Liquidity in Credit Default Swap Markets

Armen Arakelyan

JOB MARKET PAPER

and

Pedro Serranoa

January 10, 2012

Abstract

We explore the relationship between Credit Default Swap (CDS) spreads and CDS liquidity supply.

We proxy the liquidity of a CDS name by the number of contributors and bid-ask spreads. We characterize

this relationship in two ways: first, we perform a panel data analysis to explore the link between our

liquidity proxies and plain CDS spreads. Second, we develop an alternative GMM approach to Pan and

Singleton (2008) to quantify the CDS default risk premium, examining its relationship with our liquidity

measures. Our results indicate that bid-ask spreads are an important factor in explaining illiquidity of

both CDS spreads and CDS implied risk premiums. The evidence on the usefulness of the number of

contributors as a measure of liquidity is weak.

JEL Classification: G01, G12, G32.

Key Words: Credit Risk, Liquidity, Risk Premia.

aA. Arakelyan and P. Serrano are from Department of Business Administration, Universidad Carlos III de Madrid, c/Madrid,126, 28903 Getafe (Madrid), Spain. Phone: (34)91 624 89 26. Fax: (34)91 624 96. We thank José Penalva, Garen Markarian,Maxim Mironov, Juan Pedro Gómez, Paolo Porchia, Artashes Karapetyan, Bogdan Stacescu for useful comments, as well as seminarparticipants at BI Norwegian Business School (2011) and UC3M (2011). P. Serrano gratefully acknowledges financial support bygrants ECO2008-03058 and P08-SEJ-03917 and CAM CCG10-UC3M/HUM-5237. Corresponding author is A. Arakelyan (e-mail:aarakely@uc3m.es).

1 Introduction

Credit Default Swap (CDS) contracts allow to trade on and transfer the credit risk of a company. Traditionally,

CDS spreads represent the fair insurance price for the credit risk of a company. Because of their contractual

nature, CDS contracts are less influenced by convenience or liquidity factors than bond assets (Longstaff et al.

(2005)). However, recent empirical evidence suggests that CDS spreads may not be fully explained by credit

risk factors related to the underlying company (Collin-Dufresne et al. (2001), Blanco et al. (2005), Tang and

Yan (2010) or Fulop and Lescourret (2007), among others). Additionally, the soaring CDS spreads during the

recent financial crisis raise the question of whether CDS prices are affected by factors other than default risk.

Given the central role of CDS markets nowadays on assessing the crediworthiness of firms and institutions

and their ability to lead other markets (see Blanco et al., 2005; Forte and Peña, 2009), this question is of

paramount importance.

We hypothesize that liquidity is an important element in CDS markets. Firstly, liquidity can be a sig-

nificant factor in CDS markets due to the OTC nature of CDS markets. There is no central organized place

or exchange where trading orders are matched. Instead, a CDS market operates through a decentralized and

opaque dealer network. As a consequence, costs of search and other friction can be comparatively higher

relative to other markets, resulting in lower liquidity in OTC derivative markets (Duffie et al. (2007)).

Other factors such as information asymmetries suggest that liquidity plays an important role in CDS

markets. For instance, Acharya and Johnson (2007) find evidence of insider trading in credit derivatives

markets. They hypothesize that many banks and financial institutions trade CDSs of companies for whom

they provide financing. This may be because CDSs allow them to exploit private information about their

clients which is not available to the public. As a result, the asymmetry of information can lead to reduced

liquidity (see, for instance, Easley et al. (1996), Brockman and Chung (2003)). As pointed out by Acharya

and Johnson (2007), credit derivative markets may be especially vulnerable to asymmetric information and

insider trading problems because most of the players in CDS markets are insiders.

Finally, the CDS market is an opaque market controlled by a small number of financial institutions.1 This

fact has important implications for liquidity as small markets are likely to be less competitive, and hence

less liquid. The reason for the small number of market players and low liquidity may be the high cost of

1See "EU hits banks with credit default swap probe", Reuters, April 29, 2011

2

entry into CDS markets. As of the second half of 2010, the CDS market constituted approximately 5% of

the OTC derivatives market in terms of the notional amount outstanding. In nominal terms, the total amount

outstanding of CDS market was 29,898 billion US dollars as opposed to 601,048 billion US dollars of the

overall OTC derivatives market. 2

This article analyzes empirically the relationship between CDS spreads and liquidity. We proxy liquidity

by the number of contributors (NOC) providing quotes and bid-ask spreads. We develop our analysis in two

parts. First, we construct two measures of liquidty and use them in panel data analysis in order to capture

the relationship between changes in plain CDS spreads and changes in our liquidity measures. Second, we

analyse the effect of liquidity on the risk premium component of CDS spreads. To do this we first apply

the methodology of Pan and Singleton (2008) and Longstaff et al. (2008) to disentangle how much of the

CDS spreads are due to pure effects of default and to risk premium compensation. Within the framework of

Duffie and Singleton (1999) or Jarrow et al. (2005), we focus on the compensation demanded by protection

sellers for changes in the default risk environment, or distress risk premium, as opposed to the default event

premia, which embodies the reward for changes in the bond price in the event of default (See Driessen (2005)

or Berndt et al. (2005)). Our methodology extend that of Pan and Singleton (2008) by employing a GMM

technique. We then study the possible effects of liquidity on the risk premium component of CDS spreads

obtained from the previous analysis.

