Component Structure of Credit Default Swap Spreads and Their Determinants

In this paper, we decompose credit default swap (CDS) spreads into a transitory component and a persistent component and test how these components are affected by the theoretical explanatory variables. We use three benchmark iTraxx Europe indices of two different maturities (5 and 10 years) and extract the components in the framework of Schwartz and Smith (2000). We then regress these components against proxies for several commonly used explanatory variables. We find significant but differing impacts of these explanatory variables on the extracted components. For example, equity volatility seems to have a larger influence on the transitory component, suggesting that its effect may be mostly short-lived, while our proxy for illiquidity has a bigger impact on the persistent component, which suggests that its effect is more enduring. Surprisingly, our proxy for the credit rating premium is not even significant in explaining two of the 10-year indices, but has a large effect on the persistent component. Finally, the slope of the yield curve has impacts with opposite signs on the two components and thus helps address the conflicting results reported in earlier studies without such a component framework. These results indicate that a two factor formulation, similar to Hull and White (1994) interest rate model, may be needed to model CDS options.


Introduction
Research on credit risk has developed rapidly over the last decade or so. Stimulated by proactive regulatory developments, different classes of models have been put forward to measure, manage, price and forecast credit risk. Coupled with other developments in the credit derivatives market, more incisive research in this market is not only attractive but necessary for better understanding by all participants. Its importance lies not only in risk management activities using Credit Default Swaps (CDS) for hedging purposes, but also for anyone trying to profit from arbitrage possibilities within the CDS market.
A credit derivative is an over-the-counter derivative that is designed to transfer credit risk from one party to another. By dynamically adjusting credit exposures, they allow institutions to manage credit risk more effectively. Not only is the credit derivatives market growing in total nominal amounts outstanding, it also is attracting an increasingly diversified group of users. Except for the risk management units in large commercial banks, who are the traditional users, investment banks, hedge funds, and other investors are using credit derivatives to profit from arbitrage opportunities in the market. Many are attempting to exploit arbitrage opportunities between the credit derivatives market and the underlying bond and stock market, to hedge positions taken in other markets and also for pure speculation or regulatory arbitrage (Bystrom (2006)).
While there are many variations of credit derivatives, the Credit Default Swap (CDS) is among the most intuitive, and is commonly cited as a basic "building block" for more complex structures. The owner of a CDS receives the bond's face value if the underlying bond defaults. Rather than paying for this default insurance in a lump sum, the holder makes periodic payments until the underlying bond either defaults or matures. If one writes these periodic payments as a percentage of the face value per annum, this quantity is known as the CDS spread (or sometimes, as a CDS price).
The CDS spread does behave much like a credit spread. In our data (which essentially consists of averages of CDS spreads, as we discuss in section 4) we observe CDS spreads ranging from 20 basis points to 500 basis points, roughly. Note that there are also bid CDS spreads and ask CDS spreads. It is commonly recognized that the credit default swap spread is a comparatively "pure" measure of credit risk (Ericsson et al. (2004)). Therefore, the study exploring the determinants and the dynamics of the CDS plays a central role when evaluating credit risk related securities and projects. This paper is closely related to these works mentioned above, but with a difference. Firstly, we decompose the CDS series of two different maturities into its component structures -a short-term factor and a long-term factor. Secondly, we explore the determinants for each of them separately. To the best of our knowledge this paper is the first such attempt to look at the determinants of credit default swap spreads form the perspective of short-term and long-term dynamics.
