**ADI Schemes for Pricing Options under the Heston model**

**Presenter: Karel in't Hout: Professor of Applied Mathematics and Numerical Analysis, University of Antwerp**

**Video Lectures:**

**Part 1: (Running Time: 32:21)
1. Option valuation under the Heston model
2. Finite difference discretization Heston PDE
3. Numerical experiments**

**Part 2: (Running Time: 45:17)**

**4. Formulas for A and g**

**Part 3: (Running Time: 51:25)**

**5. ADI schemes for semidiscrete Heston PDE
6. Stability analysis of ADI schemes**

**Part 4: (Running Time: 1.06.28)**

**7. Numerical experiments
8. Extensions
9. HestonADI Matlab code
10. Literature**

This training course includes the Matlab source code for computing vanilla and barrier option prices, together with their Greeks, under the Heston model. The numerical solution technique is based on a suitable finite difference discretization on nonuniform spatial grids followed by a state-of-the-art ADI time discretization scheme.

- Heston PDE for vanilla and barrier option prices
- Initial and boundary conditions
- Specific issues: mixed derivative, Feller condition
- Domain truncation
- Nonuniform spatial grids
- Spatial discretization: finite difference (FD) schemes
- Temporal discretization: four state-of-the-art ADI schemes
- Linear systems: LU factorization
- Stability and convergence analysis
- Specific issues: damping procedure, cell averaging
- Step-by-step discussion of the HestonADI code (Matlab)
- Numerical experiments
- Approximation of the Greeks