1. Applications of Lattice Methods
Dr. DAI Min

2. Lookback options and Neumann boundary condition

3. Single-state BTM for lookback options

4. Understanding BTM: explicit difference

5. Explicit difference: Neumann boundary condition

6. An improved finite difference

7. Modified BTM

8. Numerical results

9. Lattice methods for American options
BTM
Explicit difference for transformed equation

10. Explicit difference for American options

11. Implicit schemes for American options

12. Solution region and boundary conditions
One should exercise the American put when the stock price is low enough
When the stock price is high enough, the option value is approximately zero.

13. Implicit treatment of the constraint

14. Implicit treatment of the constraint: Projected SOR method

15. Penalty method

16. Financial interpretation of penalty approximation

17. Fully implicit scheme for penalty approximation
Difference scheme
Linearization of penalty term

18. Options on two assets

19. Pricing model of options on two assets (1)

20. Pricing model of options on two assets (2)

21. Exchange options

22. Finite difference schemes for options on two assets

23. Boundary conditions

24. Discretization of the cross derivative