ABSTRACT
This chapter discusses the computer implementation of the interest rate option models. It aims to study the reparameterization and the resulting continuous-time limit. The chapter demonstrates how to construct arbitrage-free zero-coupon bond price evolutions. It discusses the intuition behind the construction of the discrete time approximation to the continuous-time limit economy. Analogous to the discrete-time case, the assumption of no arbitrage in the continuous-time model gives the existence of unique pseudo probabilities, which are used for the valuation of contingent claims. The chapter shows how to use the previous expressions to compute an arbitrage-free term structure evolution. It also discusses the computational issues involved in implementing the one, two, or three-factor model on a computer and three techniques: bushy trees, lattice computations, and Monte Carlo simulation. Special cases of the one-factor model allow for more efficient computation. Monte Carlo techniques are well suited for such computations.
