다요인 이자율 기간구조 모형의 SMM 추정을 통한 실증 분석 (Simulated Method of Moments for Multi-factor Term Structure Models: An Empirical Study in Korea)

서지정보

· 발행기관 : 한국금융학회
· 수록지 정보 : 금융연구 / 32권 / 2호 / 93 ~ 128페이지
· 저자명 : 박준규, 김배호, 강대일

초록

본고는 연금기금 등에서 필요한 자산부채 종합관리(Asset Liability Management, ALM)를 위한이자율 기간구조 모형에 대해 고찰한다. 기존의 국내 이자율 관련 연구가 주로 단기 동태성추정에 한정되어 왔으나, 종합적인 ALM를 위해서는 중장기적 관점의 분석이 필요하다는 점에서무차익조건 및 균형 이자율 등의 이론적 평형 조건을 기반으로 한 다요인 이자율 기간구조 모형을개발하여 이를 추정하는 모듈을 구현하고, 결과를 통계적인 방식으로 검증하였다. 본 연구에서사용된 이자율 기간구조 모형은 국내 채권 자료를 이용하여 거래되는 모든 만기의 이자율 기간구조자료를 기반으로 기존의 Black and Karasinski(1991) 모형을 확장한 형태로, 모형의 유연성을 확보한대신, 무차익 채권 가격의 닫힌 해가 더 이상 존재하지 않아 모수 추정을 위해 SMM (Simulated Method of Moments) 기법을 적용하였다. 특히, 본 연구에서 새롭게 제안한 일반화된 형태의Black and Karasinski(1991) 2요인 모형은 추정된 모수를 이용하여 쉽고 직관적으로 이자율기간구조의 동태적인 움직임에 대한 시나리오를 시계열 측면과 횡단면 측면에 대해 일관성 있게생성할 수 있다는 커다란 장점이 있다. 실증 분석 결과, 추정된 모형이 중장기적으로도 높은통계적인 적합도를 보여 중장기 영역까지 고려한 ALM 분석에 더욱 적절하게 사용될 수 있음을확인하였다.

영어초록

Term structure of interest rates, also known as yield curve, shows the market-driven trend of risk-free bond yields across different time-tomaturities.
Its shape contains crucial information towards mid- and longterm asset allocation strategies as well as their ex-post performance evaluation.
The selected term structure model is the main toolkit in terms of the asset liability managements (ALM) of financial institutions and funds along with their market, credit, and operational risk management standard.
In line with the introduction of Solvency Ⅱ, global financial institutions are supposed to be equipped with a more sophisticated ALM system based on reliable interest rate models.
In Korea, unfortunately, little attention has been paid to the related research topics on the mid- and long-term ALM analysis with domestic bond market data. The practical interest rate models employed in domestic financial industry tend to focus on the statistical goodness-of-fit to the short-term market data, even if there is no guarantee that the same model is suitable for a long-term ALM strategy. More importantly, many of those myopic models generally fail to satisfy the requirements suggested by Ziemba and Mulvey (2004): theoretical balance conditions such as the economic equilibrium within the arbitrage-free constraint, the reality of the shape of model-implied term structure, and its integration capacity with sufficient explanatory power of historical data and the exogenous economic anecdotes. For example, the Nelson-Siegel (1994) one-factor model is a widely-used statistical model, which neglects the theoretical balance conditions. It is also known to be difficult to construct sufficiently flexible shapes of term structures; thereby the ensuing scenarios implied by the theoretically unfounded single-factor model become less realistic in that they are limited in reflecting economic intuitions from the ad-hoc numerical approximation without careful economic justification. Therefore, a multi-factor term structure model is suitable for satisfying the conditions to capture market-wide environments as long as one can verify the procedure of its estimation methods.
This paper proposes a theoretically motivated multi-factor model for ALM analysis across various risk horizons to illustrate the time-series behavior of term structures extracted from the domestic bond market data.
Our proposed term structure model respects theoretical requirements as a basis of simulation-based analysis with statistical accuracy. For this purpose, we adopt the Black and Karasinski (1991) model as a primitive of our multi-factor interest rate model. Specifically, we extend the Black & Karasinski (1991) model as a two-factor model with the square-root stochastic volatility process instead of a constant long-term mean parameter.
We further propose the simulated method of moments (SMM) to estimate the model-based term structure by fitting the two-factor model to the real bond market data.
Our extended Black and Karasinski (1991) two-factor model contributes to the related literature in many aspects. We estimated our proposed model by SMM using Monte-carlo simulations with domestic interest data.
Our findings confirm that the newly proposed model is more appropriate for the ALM analysis across different risk horizons. The generalized form of the extended Black & Karasinski (1991) two-factor model can intuitively generate realistic scenarios of the dynamics in the shape of term structures implied by the calibrated parameters in a consistent manner.
Our methodology is applicable to the estimation of more advanced but complicated models. For instance, Johannes (2004) and Das (2001) finds that including a jump-risk factor is necessary to represent the fat-tailed distribution of interest rate movements in the U.S. bond market. In fact, the empirical observation exhibits substantial evidence in favor of jump-risk component in the form of regime-changing policy decisions or systemic shocks. We suggest our future research topics in this direction.

참고자료

· 없음