단기이자율 확률변동성모형 비교: 베이지언 모형 비교 (Bayesian Model Comparison for Stochastic Volatility Models of Short Term Interest Rates)

서지정보

· 발행기관 : 한국금융학회
· 수록지 정보 : 금융연구 / 31권 / 3호 / 179 ~ 233페이지
· 저자명 : 김태형, 박정민

초록

본 연구는 베이지언 접근법에서 조건부분산이 Feller제곱근과정을 따르는 단기이자율 확률변동성모형과 로그조건부분산이 OU과정을 따르는 단기이자율 확률변동성모형을 비교․분석하였다.
또한 본 연구는 비선형 평균회귀성향, 수준효과, 단기이자율 조건부분포의 두꺼운 꼬리를 설명할수 있는 특성을 가지고 있는 단기이자율 확률변동성모형에 대한 베이지언 분석을 통해 서로다른 조건부분산 확률과정을 가지는 모형들을 비교 분석하였다. 대표적인 단기이자율인 1954년1월 8일~2013년 12월 27일 기간의 3개월 만기 미국재무부채권(TB3M) 수익률 주간자료에 대한베이지언 분석 결과, TB3M 수익률 주간자료의 동태적인 특성을 설명하기 위해 확률변동성과함께 수준효과와 두꺼운 꼬리를 가지는 단기이자율 조건부분포가 필요함을 확인할 수 있었다.
특히 베이지언 모형 비교 결과, 로그조건부분산이 OU과정을 따르는 확률변동성모형이 조건부분산이 Feller제곱근과정을 따르는 확률변동성모형보다 TB3M 수익률의 동태적 특성을 더 잘설명하는 것으로 나타났다. 고전적 접근법의 Rivers and Vuong(2002) 검정과 Johannes et al.(2009)의순차로그우도비 검정에서도 동일한 모형 비교 결과를 얻었다. 이러한 단기이자율 확률변동성모형에대한 비교 분석결과는 Feller제곱근과정에 기반한 이자율 기간구조모형과 이자율 파생상품가격결정 모형이 단기이자율 조건부분산의 동학을 충분히 반영하기 어려울 수 있으므로 조건부분산의 동학을 충분히 설명할 수 있는 방향으로 기존 이자율 기간구조모형과 이자율 파생상품가격결정모형을 개선하는 것이 필요함을 시사한다.

영어초록

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.

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