Enhancing Estimation for Interest Rate Diffusion Models With Bond Prices

Abstract

We consider improving estimating parameters of diffusion processes for interest rates by incorporating information in bond prices. This is designed to improve the estimation of the drift parameters, which are known to be subject to large estimation errors. It is shown that having the bond prices together with the short rates leads to more efficient estimation of all parameters for the interest rate models. It enhances the estimation efficiency of the maximum likelihood estimation based on the interest rate dynamics alone. The combined estimation based on the bond prices and the interest rate dynamics can also provide inference to the risk premium parameter. Simulation experiments were conducted to confirm the theoretical properties of the estimators concerned. We analyze the overnight Fed fund rates together with the U.S. Treasury bond prices.JEL CLASSIFICATION: C50, C58.

Inference on covariance-mean regression

“…Remark: This condition is standard for ensuring the identification of the parameter γ when we use the Z -estimation approach in Section 3.1. Similar conditions can be found in Assumption A.1 of Zou and Chen (2017).…”

Variable bandwidth local maximum likelihood type estimation for diffusion processes

“…For example, [1] investigated an application of Ornstein-Uhlenbeck process to commodity pricing in Thailand. Reference [2] improved estimation of drift parameters of diffusion processes for interest rates by incorporating information in bond prices. So, recently in the literature, the statistical inference for diffusion processes based on discrete observations has often been of concern; for example, see [3][4][5][6] and its references for parametric estimation, see [7][8][9] and the references therein for a semi-parametric estimation and see [10][11][12][13][14][15][16] and the references therein for a nonparametric estimation.…”