Options, Futures, and Other Derivatives, Ninth Edition

Chapter 21 Basic Numerical Procedures

This chapter discusses three numerical procedures for valuing derivatives when analytic results such as the Black–Scholes–Merton formulas do not exist. The first represents the asset price movements in the form of a tree and was introduced in Chapter 13. The second is Monte Carlo simulation, which we encountered briefly in Chapter 14 when stochastic processes were explained. The third involves finite difference methods.

Monte Carlo simulation is usually used for derivatives where the payoff is dependent on the history of the underlying variable or where there are several underlying variables. Trees and finite difference methods are usually used for American options and other derivatives where the holder ...