단기이자율 확률변동성모형 비교: 베이지언 모형 비교

Since the risk-free short-term interest rate is a key economic variable that is of fundamental importance for financial applications such as derivative and bond pricing and portfolio risk management, extensive empirical studies have been proposed to identify its dynamic characteristics. It is well-known that the short-term interest rate has not only the typical characteristics of mean-reversion, volatility clustering, fat-tailed conditional distributions such as stock prices and exchange rates, but also the level effect that volatility depends the level of short-term interest rate. Those characteristics of short-term interest rate is intimately related with the specification of dynamic term structure models of interest rates such as ATSMs(exponential affine term structure models) which are specified as a linear combination of state variables following the Ornstein-Uhlenbeck process or the Feller square-root process and QTSMs(gaussian quadratic term structure models) which are specified as a quadratic form of state variables following the Ornstein-Uhlenbeck process in order to explain the term structures of interest rates based on the dynamic characteristics such as linear or nonlinear mean-reversion and stochastic volatility of the short-term interest rate. The main reason why the stochastic processes of state variables in ATSM and QTSM are specified as the Feller square root process or the Ornstein- Uhlenbeck process is the mathematical convenience that allows for analytically tractable closed-form bond prices. In contrast, log stochastic volatility models in which log-conditional variance follows the Ornstein-Uhlenbeck process have been frequently employed in empirical literatures. The respective conditional volatility processes implied by the Feller square-root stochastic volatility model and the log stochastic volatility model have quite different diffusion functions. In this paper, we analyze and compare the performance of log stochastic volatility models with that of Feller square-root stochastic volatility models using the Bayesian inference for stochastic volatility models including the typical characteristics of nonlinear mean reversion, level effect and fat-tailed conditional distribution of short term interest rates. we conduct bayesian inference, hypothesis tests and model comparison for stochastic volatility models for weekly data of 3 month U.S. T-bill rates over the period January 8, 1954 to December 27, 2013. Our Bayesian model comparison results show that log stochastic volatility models perform better than Feller square-root stochastic volatility models in explaining the dynamics of conditional variances of 3 month U.S. T-bill rates. In addition, we find strong statistical evidence for the fat-tailed conditional distribution and the level effect, but no evidence for the nonlinear mean-reversion. Rivers and Vuong (2002)’s nonnested model comparisons and Johannes et al. (2009)’s sequential loglikelihood ratio tests in the classical approach yield the same model comparison results as in the Bayesian model comparison. Our empirical results imply that dynamic term structure models of interest rates and interest rate derivative pricing models based on the Feller square-root stochastic volatility process may not capture the dynamics of conditional variance processes of short term interest rates sufficiently and that those models need to be improved.