Our empirical analysis is based on a comprehensive sample of CDS spreads for 143 US firms taken

from Markit. Our dataset consists of a diversified sample of CDS names across different rating categories

and sectors for a time period that spans from January 2001 to December 2009, covering the recent financial

crisis period. Moreover, there is also at our disposal extensive information about bid-ask spreads and default

probabilities from CMA Datastream and Moody’s, respectively.

Our results show that the size of bid-ask spreads is strongly related to the level of plain CDS spreads.

More specifically, changes in bid-ask spreads are significant determinant for changes in plain CDS spreads

before and after August 2007. The number of contributors has a positive and significant effect on changes in

CDS spreads only before August 2007. However, the positive sign is puzzling.

Our results are obtained using a mean-reverting (CIR) structure for the instantaneous arrival rate of a credit

event λ Q. Our results suggest that one factor models are flexible enough to capture the term structure of CDS

2See BIS(2011) May report

3

spreads. Moreover, the GMM model estimates reveal considerable differences in the parameters governing

the dynamics of the default intensity under risk neutral (Q) and physical (P) measures. In particular, we find

strong divergences in mean-reversion rates under actual and risk-neutral measures, suggesting a worsening

in the risk-neutral environment through time. Pan and Singleton (2008) find similar results in a sample of

sovereign CDS sample, and interprete this as an evidence that an important fraction of systematic risk is being

priced in the market via distress premium. How much of this gain in risk premium is due to liquidity factors

is a matter of interest in our study.

Our analysis of risk premia reveals that protection sellers ask for higher premia as the environment be-

comes more illiquid. In particular, changes in bid-ask spreads are associated with higher risk premia after

August 2007, which might suggest that protection sellers ask for a higher premium for providing credit pro-

tection during the recent period of financial crises. Note however that this interpretation is not valid for our

both measures of liquidty. In particular, changes in the number of contributors seems not to be a significant

factor for changes in risk premia.

Liquidity in credit markets is a subject of active research. From a theoretical perspective, the problem

of frictions in OTC markets has been studied in Lagos et al. (2011) and Brunnermeier and Pedersen (2009).

Empirically, Ericsson and Renault (2006), Bao et al. (2011) and Lin et al. (2011) have analyzed liquidity

concerns in corporate bond markets. The studies of Tang and Yan (2007) and Bongaerts et al. (2011) focus

on the CDS market. This article mainly continues and extends Tang and Yan (2007), who also explore the

interaction between liquidity and CDS spreads. Our paper differs from Tang and Yan (2007) by providing

a model that quantifies the risk premium inherent in CDS prices. Additionally, we employ a more recent

sample period which includes the recent financial crisis.

Literature on default premia and their link with liquidity factors is scarce. Some standard references

on analyzing the risk premium in the corporate bond markets are the works of Duffee (1999) and Driessen

(2005). Berndt et al. (2005) and Longstaff et al. (2005) employ corporate CDS spreads in order to extract

information about risk premia. Our approach is mainly inspired by Pan and Singleton (2008) and Longstaff

et al. (2008), who extract the risk premia from sovereign CDS spreads. By contrast, the empirical studies

about the link between default risk and liquidity remains scarce. This article is pioneer in quantifying the risk

premium in CDS due to liquidity related components.

4

To summarize, this article analyzes the impact of CDS liquidity supply on both plain CDS spreads and the

risk premia embedded in them. The remainder of the article is structured as follows: Section 2 overviews the

CDS market and presents our dataset. Section 3 discusses the liquidity variables and their relationship with

CDS spreads. Sections 4 introduces the modelling framework. Estimation methodology and risk premium

results are included in Section 5. Section 6 provides some robustness checks for our modelling choice.

Finally, some conclusions are drawn in Section 7.

2 The CDS Market

In this section we describe the structure of CDS markets, characterizing the general features of a CDS con-

tract. In addition, we summarize the main characteristics of our sample of data.

2.1 The structure of the market

The CDS market was one of the fastest growing OTC derivative markets before the financial crisis. In terms

of notional amount outstanding CDS market size was 6,396 billion US dollars by the end of December

2004, 13,908 by the end of December 2005, 28,838 by the end of December 2006 and 57,894 by the end of

December 2007. After the financial crisis the CDS market size dropped considerably down to 29,898 billion

US dollars by the end of December 2010 (BIS, 2011).

Credit derivative (CD) contracts can be classified into single- and multi-name contracts. On average,

single name CDS contracts accounted for 60 percent of the overall CD market for the second half of 2010

as opposed to 40 percent share of multi-name CD contracts, such as Basket Default Swaps, Index products,

Tranched Index products, CDOs etc. Out of the 60 percent share of single name CDS contracts (18,145 billion

US dollars in nominal amounts), corporate (non-sovereign) single name CDS contracts accounted for 86% of

the overall single name CDS market. In terms of maturity, single name CDS contracts with maturity ranging

from 1 to 5 years accounted for the 70% of the single name CDS market share. In terms of ratings, investment

grade single name CDS contracts (AAA-BBB) accounted for 70% of the single name CDS market.

