1. 1 Advanced Finite Difference Methods for Financial Instrument Pricing Structure of Course Incremental approach Build on expertise already gained Start with model problems; understand thoroughly Generalise to more advanced and difficult problems

2. 2 Advanced Finite Difference Methods for Financial Instrument Pricing Course Buildup Block 1: Basics of PDE and numerical methods Block 2: FDM for one-factor Black- Scholes PDE model Block 3: FDM for two-factor models Block 4: Advanced issues Block 5: Algorithms

3. 3 Advanced Finite Difference Methods for Financial Instrument Pricing Block 1 Classification of options and PDE Motivating FDM for ODE and SDE Method of Lines Standard difference schemes for Black Scholes

4. 4 Advanced Finite Difference Methods for Financial Instrument Pricing Block 2 Special schemes for special problems Approximating the Greeks Comparing FDM with binomial and trinomial methods How good are our schemes?

5. 5 Advanced Finite Difference Methods for Financial Instrument Pricing Block 3 ADI and splitting method for two-factor models Stability and convergence Applications in financial engineering Comparisons with other methods

6. 6 Advanced Finite Difference Methods for Financial Instrument Pricing Block 4 An introduction to parabolic variational inequalities (PVI) Numerical solution of PVI An introduction to spectral methods An introduction to Finite Element Method (FEM)

7. 7 Advanced Finite Difference Methods for Financial Instrument Pricing Block 5 Algorithms and documentation Mapping algorithms to code Performance Coupling with Excel