Here we develop the argument in favour of analysing the CDS spreads from the viewpoint of component structures. It may be argued that the common factors should be relevant for all maturities of CDSs whether long or short. However, the incorporation of information from different explanatory variables affects CDS spreads differently in time and speed. For example, bad or negative news has an almost instant impact on credit spread changes while the impact of good or positive news is much more restrained (Hull et al. (2004)). Also, Norden and Weber (2004) find that the CDS spreads are influenced by the level of the old rating, previous rating events and the pre-event average rating level of agencies. Obviously, the time these influences last is different based on their previous credit rating. For credit default swap spreads with underlying entities having higher credit ratings, the influence of micro and macro elements does not differ much in the short-term and the long-term. On the other hand, for credit default swap spreads with underlying entities having lower credit ratings, the impact of these elements should differ in the short-term and long-term. The credit default swap spreads with underlying firms having lower credit ratings will be more sensitive to the bad news than that of their higher credit rating counterpart firms in the short-term.
Another example of differing influences could be seen as follows. The probability that a firm, which is currently in a rather low credit rating category, would be upgraded is higher in the long run compared to that of a firm which is already in a relatively higher credit rating category. Also just as illiquidity could affect bonds with different maturities to a different extent, the illiquidity could also affect long-term CDSs and short-term CDSs to a different extent. Moreover the assessment of overall economic health of investors in the future would influence the long-term factor differently from that of the short-term factor. Now that we have established the case for component structures for CDS spreads the question is how we infer these components given that we only have observations on CDS spreads directly. In this respect we follow the framework of Schwartz and Smith (2000). We include two unobserved components in the model in such a way that one would capture the long-term dynamics and the other one would capture the short-term dynamics. The long-term factor is thought to describe the equilibrium spread level (representing a constant fundamental spread level) and is assumed to evolve according to a Brownian motion with drift reflecting the business cycle, development of the credit derivatives market, as well as political and regulatory effects. The short-term deviations, which are defined as the difference between spot and equilibrium prices, are expected to follow a mean reverting process. These deviations may reflect, for example, portfolio adjustments or intermittent market disruptions, and temporary credit changes. Since neither of these factors is directly observable, we can set up the problem in a state space framework and use standard Kalman filtering techniques to make optimum inferences about the state variables.
In this paper we focus on different indices of CDS spreads, namely the iTraxx family which can be treated as portfolios, so the idiosyncratic differences are rendered trivial. We, thus, care more about the common factors behind all these CDS spreads.
Also we choose three benchmark iTraxx indices, namely iTraxx Europe, iTraxx Europe Hivol and iTraxx Europe Crossover. This allows us to have a whole view of the European CDS market just by examining these three indices. Overall, our results show that with the quick development of the CDS market (or credit derivatives market) the level of CDS spreads is falling during the sample period. This may mainly result from the enhanced efficiency and liquidity of this market. For firms in different credit rating categories, the short-term and long-term behavior is different. The credit default swap spread for underlying entities with higher credit ratings tends to be more volatile in the long-term while the credit default swap spread for underlying entities with lower credit rating tends to be more volatile in the short-term. Our results also demonstrate that most theoretical explanatory variables, as documented by other researchers, have significant impacts on credit default swap spreads and they do impact short-term and long-term dynamic of CDS spreads differently. Moreover, these variables can explain more variations of long-term dynamic in CDS spreads compared to those of short-term dynamic.
The remainder of this paper is organized as follows. Section 2 gives the related literature review. Section 3 presents a description of the recent development of the Credit derivatives market and the iTraxx index which is the research objective in this paper. Section 4 provides the data and the methodology. In sector 5 we give the empirical results and explanations of our findings. Section 6 concludes the paper.

