Mathematical Finance

  1. Numerical Methods in Finance
    1. Monte Carlo Methods
      1. Random Number Generation
        1. Pseudo-Random Numbers
          1. Quasi-Random Numbers
            1. Random Variable Generation
            2. Path Simulation
              1. Euler-Maruyama Scheme
                1. Milstein Scheme
                  1. Higher-Order Schemes
                  2. Variance Reduction
                    1. Antithetic Variates
                      1. Control Variates
                        1. Importance Sampling
                          1. Stratified Sampling
                          2. Applications
                            1. European Option Pricing
                              1. Path-Dependent Options
                                1. Multi-Asset Derivatives
                                  1. Interest Rate Derivatives
                                2. Finite Difference Methods
                                  1. PDE Discretization
                                    1. Spatial Discretization
                                      1. Time Discretization
                                        1. Boundary Conditions
                                        2. Numerical Schemes
                                          1. Explicit Finite Difference
                                            1. Implicit Finite Difference
                                              1. Crank-Nicolson Scheme
                                                1. Alternating Direction Implicit
                                                2. Stability and Convergence
                                                  1. Von Neumann Analysis
                                                    1. CFL Condition
                                                      1. Consistency and Convergence
                                                      2. Applications
                                                        1. Black-Scholes PDE
                                                          1. American Options
                                                            1. Multi-Dimensional Problems
                                                          2. Tree Methods
                                                            1. Binomial Trees
                                                              1. Cox-Ross-Rubinstein Model
                                                                1. Jarrow-Rudd Model
                                                                  1. Parameter Selection
                                                                  2. Trinomial Trees
                                                                    1. Construction
                                                                      1. Stability Conditions
                                                                      2. Applications
                                                                        1. American Option Pricing
                                                                          1. Interest Rate Models
                                                                            1. Exotic Options
                                                                          2. Fourier Transform Methods
                                                                            1. Characteristic Functions
                                                                              1. Definition and Properties
                                                                                1. Lévy Processes
                                                                                  1. Affine Models
                                                                                  2. Fast Fourier Transform
                                                                                    1. FFT Algorithm
                                                                                      1. Option Pricing Applications
                                                                                      2. Fractional FFT
                                                                                        1. Carr-Madan Method
                                                                                          1. Lewis Method

                                                                                      Previous

                                                                                      10. Risk Management

                                                                                      Go to top

                                                                                      Back to Start

                                                                                      1. Foundations of Mathematical Finance