Mathematical Finance

  1. Continuous-Time Models and Derivative Pricing
    1. Black-Scholes-Merton Framework
      1. Model Assumptions
        1. Market Assumptions
          1. No Arbitrage
            1. Complete Markets
              1. Constant Parameters
              2. Asset Price Dynamics
                1. Geometric Brownian Motion
                  1. Risk-Free Asset
                    1. Dividend Yield
                    2. Derivation of Black-Scholes PDE
                      1. Delta Hedging Argument
                        1. Risk-Neutral Valuation
                          1. Boundary Conditions
                          2. Black-Scholes-Merton Formulas
                            1. European Call Option
                              1. European Put Option
                                1. Greeks Formulas
                                  1. Dividend Adjustments
                                  2. Put-Call Parity
                                    1. European Options
                                      1. American Options
                                        1. Dividend Effects
                                      2. Risk-Neutral Valuation
                                        1. Change of Measure
                                          1. Girsanov's Theorem
                                            1. Radon-Nikodym Derivative
                                              1. Market Price of Risk
                                              2. Risk-Neutral Measure
                                                1. Construction
                                                  1. Uniqueness
                                                  2. Fundamental Theorems of Asset Pricing
                                                    1. First Fundamental Theorem
                                                      1. Second Fundamental Theorem
                                                        1. Economic Interpretation
                                                        2. Pricing under Risk-Neutral Measure
                                                          1. Expectation Formula
                                                            1. Feynman-Kac Theorem
                                                              1. PDE Approach
                                                            2. Sensitivity Analysis and Hedging
                                                              1. The Greeks
                                                                1. Delta
                                                                  1. Calculation
                                                                    1. Hedging Applications
                                                                    2. Gamma
                                                                      1. Calculation
                                                                        1. Risk Management
                                                                        2. Theta
                                                                          1. Time Decay
                                                                            1. Portfolio Management
                                                                            2. Vega
                                                                              1. Volatility Risk
                                                                                1. Hedging Strategies
                                                                                2. Rho
                                                                                  1. Interest Rate Risk
                                                                                3. Dynamic Hedging
                                                                                  1. Delta Hedging Strategy
                                                                                    1. Gamma Hedging
                                                                                      1. Vega Hedging
                                                                                        1. Portfolio Hedging
                                                                                        2. Hedging in Practice
                                                                                          1. Transaction Costs
                                                                                            1. Discrete Rebalancing
                                                                                              1. Model Risk
                                                                                                1. Liquidity Constraints

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                                                                                            4. Stochastic Calculus

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                                                                                            6. Interest Rate Modeling