4 - Finite Sample Theory in Continuous-Time Models

Summary

Continuous-time models have found broad applications in many core areas of economics and finance. This chapter first briefly introduces the applications of the continuous-time models for modeling the dynamics of the short-term interest rates. While many estimation methods have been proposed to estimate continuous-time models with discrete samples over the past 40 years, almost all suffer from finite-sample bias. The bias problem is particularly severe for the mean-reversion parameter, which measures the persistence level of the interest-rate process. Moreover, such bias propagates and leads to considerable bias in price calculations of the interest-rate contingent claims, such as bonds and bond options. The focus of this chapter is to give a detailed review of the bias issue. Two bias-correction methods are discussed: the jackknife method and the indirect inference method, which can effectively reduce the estimation bias of the mean-reversion parameter and the bias in pricing contingent claims. Monte Carlo studies are provided to illustrate the characteristics of the bias and investigate the performance of the two bias-correction methods.