Literature Review
In the contemporary literature on credit derivatives, theoretical and empirical work has mostly concentrated on estimation of default probabilities and determinants of credit risk. Most of these studies, however, use the corporate bond spread, also called the credit spread. The credit spread is generally defined as the yield of corporate bond minus the yield on a government bond with comparable maturity. Longstaff and Schwartz (1995a, b) use annual data from 1977 to 1992 in a regression based analysis of the change in credit spread against the change in the 30year-Treasury rate and the return on an appropriate equity index. Irrespective of maturity, they find the intercept term and coefficients of change of the 30-year-Treasury rate increase in absolute magnitude as the credit quality decreases. Wilson (1997a, b) examined the effects of macro-economic variables, namely, GDP growth rate, unemployment rate, long-term interest rate, foreign exchange rate and aggregate savings rate, in estimating the default rate level. Collin-Dufresne, Goldstein and Martin (2001), on the other hand, investigated the determinants of credit spread changes using dealer's quotes and transition prices on industrial bonds. They show that the proxies for three theoretical determinants namely, default risk, recovery rate upon default and liquidity have rather limited explanatory power. Their results actually suggest that monthly credit spread changes are mainly driven by local supply/demand shocks that are independent of both credit-risk and standard proxies for liquidity.
Studies which directly focus on the determinants of CDS spreads are also developing rapidly in recent years. Skinner et al. (2003) use arguments from option pricing theory and suggest that the CDS spread should be highly dependent on the risk-free short rate, the yield of the reference obligation, the interest rate volatility, the time to maturity and the recovery rate. They find that four of these variables, namely the risk-free short rate, the yield of the reference obligation, the interest rate volatility and the time to maturity, contain significant information. Benkert (2004) conducts a regression analysis using CDS panel data, incorporating variables such as credit rating, liquidity, leverage, historical volatility and implied volatility. He finds that implied volatility has a stronger effect than the historical volatility, and that both remain relevant in the presence of credit ratings which contribute an equal amount of explanatory power.
The goal of this paper is to develop a model that is realistic but simple enough to capture the dynamic behaviour of CDS spreads and explore its potential determinants through its component representation. Schwartz and Smith (2000) devise such a component modelling approach by considering short-term variation and longterm dynamics in commodity prices. In their model the natural logarithm of the commodity price is assumed to be the sum of these two components. The short-term component is assumed to revert back to zero based upon its mean reversion speed and the long-term component is assumed to be a random walk with a deterministic trend.
In essence, the interpretation of long-term and short-term factors in their model is in line with persistent and temporary components, respectively. Zhou and Qing (2000) take a similar approach, working with logarithmic stock prices.

Credit Derivatives Market and iTraxx Indices
The structured credit derivatives market encompasses a wide range of capital market products designed to transfer credit risk among investors through over-the-counter transactions. According to a recent survey by the British Banker's Association (BBA), which is carried out every two years, the growth of the global credit derivatives market has outperformed expectations from the 2004 BBA survey which predicted a market size of $8.2 trillion by 2006. But in its 2006 survey report, the estimated size of the market was $20 trillion and at the end of 2008 the global credit derivatives market is expected to expand to $33 trillion. Figure 1 plots the global market size of credit derivatives from 1996 to 2008 (estimated). This growth may have been driven by several factors. For example, it is well known that credit derivatives are designed to meet the needs of risk management as well as develop credit arbitrage techniques to create new investment products. Under increasing pressure to improve financial performance, banks have turned to the credit derivatives market to diversify their credit risk exposures and to free up capital from regulatory constraints (Duffee and Zhou (2001)). Another reason would be the presence of significant credit arbitrage opportunities across different market sectors, for example, loans and bonds and across different countries. Structured credit entails applying financial engineering techniques to leverage these opportunities and create customised financial products for investors including credit linked notes and repackaged notes. The iTraxx indices typically trade 5 and 10-year maturities and a new series is determined by a dealer liquidity poll every 6 months. The Europe and Hivol indices also trade 3 and 7-year maturities. The indices are managed and administrated by the International Index Company that is owned by a group of the largest global investment banks. All index quotes for our study have been made available by the International Index Company.

Data and Methodology
This section provides the detailed description of the data and methodology we adopted in this paper. These include the iTraxx indices, the theoretical explanatory variables of credit default spreads, and the state-space model for extracting the components.

