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국면전환 확산과정모형을 이용한 콜금리행태 분석

Analysis of Call Rate Behaviour Using Regime-switching Diffusion Process Model

최승문|김병국
한국은행|2017.03|경제분석 (Economic Analysis)|제23권 제1호|pp. 23-54|DOI 10.23299/bokeri.2017.23.1.002

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키워드

Maximum likelihood estimation국면전환Regime-switching확산과정모형콜금리행태최우도추정전이확률밀도 함수Diffusion process modelCall rate behaviourTransition probability density function
주제분류경제학

초록

이 논문에서는 한국의 주별 익일물 콜금리를 사용해 국면전환 확산과정모형을 추정했다. 일반적인 비선형 추세 함수와 분산 탄력성이 상수인 변동성 함수를 갖는 확산과정모형에서 모수들이 경제상황에 따라 서로 다른 두 가지 값을 가질 수 있도록 모형을 설정한 후에 최우도추정법을 이용해 모형을 추정했다. 우도를 계산하기 위해 해밀턴의 알고리즘을 이용하고, 확산과정의 전이확률밀도 함수가 알려져 있지 않기 때문에 Aït-Sahalia (2008)의 축소가능하지 않은 방법을 이용해 근사적 로그-전이확률밀도 함수를 구체적인 식으로 구한 후에 Choi (2015a)의 방법으로 전이확률밀도 함수를 구했다. 서로 다른 두 국면 L과 H가 존재한다는 여러 가지 증거들을 확인할 수 있었으며 추세 함수보다는 변동성 함수가 두 국면 모두에서 이자율의 움직임을 설명하는 데 중요한 역할을 한다는 사실을 밝혔다. 또한 국면변수의 변화를 결정하는 전이 확률이 이자율에 의존해 시간에 따라 변하며 이자율이 늘어날수록 다음 기에도 같은 국면 L에 머무를 확률은 줄어들고 같은 국면 H에 머무를 확률은 증가함을 알 수 있었다. 각 데이터 시점에서 추정된 국면 H의 평활확률은 시계열 자료에서 대체로 변동성이 큰 부분은 1과 가깝고 작은 부분은 0과 가까워 뚜렷하게 다른 두 국면이 있다는 증거가 된다. 마지막으로 주요 모형과 이 모형에 포함된 기존의 연구들에서 사용됐던 다른 모형들을 비교했을 때 일반적인 모형이 더 선호됨을 알 수 있었다.

Abstract

This paper estimates a regime-switching diffusion process model for Korean call rate. Parameters of the diffusion model with nonlinear general drift and volatility function vary depending on the economic states and are estimated using maximum likelihood method. In order to obtain the maximum likelihood estimates, we use the algorithm of Hamilton (1989) and calculate transition probability density function(TPDF) using Choi (2015a)’s method from the approximate log-TPDF obtained by Aït-Sahalia (2008)’s irreducible method. We find evidences that there exist two different regime and that the volatility term of the model explains the movements of the call rate better than the drift term. Also, the model shows that the transition probability varies depending on the level of interest rate. As interest rate increases, the probability of remaining at the same regime “L” next period decreases while the probability for the regime “H” increases. The estimated smoothed probability of regime “H,” which is close to 1 and 0 during the period with high and low volatility respectively, is a clear evidence of the existence of two different regimes. Lastly, comparison with existing models demonstrates that the generalized model in this paper is preferred in explaining the call rate behaviour.

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