SOLVING P.D.E.s NUMERICALLY

The following sections are included:

• Mechanics

  • Approximating the Derivatives

  • Constructing a Discrete Time/Price Grid

  • Specifying Boundary Conditions

• Obtaining a Solution

  • The ‘Explicit’ Method

  • A First-Order ‘Implicit’ Method

  • Crank-Nicolson's Second-Order Implicit Method

  • Comparison of Methods

• Extensions

  • More General PDEs

  • Allowing for Lump-Sum Dividends