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Asian Review of Financial Research Vol.27 No.4 pp.709-748
An Empirical Study on Distress Risk Premiums Implicit in the Term Structure of Korean Corporate CDS Spreads
Jungmu Kim Research Assistant Professor, College of Business, KAIST
Yuen Jung Park* Assistant Professor, College of Business, Hallym University
Changjun Lee Assistant Professor, College of Business Administration, Hankuk University of Foreign Studies
Key Words : Crank-Nicholson Finite Difference Method,Monte Carlo Simulation,Credit Default Swap,Reduced-form Model,Distress Risk Premium


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 Díaz, 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.
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