1 Data
This paper examines the natural logarithm of the CDS index represented by three benchmark iTraxx indices. The theoretical explanatory variables considered in this paper are: the short interest rate, the slope of yield curve, the stock market volatility, the bid-ask spread for each iTraxx index and each maturity and credit rating premia.

iTraxx Index Characteristics
The three benchmark iTraxx indices used in this study are iTraxx Europe, iTraxx Europe Hivol and iTraxx Europe Crossover. These three benchmark iTraxx indices give us a complete overview of the whole European CDS market. All these indices are traded with 5-year as well as 10-year maturity and are denominated in Euro.
iTraxx Europe is made up of 125 equally weighted investment grade Europe names, and is used as a benchmark index. These 125 component names are updated every 6 months by a dealer poll based on CDS volume traded over the previous 6 months.   Table 2 gives descriptive statistics for both (the natural logarithm of) the iTraxx index level and its first difference. For example, in logarithmic form, index levels range from 3.0143 to 6.2222, which correspond to CDS spreads of exp(3.0143) = 20.4 basis points to exp(6.2222) = 503.8 basis points.
There are several points we would like to emphasize based on Figure 2.
Firstly, it is not surprising that the iTraxx index level is monotonically increasing with the maturity which is consistent with the upward slope of the term structure of CDS spreads. Secondly, we notice that there is a less obvious downward trend in our sample period which is quite different from recent credit derivatives markets which suffered from the collapse of the U.S. subprime market. Also, during the sample period, the most obvious downward trend, which is a narrowing of the spread, demonstrated in the first nine months before the problems faced by General Motors (GM) and Ford. Ford and General Motors are two of the world's biggest car companies, as recorded by the web site of www.financialpolicy.org. GM had $290 billion in outstanding debt and Ford had another $160 for a total of $450 billion.
Given the massive size of the auto makers' debt, this turbulence seems to have spread across the Atlantic to the European auto sector and thus affected the whole iTraxx. Thirdly, it is interesting to notice that the spreads between the 5-year maturity and the 10-year maturity are wider with passing time, which may be because the 5year contract became more actively traded than the 10-year maturity with the development of the CDS market. It also may be the impact of the leverage ratio. The mean-reversion feature (Collin-Dufresne and Goldstein (2001)) in the leverage ratio can significantly increase the credit spreads of long-term debt but has little impact on the short-term credit spreads since the change in the default boundary in the short term is negligible.
Fourthly, turning to Table 2, to the extent that the spread is a compensation for credit risk, it is not surprising that the sub-investment-grade firms are considered riskier by the market. Accordingly, the iTraxx Europe Crossover index gives the widest CDS index spread in the sample period which is consistent with theoretical and empirical results that the credit rating is the main determinant of the credit default swap spread. For example, the average credit rating for iTraxx Europe is A2/A2, while it is Ba3/B1 for iTraxx Europe Crossover. More detailed description about credit rating can be found in a later section. The standard deviations for each spread are quite close to each other, with a standard deviation about 219% on an annual basis and this deviation is much higher than that of a stock index.
When it comes to the distribution of daily log differences on iTraxx index and stock index we find that the distribution for a CDS index is much more skewed and leptokurtic than that of log differences on a stock index. This log difference on the iTraxx index is also at least two to three times more volatile compared to stock index return. The volatilities for CDS spreads range from 23.8% -42.7% on an annual basis, while in the case of stock index the volatility is around 12.6% on an annual basis. All these observations tend to indicate that the CDS market is reacting relatively more strongly to credit deteriorations than credit improvement in comparison to the stock market. With reference to the three iTraxx indices, the iTraxx Europe Crossover index has especially significant large positive skewness and kurtosis. This may indicate that the CDSs with lower previous grade react relatively more strongly to credit deteriorations than credit improvements as suggested by Norden & Weber (2004).
While adopting the framework of Schwartz and Smith (2000) to decompose the iTraxx index into the two components, that is the short-term and the long-term dynamics, we need to confirm the non-stationarity of the original iTraxx indices. In order to do that, we perform both the Augmented Dickey-Fuller test and the Phillips-Perron test for these series. For robustness, we try different model specifications and different lags. The results are quite similar and for simplicity, here we just list the results for the unit root test without trend and with four lags. The Unit Root test shows that all iTraxx indices are non-stationary at the 5% significance level while all daily log-difference on iTraxx indices are stationary.

