Bayesian, MLE, and GMM Estimation of a Spot Rate Model

ABSTRACT

We develop Markov chain Monte Carlo algorithms for estimating the parameters of the short-term interest rate model. Using Monte Carlo experiments we compare the Bayes estimators with the maximum likelihood and generalized method of moments estimators. We estimate the model using the Japanese overnight call rate data.

Keywords:

• Generalized method of moments
• Griddy Gibbs
• Japanese call rate
• Markov chain Monte Carlo algorithms
• Maximum likelihood estimator
• Monte Carlo experiments
• Volatility elasticity

Mathematics Subject Classification:

• 62F15
• 62G08

Acknowledgment

The authors thank seminar participants at Rutgers University and an anonymous referee for helpful comments on an earlier version of this article.

Notes

¹The scenario α = 0.03, β = −0.006, σ = 1.1, λ = 1.5 is not included in our experiment because the process is non stationary.

Note: For scenario 7, GMM estimation algorithm does not converge.

Notes: u _t in Eq. (2.1) is drawn from N (0,1) × IVG(1.8,3).

Notes: (1) Figures in parentheses are standard deviations.

(2) For MLE and GMM the summary statistics are means and standard deviations.

(3) For Bayesian the summary statistics are posterior means and standard deviations.