Monte Carlo and Finite Differences Methods with Applications to Finance
Ects : 6
Enseignant responsable :
Volume horaire : 30Description du contenu de l'enseignement :
Chapter 1. Foundations of Monte-Carlo
- Principle of Monte Carlo Methods
- Random Number Generation
- Inverse Transform Method
- Acceptance-Rejection Method
- Gaussian Distribution
Chapter 2. Variance Reduction Techniques
- Antithetic variable
- Control Variates
- Importance Sampling
Chapter 3. Simulation of Diffusion Processes
- Exact Simulation( Brownian Motion and Black–Scholes Model)
- Euler Scheme (Construction, Strong and week error)
Chapter 4. Brownian Bridge Approach
- Brownian Bridge
- Exit Times and Barrier Options (Naive approach and Brownian Bridge Approach)
Chapter 5. Computation of Sensitivities (Greeks in finance)
- Finite Differences
- Black–Scholes Model
- Pathwise Differentiation
- Malliavin Differentiation
Chapter 6. American Options
- Discretization
- Naive Approach
- Regression Methods
Chapter 7. Finite Difference Method for Linear PDE
- Construction ( Space Discretization, Time Discretization)
- Convergence ( Consistency, Stability, Convergence )
Chapter 8. Finite Difference Method for Non-Linear PDE
- Non–Linear PDE
- The Linear Case Revisited
- Variational Inequality
- Hamilton–Jacobi–Bellman Equation
Compétence à acquérir :
This course provides an in-depth presentation of the main techniques for the evaluating of options using Monte Carlo techniques.