Discussion on Explanatory Variables
Published literature, for example Ericsson et al (2005) and , has argued about the importance of several explanatory variables to determine the market wide movements of credit spreads. In the context of CDS spreads it is customary to use these variables to explain their variations. In this paper we also use those variables to analyse the components of CDS spreads. Specifically, the explanatory variables in this paper include credit ratings, the short-term interest rate, the slope of the yield curve, equity volatility and some measure of liquidity.
Credit Rating: The premium related to credit rating is a very important determinant of credit related securities including CDSs. In this paper, we use the difference between the iTraxx Europe Crossover index level and the iTraxx Europe index level to proxy the credit rating premia effect. We would expect it be more related to the short-term factor. As pointed out by Norden and Weber (2004) the abnormal performance in the CDS market is influenced by the level of the old rating, previous rating events and also the pre-event average rating level of all agencies. This means that the credit default swap spreads of the underlying entity with lower credit rating are more sensitive in the short-term. But of course it should have an impact on the long-term factor as well but the extent of this influence should not be as strong.
Credit ratings for sovereign and corporate bond issues have been produced by rating agencies such as Moody's and Standard and Poor's (S&P) for many years. In the case of Moody's the best rating is Aaa. Bonds with this rating are considered to have almost no chance of defaulting in the near future. The next best rating is Aa.
After that comes A, Baa, Ba, B and Caa. The S&P ratings corresponding to Moody's Aaa, Aa, A, Baa, Ba, B, and Caa are AAA, AA, A, BBB, BB, B, and CCC, respectively. To create finer rating categories Moody's divides its Aa category into Aa1, Aa2, and Aa3 and so on. Similarly S&P divides its AA category into AA+, AA, and AA-. Only the Moody's Aaa and S&P AAA categories are not subdivided.
Ratings above or on Baa3 (Moody's) and BBB-(S&P) are referred to as investment grade.
Since there is no credit rating assigned to the iTraxx index directly, the rating of iTraxx index in this paper is calculated as the average of the ratings of its component companies. Although each new series of iTraxx index is determined every 6 months and the entity name incorporated in each index may change over different series, the change in average credit ratings is thought to be trivial. So in this paper we calculate the average credit rating based on iTraxx Europe Series 7 membership list which can be found on the web site of International Index Company. The rating assessed for each issuer by Moody's and S&P are quite similar and we adopt the rating of Moody's if there is a rating provided; otherwise, we adopt the rating of S&P.
We use a numerical equivalent of the credit rating exhibited on Table 3. In Table 4 we provide the average credit rating for each of our three benchmark iTraxx indices. It is not surprising that the iTraxx Europe Crossover has the lowest credit rating with average Ba3/B1, while the iTraxx Europe has the highest credit rating corresponding to the lowest CDS spread. Figure 3 plots the credit rating premia for both 5-year maturity indices and 10year maturity indices, which is calculated as the logarithm of the level of the iTraxx Europe Crossover index minus the logarithm of the level of the corresponding iTraxx Europe index. The two curves are almost parallel, which on one hand confirms that the credit rating is a key determinant of a credit default swap spread as well as time to maturity. It also shows that the proxy for the credit ratings formed in this paper is quite reasonable.

