credit Risk Modeling
    1. Structural Models
      1. Merton Model
        1. Firm Value Process
          1. Default Mechanism
            1. Equity and Debt Valuation
              1. Distance to Default
              2. First-Passage Models
                1. Black-Cox Model
                  1. Longstaff-Schwartz Model
                    1. Barrier Models
                    2. Extensions and Applications
                      1. Stochastic Interest Rates
                        1. Stochastic Volatility
                          1. Jump-Diffusion Extensions
                        2. Reduced-Form Models
                          1. Intensity-Based Models
                            1. Default Intensity Process
                              1. Survival Probability
                                1. Hazard Rate Functions
                                2. Cox Process Models
                                  1. Doubly Stochastic Poisson Process
                                    1. Stochastic Intensity
                                      1. Affine Models
                                      2. Recovery Modeling
                                        1. Recovery Rate Assumptions
                                          1. Stochastic Recovery
                                            1. Market-Based Recovery
                                          2. Credit Derivatives
                                            1. Credit Default Swaps
                                              1. CDS Structure
                                                1. CDS Pricing
                                                  1. Credit Spread Calculation
                                                    1. CDS Index Products
                                                    2. Collateralized Debt Obligations
                                                      1. CDO Structure
                                                        1. Tranching Mechanism
                                                          1. Correlation Modeling
                                                            1. Valuation Methods
                                                            2. Credit Portfolio Models
                                                              1. Gaussian Copula Model
                                                                1. Factor Models
                                                                  1. Loss Distribution

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                                                              7. Advanced Derivative Pricing

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                                                              9. Portfolio Theory and Optimization