Continuous-time approximation of short-term interest rates in generalized Ho-Lee framework

In this paper, we study the weak convergence of short-term interest rate processes in multinomial (one-factor) and squared binomial (two-factor) generalizations of the Ho-Lee framework. We show that, under appropriate conditions on the rate of convergence of state probabilities and volatility parameter, in the one-factor case, the spot interest rate process converges to either Wiener process or superposition of Poisson processes. In the two-factor case, the limit process can have the form of the superposition of Wiener and Poisson components. The asymptotic results are proved under risk-neutral probability and local alternatives. © 2005 Springer Science+Business Media, Inc.