Short Term Interest Rate:
It is widely argued that credit risk cannot be priced independently from market risk, especially interest rate risk (Jarrow & Yildirim (2002)). For example, Duffie and singleton (1999) assume that the intensity of default in reduced form models is a stochastic process that derives its randomness from a set of variables such as the short term interest rate. Several choices can be made for the short interest rate proxy. Ait-Sahalia (1996a, b) used seven-day Eurodollar rates and Stanton (1997) used threemonth Treasury bill rates, for example. Taking consideration of market region and data accessibility, we use the 3-month Euribor rate as the proxy for the short term interest rate. We obtained this data from Datastream. Daily observations are used and we apply the 3-month Euribor rate for the day prior to the credit default swap quote. Figure 4 plots these 3-month Euribor rates covering our sample period. A negative relationship between the level of the short term interest rate and the credit spread has been documented for several datasets; see for example Longstaff and Schwartz (1995 a, b) or Duffee (1998). Similarly, Abid and Naifar (2005) find the use of the risk-free interest rate as an explanatory variable increases the total adjusted 2 R and the variable risk-free interest rate is negatively correlated to the levels of credit default swap spreads. That is, an increase in the short term interest rate leads to a reduction in the spreads. Generally credit risk results from the default of punctual commitment represented by the principal and interest payments owed to a debt holder.
Therefore when we examine its influence on both the short-term and the long term factors, it is reasonable to hypothesize that the short term interest rate will have more influence on the short-term factor compared to the long-term factor.
Slope of the Yield Curve: The slope of yield curve, which can be interpreted as an indication of overall economic health, has the following predicted impact on CDS spreads. Theoretically, an increase in the slope of the yield curve should increase the expected future short term interest rate and as a result, a decrease in CDS spreads if the negative relationship between credit risk and the short term interest rate hold. The slope of the yield curve is measured as the difference between the long term interest rate and short term interest rate. Here we use the European 10-year government bond yield minus the European 2-year government bond yield. All these daily data are download form Datastream and as with the short term interest rate, we take the data for the day prior to the credit default swap quote and plot it in Figure 4. Figure 4 demonstrates two different patterns with the short term interest rate and the slope of yield curve. For the short term interest rate, it is more or less flat during the first 16 months of our sample period and then keeps increasing during the rest of the period while the slope of yield curve goes the other way, decreasing with time passing. When we take a detailed look at the slope of yield curve, we find that the decrease in the slope mainly results from the increasing short-term interest rate, which is the European 2-year government bond yield and the relatively flat long-term interest rate, which is European 10-year government bond yield, during the sample period.
Conflicting empirical results about the relationship between the slope of the

Volatility of Equity:
The volatility of equity is the main driver of credit risk in structural models. A recent paper by  find that the equity return volatility of reference entities can be a proxy for default risk. The volatility they used is estimated from a GARCH(1, 1) model. It is now commonplace to measure volatility in financial time series using GARCH models. These models are based on the notion that the innovations of a time series unconditionally have a fixed variance, but that volatility clustering occurs in the sense that the conditional variance of the process varies over time. The GARCH(1, 1) can be expressed as following: where t ε is the innovation in the levels and is the conditional variance on date . In order to estimate time-varying volatility from a GARCH(1, 1) model, we also need to choose a mean equation. In this paper, we adopt the following return specification in order to generate time varying volatility estimates of the equity market as a whole: This constant c is the mean of the series and t ε is the residual or the difference between the realised value and the mean. If there is autocorrelation and partial autocorrelation in these squared residual series 2 t ε , it is a signal that the variance is a predictable process. The statistic to be used here to test for autocorrelation and partial autocorrelation is the Ljung-Box Q-Statistic. Our Q-Statistic value is quite large which suggests the existence of autocorrelation and partial autocorrelation. When we regress 2 t ε on its k lagged values, the results suggest the presence of an ARCH effect.
Thus, it is very reasonable for us to use a GARCH(1, 1) model to estimate timevarying volatility.
In order to obtain robust results we test several other time series dynamics (ARMA) for the mean of the equity return data as well as different lag specifications for the GARCH variance part. Using the Akaike (AIC) and the Bayesian (BIC) information criteria we compare the alternative models. We finally choose a model that is as simple as possible given their comparable performance and focus on the constant mean and GARCH(1, 1) version. Intuitively, we expect this equity market volatility to be more related to the temporary component. Figure 5 plots the estimated time varying volatility over our sample period.
Bid-Ask Spread (Proxy for Liquidity): We use the bid-ask spread as a proxy variable for the liquidity factor. It has been widely suggested that financial securities subject to default risk also contain a premia for bearing illiquidity risk; see for example Driessen (2005) for liquidity factors in credit spreads, or Longstaff et al. (2005) for liquidity factors in credit default swaps.
Theoretically assets with more liquidity have lower credit spread. A higher bid-ask spread means low liquidity which would leads to a higher CDS spread.
For the liquidity proxy used in this paper we calculate the ask quote minus the bid quote and then take its natural logarithm for each iTraxx index with 5-year maturity as well as 10-year maturity. We plot these liquidity proxies in Figure 6.
Usually, bid-ask spreads of 10-year maturity contracts are higher than those of 5-year maturity contracts for the same iTraxx series. Among all these iTraxx indices, iTraxx Europe Crossover has highest bid-ask spread because of its sub-investment grade components. In our analysis, we would expect to find that the liquidity proxy is positively correlated with the iTraxx index level, especially with the transitory component in our paper.

