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축약형 모형을 이용한 CDS 기간 구조의 추정

  • 김정무 KAIST 경영대학 연구교수
  • 박윤정 한림대학교 경영대학 교수
  • 이창준 한국외국어대학교 글로벌경영대학 교수
본 연구에서는 국내 기업의 CDS(Credit Default Swap) 스프레드 자료를 이용하여 Pan and Singleton(2008)의 모형을 실증분석 하였다. 실증분석에 앞서, 모형가격 계산 방법론으로써 유한차분법의 적용법을 탐색하였다. 유한차분법 적용을 위한 몇 가지 가정에도 불구하고, CDS 거래의 실제를 잘 반영한 몬테칼로 시뮬레이션의 결과와 크게 다르지 않았다. 또한, 120×120 격자를 이용한 유한차분법은 실증분석을 하기에 적절한 오차와 속도로 이론가격을 계산할 수 있었다. 이러한 유한차분법을 이용하여 2006년 1월부터 2012년 11월까지의 기간 동안 국내 19개 기업의 CDS 기간구조를 최우추정 하였다. 추정된 모수는 Q-측도와 P-측도 하에서 상당히 다른 양상을 나타내었다. 두 측도 하에서의 부도확률을 계산한 결과, 투자자들은 Q-측도 하에서 더 높은 부도확률을 평가하고 있음을 확인하였으며, 이는 미래부도확률의 불확실한 변화에 대한 보상인 곤경 위험 프리미엄을 요구하는 것으로 해석된다. 또한, CDS 스프레드를 분해하여 곤경 위험 프리미엄을 계산한 결과, 평균적으로 42%의 스프레드가 곤경 위험에 대한 보상임을 확인하였다. 마지막으로, 곤경 위험 프리미엄의 결정요인을 분석한 결과 국내 변수로는 한국 외평채 CDS의 곤경프리미엄, 글로벌 변수로는 VIX(Volatility Index)가 각각 곤경 위험 프리미엄의 상당부분을 설명하는 것으로 드러났다. 이러한 결과들은 국내 기업의 곤경 위험 프리미엄은 국내 및 국외의 위험회피성향에 크게 영향을 받고 있음을 시사한다.
Crank-Nicholson 유한차분법; 몬테칼로 시뮬레이션; 신용부도스왑; 축약형 모형; 곤경위험 프리미엄; Crank-Nicholson Finite Difference Method; Monte Carlo Simulation; Credit Default Swap; Reduced-form Model; Distress Risk Premium

An Empirical Study on Distress Risk Premiums Implicit in the Term Structure of Korean Corporate CDS Spreads

  • Jungmu Kim
  • Yuen Jung Park
  • Changjun Lee
We investigate the term structures of corporate credit default swap (CDS) spreads in the Korean market based on Pan and Singleton’s (2008) model. To this end, we first consider an algorithm of numerical methods to calculate the theoretical price of CDSs. Specifically, we consider the finite difference method (FDM) and Monte Carlo simulation, and then, we examine the time efficiency and accuracy of the FDM. Monte Carlo simulation might be an accurate way to calculate the model price but it is time-consuming and not appropriate for estimating the term structure in our empirical study. In contrast, our analysis shows that the FDM meets our empirical goal in terms of error and speed. In particular, we use the Crank-Nicholson FDM with a 120×120 grid in our empirical analysis, as it performs relatively well in terms of speed and accuracy. Next, by employing the suggested FDM, we estimate the default probability implicit in the term structure of the CDS spreads for 19 domestic firms over the sample period from 2006 to 2012. We use the ML estimation for our econometric framework, and we estimate the 1-year, 3-year, and 5-year CDS spreads by assuming that the spread of CDSs maturing in three years is observed without error. Our estimation reveals that investors require a significant amount of premiums for bearing the risk of future variation in intensity, defined as the distress risk premium (DRP), when they invest in CDSs. We verify the argument in several ways. First, the ML estimates based on the Q-measure are very different from those based on the P-measure. The ML estimates imply that investors view the intensity dynamics more negatively under the Q-measure than under the P-measure. This result in the Korean corporate CDS market supports the finding of Pan and Singleton (2008) in two emerging sovereign markets. To take a deeper look at the significant difference between the Q- and P-dynamics of intensity, we next compute and examine the default probabilities within five years with the estimated parameters and implied intensity under both the Q- and P-measures. The results show that the Q-probability of default is much higher than its P-counterpart, implying that investors require premiums by adding more probability on real default probability. Finally, we directly calculate the amount of DRP to see how much it accounts for CDS spreads. In doing so, we follow the methodology first suggested by Pan and Singleton (2008) and then employed by Longstaff, Pan, Pedersen, and Singleton (2011) and Diaz, Groba, Lafuente, and Serrano (2013). There are two steps involved in obtaining the DRP. We first calculate the “pseudo- CDS” spread, denoted CDSP using expectations under the P-measure instead of the Q-measure to evaluate the model’s spread. Then, the DRP is obtained from the difference between the market CDS spread and pseudo-CDS spread. The results show that, on the average, the DRP accounts for 42% of the CDS spreads observed in the market. We also find that the DRP varies over time as the economy state changes, and particularly, it soars during the recent financial crisis. To explain our empirical finding that the DRP accounts for a substantial portion of the CDS spread and varies over time, we further investigate what determines the DRP and what drives it to change. To this end, we analyze the principal components of the cross-section of the DRPs. Our investigation shows that the first principal component explains about 97% or more of DRP variation, which implies that Korean companies’ DRPs are associated with investors’ appetites for the market-wide risk. To find what drives the first principal component, we regress the first principal component on a couple of domestic and global financial variables, which serve as proxies for the market risk premium. Specifically, the Volatility Index (VIX) is used as a proxy for a global variable of risk premium, and equity market risk premium, term premium, credit premium, and sovereign distress risk premium are examined as proxies for domestic risk premiums. The result shows that the VIX is statistically significant and has a striking power to explain the time-variation of the first principal component of corporate DRP. Among the domestic variables, equity market risk premium, term premium, and credit premium are statistically significant. However, sovereign distress risk premium (DRP implied in the Korean sovereign CDS spread) subsumes the explanatory power of the other domestic variables when added to the multiple regression. This finding indicates that sovereign DRP is the most important determinant of the co-movement of corporate distress risk premiums among the domestic variables. To control the endogeneity problem, the sovereign distress risk premium is orthogonalized to all other premiums, including VIX, the equity market risk premium, the term premium, and the credit premium. We then regress the first principal component of corporate DRPs on the orthogonalized sovereign DRP. This experiment shows that the orthogonalized sovereign DRP is statistically significant and explains the first principal component of corporate DRPs. This finding implies that sovereign DRP has additional information that is not contained in other risk premium proxies.