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무위험단기이자율 대용치의 안정성과 이자율기간구조모형과의 양립성 분석

Investigation into the compatibility of stationarity of short-term interest rate proxies with the dynamic term structure models of interest rates

박정민|김태형
한국계량경제학회|2015.03|계량경제학보 (Journal of Economic Theory and Econometrics)|제26권 제1호|pp. 70-126|DOI 10.22812/jetem.2015.26.1.003

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참고문헌

키워드

이자율기간구조모형수준효과확률변동성모형drift-induced stationarity(DIS)volatility- induced stationarity(VIS)몬테카를로 최우추정(MCML)보조파티클필터(APF)Dynamic Term Structure Model of Interest RatesStochastic Volatility ModelLevel EffectDrift-induced Stationarity(DIS)Volatility-induced Stationarity(VIS)Monte Carlo Maximum LikelihoodAuxiliary Particle Filter(APF)
주제분류경제학

초록

본 연구에서는 단기이자율 확률과정의 안정성의 특성을 규명하고 이를 통해 단기이자율의 동태적인 안정성의 특성이 기존 이자율기간구조모형의 가정과 부합하는지를 살펴보고자 한다. 단기이자율 확률과정 안정성에 대한 Conley et al. (1997)의 연구를 확장한 수준효과를 포함하는 일반적인 확률변동성모형을 이용하여 안정성을 특징짓는 수준효과의 크기를 식별하고자 하였다. 기존 단기이자율 확률변동성모형의 한계를 극복하는 일반적인 단기이자율 확률변동성모형 추정을 위해 효율적인 MCML추정법을 이용하였으며, 안정성을 특징짓는 수준효과의 크기에 대한 통계적인 추론을 위해 보조파티클필터(auxiliary particle filter)를 통해 얻은 PIT(probability integral transform)를 표준정규분포로 역변환한 의사표준예측오차를 이용한 모형 진단과 모형 적합성 비교를 하였다. 다양한 단기이자율 대용치들에 대한 실증분석 결과, 3개월 만기 미재무부채권 수익률과 한국의 익일물 콜금리는 ATSM 및 QTSM 등의 기존 이자율기간구조모형과 부합하는 ‘drift-induced stationarity’의 특성을 가지는 반면, 1개월 만기 유로달러 이자율, 한국의 잔존만기 3개월 국고채, MMF 7일물, 91일물 CD, 91일물 CP 수익률은 ‘volatility-induced stationarity’의 특성을 가지는 것으로 나타났다. 이와 같은 결과는 단기이자율 대용치의 안정성의 특성을 충분히 고려하지 않고 ‘drift-induced stationarity’를 가정하는 기존 이론모형을 이용하는 경우 파생상품가격결정과 리스크관리에 심각한 문제가 발생할 수 있음을 시사한다.

Abstract

By building on the work of Conley et al. (1997), we investigate the stationarity of riskless short-term interest rate processes, analyzing generalized stochastic volatility models with level effects and examine the compatibility of stationarity of short-term interest rates with the popular dynamic term structure of models of interest rates, such as ATSM and QTSM. We extend extant stochastic volatility models with level effects crucial in characterizing the stationarity of a continuous time stochastic process, estimate the extended models using an efficient simulation-based MCML(Monte Carlo Maximum Likelihood) estimation method using importance sampling and implement model diagnostics using the inverse of standard normal distribution of the dynamic probability integral transform obtained via an auxiliary particle filter. Empirical estimation results indicate that TB3M and Call1d exhibit drift-induced stationarity compatible with both ATSM and QTSM, and that ED1M, KTB3M, MMF7d, CD91d and CP91d are of volatility-induced stationarity. Consequently, the results imply that, without careful consideration for the nature of stationarity of a short-term interest rate, indiscriminate application of theoretical models assuming the drift-induced stationarity of short-term interest rates may cause serious failure in derivative pricing and risk management.

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