Latent Two-Component Model for iTraxx Indices
Our previous Unit root test shows that all iTraxx indices of interest are non-stationary at the 5% significant level. Similar to Schwartz and Smith (2000) and Zhou and Qing (2000), we describe our natural logarithm iTraxx index as a linear combination of a temporary component and a persistent component. The temporary component is assumed to be stationary and the persistent component is represented by a nonstationary dynamic. We present our model for the dynamic behaviour of the natural logarithm of CDS spreads for two different maturities as follows: 10 t CDS , i t ε is the error term, which is assumed to have an independent identical distribution with mean 0 and variance 2 ,i ε σ 1, 2 i = ; The temporary component follows an Ornstein-Uhlenbeck process which is also known as a mean-reverting stochastic process. It is generally given by the following 1 X stochastic differential equation, where θ is the level to which 1,t X reverts: Settingθ in our case equal to 0 and integrating equation (6) Similarly we can transform equation (5) and get, If we express it in matrix form, then we get The parameter set is 2, The measurement equation (3) and the state dynamics (10) may be cast into State Space framework, and we get: , and as defined in equation (11). Q = Ω

State-Space Model and the Kalman Filter
State-space frameworks typically deal with dynamic time series models that involve unobserved components, and are becoming more widespread in applied econometric and financial applications. Compared with the multivariate regression models, the state-space model does not require an a priori specification of the predictive variables (Zhou & Qing (2000)). In the literature, considerable effort has been devoted to The Kalman filter recursive formulas for our model, as presented in Harvey (1989), are described by following set of equations: The log-likelihood function is given below:

Linear Regression Model for the Determinant of CDS Components
We use a regression technique to examine the possible relationships between the temporary component and persistent component extracted form the iTraxx indices and the potential drivers, namely, the short-term interest rate, the slope of the yield curve, equity volatility, liquidity (i.e., the bid-ask spread) and credit rating premia.
The specific regression model is as below, All these explanatory variables and their potential influences have been discussed in an intuitive manner in a previous section. In the next section we will discuss the model estimated parameters as well as the nature of the inferred components of the CDS series.

Empirical Results
In this section we provide the main results and analysis of these results.

Estimation Results for the Component Structure
The adaptive filtering algorithm due to Kalman allows us to estimate the unknown parameters of the model by maximising the log likelihood function identified earlier.
At the same time it produces optimal inference about the state variables. These filtered state variables are our extracted components consistent with the dynamic specification of the model. Europe is only marginal. The reason for this is that this series includes more of the firms that belong to higher credit rating categories.
The differences in the pattern of behaviour of the two components of the CDS spread series are quite instructive and without such decomposition it would be hard to get such in-depth understanding. Last but not the least; it is interesting to note that all the measurement error variances are quite small indicating the efficacy of the model. Figure 7 plots the two extracted components for each of the series against time.

