Nonparametric Estimation of Multifactor Continuous Time Interest Rate Models

Abstract

In this paper we study the finite sample properties of the nonparametric method developed by Stanton and later extended by Boudoukh, et al. for the estimation of the drifts and diffusions of multifactor continuous-time term-structure models. Monte Carlo simulations from a known parametric model are employed to calculate the performance of the estimator. The paper focuses on the issue of optimal bandwidth selection. The results suggest that, for persistent data-generating processes exhibiting stochastic volatility, such as interest rate data, a bandwidth function that varies over the surface of the data is optimal. The paper also presents a computationally intensive bandwidth-selection procedure that uses dynamic graphics, combining the computational power of the machine with the pattern-recognition abilities of the human brain. The Monte Carlo simulations require the numeric solution of a system of stochastic differential equations. The paper also presents a nonparametric test for the validity of the solutions. This test is useful in other estimation algorithms, such as the efficient method of moments, where numeric solutions of stochastic differential equations are required. The test is also useful as a tool for understanding how the length of the time step used in the numeric solution of the stochastic differential solutions affects the accuracy of the solution.