Quantitative Finance

  1. Asset Pricing and Portfolio Theory
    1. No-Arbitrage Principle
      1. Law of One Price
        1. Definition and Implications
          1. Applications in Pricing
          2. Arbitrage Pricing Theory
            1. Factor Structure
              1. Multi-Factor Models
                1. Asset Pricing under APT
              2. Risk-Neutral Valuation
                1. Equivalent Martingale Measure
                  1. Change of Measure Techniques
                    1. Girsanov's Theorem
                    2. Fundamental Theorems of Asset Pricing
                      1. First Fundamental Theorem
                        1. Second Fundamental Theorem
                          1. Market Completeness
                          2. Change of Numéraire
                            1. Concept and Theory
                              1. Applications in Pricing
                                1. Different Numéraire Choices
                              2. Modern Portfolio Theory
                                1. Mean-Variance Optimization
                                  1. Portfolio Expected Return
                                    1. Portfolio Variance
                                      1. Covariance Matrix
                                        1. Efficient Portfolio Construction
                                        2. Efficient Frontier
                                          1. Definition and Construction
                                            1. Mathematical Derivation
                                              1. Interpretation and Applications
                                              2. Capital Allocation Line
                                                1. Risk-Free Asset Combinations
                                                  1. Sharpe Ratio Maximization
                                                    1. Optimal Portfolio Selection
                                                    2. Security Market Line
                                                      1. Capital Market Line
                                                        1. Beta and Expected Return
                                                          1. Market Risk Premium
                                                        2. Capital Asset Pricing Model
                                                          1. Model Assumptions
                                                            1. Market Assumptions
                                                              1. Investor Assumptions
                                                              2. Mathematical Derivation
                                                                1. Equilibrium Conditions
                                                                  1. CAPM Formula
                                                                  2. Beta as Systematic Risk Measure
                                                                    1. Calculation Methods
                                                                      1. Interpretation
                                                                        1. Empirical Estimation
                                                                      2. Factor Models
                                                                        1. Single-Factor Models
                                                                          1. Market Model
                                                                            1. Risk Attribution Applications
                                                                            2. Multi-Factor Models
                                                                              1. Fama-French Three-Factor Model
                                                                                1. Market Factor
                                                                                  1. Size Factor
                                                                                    1. Value Factor
                                                                                      1. Carhart Four-Factor Model
                                                                                        1. Momentum Factor
                                                                                          1. Model Extensions

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                                                                                      2. Stochastic Processes in Finance

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                                                                                      4. Derivatives Modeling and Pricing