Exploring the Determinants of the Components
In this section we analyse the explanatory power of several variables suggested in the literature for the components as well as for the original CDS spread series itself. This helps us understand the differences in the impact these variables have as well as reconcile some of the conflicting results reported in the literature where such a component approach is not implemented. This analysis is carried out in a linear regression framework consistent with the reported studies in this area. In some cases we may have non-stationary series on both sides of the regression equation, but it does not necessarily make the results spurious. As long as the regression residuals are stationary the usual implications of t-and F-tests and Rsquares are applicable (see Gujarati (2004), page 822-824). β , 4 β and 5 β in the iTraxx Europe and the iTraxx Europe Hivol data. However, it is not so obvious in the iTraxx Europe Crossover case. We will take up this point again later.
Most of our results (from Table 6) are consistent with those published in related studies. For example, let us examine the negative relationship between CDS and the short-term interest rate. As we would expect, the short-term interest rate has more impact on the transient component. The result also supports the proposition that the CDS spread is positive correlated with equity market volatility. Again, the corresponding coefficient of equity volatility confirms our hypothesis that this has more influence on the transient component. All the coefficients for the short-term interest rate and equity market volatility are statistically significant at the 1% level of significance.
Our results also suggest that illiquidity may cause higher CDS spread levels which is indicated by a positive coefficient for the liquidity proxy 4 β . But when we compare the extent of its impact on the two components, we find that it has more influence on the persistent component implying that the influence of illiquidity is quite persistent. However, for sub-investment grade firms, the influence of this factor does not vary much between the transient and the persistent components. This indicates that the CDSs whose underlying firms have lower credit ratings are not affected as strongly by its market liquidity as other influential elements. This result can also be verified by comparing the robust R-square for the regression model without a liquidity proxy. After omitting the liquidity proxy from the model for the transient component of iTraxx Europe Crossover, the adjusted R-square only decreases by 0.0016 to 0.7235. But when we omit the other variables, for example, the proxy of credit premia, the adjusted R-square sharply decreases by 0.2378 to 0.4973.
We have not presented these results in the tables to conserve space, but they are available on request.
Another set of interesting parameters to examine are 2 β and 5 β , the coefficients for the slope of the yield curve and the credit rating premia, respectively. The credit rating premium is another explanatory variable developed in this paper in order to capture the influence of credit rating. The positive coefficient is quite intuitive. This relationship does not appear to be significant for iTraxx Europe 10Y and iTraxx Hivol Europe 10Y. But when we look back to Figure 3, we find that the credit rating premia for 10 year maturity contracts are much lower than the credit rating premia for 5 year maturity contracts. As we would expect the importance of credit rating premia (captured by the parameter 5 β ) increases as more lower credit rated entities are included in the series and in particular for the transient components.
Next let's turn to the explanatory variable spread as well as the Table 7. In this table, we list the estimated results for regression models just omitting the credit rating premia. Most parameter estimates are statistically significant under 1% significant level. The important information that can be gleaned from Table 7 is that it confirms that credit rating premia are more of concern for the transient component, especially with lower credit rating entities in the CDS index. For example, there is not much deterioration in R-square in case of any of the persistent components. But for iTraxx Crossover the R-square drops from 73.69% (Table 6) to 49.99% (Table 7) for the transient component.
The results clearly show that the robust R-square without credit rating premia (Table 7) does not change much for both the transient and the persistent components of iTraxx Europe. But they do change for the other two iTraxx indices and especially for iTraxx Europe Crossover which is the index with lowest credit rating. So this result confirms the argument that we earlier put forward that for CDS spreads with higher credit rating underlying entities, credit rating has only marginal difference in impact for the two components. While for CDS spreads with lower credit rating underlying entities, the credit rating impact differs depending on the components.

Conclusion
Credit risk analysis is important for valuing corporate bonds, swaps and credit derivatives and plays a critical role in managing the credit risk of bank loan portfolios.
Generally it is argued that credit derivatives (especially credit default swaps) are a much better proxy for credit risk since the majority of fundamental variables predicted by credit risk pricing theories have a significant influence on credit default swap prices.
The ideas put forward in this paper are quite innovative can provide some hints for later research on the credit derivatives market and the estimated results in this paper are consistent. Firstly, we extract information from the original data using the latent two-factor model used in Schwartz and Smith (2000) and       We use Stata command "regress, robust" and the robust standard error is proved in parentheses below each estimator and robust R 2 is provided as well.
2. 1%, 5% and 10% significance levels are indicated by *** , ** , and * , respectively. Table 7 Estimation results for regression model We use Stata command "regress, robust" and the robust standard error is proved in parentheses below each estimator and robust R 2 is provided as well.