Applications of Lattice Methods Dr. DAI Min
Lookback options and Neumann boundary condition
Single-state BTM for lookback options
Understanding BTM: explicit difference
Explicit difference: Neumann boundary condition
An improved finite difference
Modified BTM
Numerical results
Lattice methods for American options BTM Explicit difference for transformed equation
Explicit difference for American options
Implicit schemes for American options
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.
Implicit treatment of the constraint
Implicit treatment of the constraint: Projected SOR method
Penalty method
Financial interpretation of penalty approximation
Fully implicit scheme for penalty approximation Difference scheme Linearization of penalty term
Options on two assets
Pricing model of options on two assets (1)
Pricing model of options on two assets (2)
Exchange options
Finite difference schemes for options on two assets
Boundary conditions
Discretization of the cross derivative