ADI Schemes for Pricing Options under the Heston model

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

Course Running Time: 3 Hours 15 Minutes

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