국제 원유 가격들의 확산과정 모형 추정
Estimation of Diffusion Models for International Crude Oil Prices
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초록
본 연구의 목적은 국제 원유 가격의 동태적 변화를 잘 설명할 수 있는 확산과정 (diffusion process) 모형을 실증분석을 통해 찾는 것이다. 이를 위해 유가의 변화에 대해 얘기할 때 대표적으로 언급되는 두바이유, 브렌트유 그리고 WTI유의 일별 자료를 이용해 선행 연구에서 이용된 대부분의 확산과정 모형들을 포함하는 GD-GV 모형과 여기에 포함되는 GD-CEV 모형, CKLS 모형, CIR 모형 그리고 Vasicek 모형을 추정했다. 최우추정법을 이용했는데 이를 위해 필요한 로그전이확률밀도 함수는 Aït-Sahalia (2008)가 개발한 방법을 이용해 근사적으로 구했다. 세 종류의 유가 모두에서 비슷한 추정 결과들을 얻었다. CKLS 모형이 유가의 움직임을 가장 잘 설명한다는 결과를 얻었다. 그리고 추세 함수 보다는 변동성 함수가 유가의 움직임에 더 중요한 역할을 한다는 사실을 알았다. 유가가 낮을 때는 평균값으로 회귀한다는 증거를 찾을 수 있었지만 중간 값 이후에서는 그러한 증거를 찾을 수 없었다. 유가에 대한 변동성의 탄력성은 약 0.75로 추정됐다.
Abstract
The aim of this study is to find a diffusion that can explain the dynamics of international crude oil price through empirical analysis. To this end, we apply daily data on three primary benchmark crude oil prices of Dubai, Brent, and WTI to the GD-GV model that encompasses most of diffusion models suggested in the literature and GD-CEV model, CKLS model, CIR model and Vasicek model which are also nested by the GD-GV model. We estimate these diffusion models by maximum likelihood estimation method for which log-transition probability density function is approximated by the method developed by Aït-Sahalia (2008). Estimation results are quite similar for all of three crude oil prices. We found that CKLS model best explained the movement of oil prices. Moreover, volatility function plays a more important role in describing the dynamics of oil prices than the drift function. We found some evidence that the price of oil tends to revert to its long-run mean value only when the oil price is low. The elasticity of volatility with respect to oil price is estimated to be about 0.75.
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