In terms of the composition of market participants for the second half of 2010, reporting dealers (commercial

and investment banks, securities houses) accounted for 54.5% of the single name CDS market involvement,

while other financial and non-financial institutions accounted for the 44.5 and 1 percent, respectively. In-

5

vestors in financial industries seem to be the key players in CDS markets.

2.2 Description of a CDS

A Credit Default Swap (CDS) is a derivative contract that hedges the credit risk of the underlying company

that it references (also know as reference entity). It is an agreement between two parties, where one party

(protection buyer) agrees to make periodic payments to the other party (protection seller) until the contract

maturity or some predefined credit events, whichever occurs first. CDS spreads are quoted in basis points

per annum of the total notional amount. The frequency of spread payments for corporate CDS names is

mostly quarterly. In case the credit event occurs before CDS maturity, and assuming physical settlement, the

protection buyer delivers the defaulted bonds to the protection seller and receives the face value of the contract

principal. In case of cash settlement, the protection seller compensates the protection buyer by paying the

difference between the notional amount of the CDS contract and the market value of the distressed bonds for

the same notional amount. Physical delivery is the dominant type of settlement in the CDS market.

The credit events that trigger payments are specified in the CDS contract. The International Swaps and

Derivatives Association (ISDA) defines several types of credit events, which generally include bankruptcy,

failure to pay and restructuring.3 Currently, there are four types of restructuring defined by ISDA: full re-

structuring (FR - any restructuring constitutes a credit event, and any bond of maturity up to 30 years is

deliverable), modified restructuring (MR - restructuring counts as a credit event, and any bond of maturity 30

months or less is deliverable after the termination date of the CDS contract), modified-modified restructuring

(MM - any bond of maturity shorter than 60 months for restructured obligations and 30 months for all other

obligations is deliverable), and no restructuring (NR - no restructuring events constitute a credit event). In

North America the type of restructuring that is most commonly used to define what constitutes a credit event,

is the MR, while in Europe it is the MM. Most frequently quoted and traded CDS contracts are the ones with

1-, 3-, 5- , 7- and 10-year maturities. The typical notional amount of a CDS contract is $5-10 million for high

grade credit names, and $2-5 millions for high yield names.

To analyze pricing, let us consider a CDS contract with maturity M and annualized premium payment

CDS(M). Additionally, assume the premium payments are made quarterly. Then, the breakeven CDS spread

3The restructuring has been a major source of controversy among the CDS market participants. The reason is that restructuringof debt may not constitute a loss for the protection buyers. See O’Kane et al. (2003).

6

with M year maturity for day t solves the following equation,

CDSQt (M) =

4LQ ∫ t+Mt EQ

t

[λQ

u e−∫ u

t (rs+λQs )ds

]du

∑4Mi=1 EQ

t

[e−

∫ t+.25it (rs+λ

Qs )ds

] , (1)

where rt denotes the risk-free rate, λQt is the intensity of the Poisson process governing default, and LQ

t is

the Loss Given Default (LGD) of the referenced bond under the Q measure. The dynamics of λQt process is

discussed in Section 4.

The numerator in equation (1) represents the default payments made by the protection seller to the pro-

tection buyer in case of default, while the denominator multiplied by the CDS spread is the quantity paid by

the protection buyer to protection seller on a quarterly basis. Without loss of generality, the notional amount

of the CDS contract is normalized to one. This implies that the LDG is 1−R, where R is the recovery rate

of the underlying bond in case of default. Expression (1) is similar to those employed in Pan and Singleton

(2008) and Longstaff et al. (2008).

Throughout the paper we assume that the risk-free rate and the default intensity processes are independent

from each other. Additionally, we use constant recovery rates that are the same under both real and risk-

neutral probability measures. Both assumptions are common in the credit risk literature.

2.3 CDS Data

Our CDS data is obtained from Markit. Our sample comprises daily quotes of a set of North American CDS

names that are or have been part of the CDX index. More specifically, we have the CDS spread term structure

with 1-, 3-, 5-, 7-, and 10-year maturities for each of the CDS names. We only consider contracts that are

denominated in USD with the modified restructured clause. For our empirical analysis, we use the monthly

data on CDS spreads by taking the last non-missing spread of a given month. We also exclude the CDS

names that have less than 70 monthly observations. Hence, there are at least 6 years of monthly data available

for each CDS name. Overall we have 143 CDS names within the sample time span from January 2001 to

December 2009. Our final sample is composed of 14327 monthly observations.

Table 2 describes the distribution of CDS names by sector and rating. Around 72% of our CDS sample

are investment grade with AA, A and BBB ratings. The most commanly represented industries are Consumer

7

Services and Industrials which represent around 24% and 19% of the sample, respectively. The financial

sector comprises around 13% of companies, so does the Consumer Goods industry.

[INSERT TABLE 2 ABOUT HERE]

Figure 1 depicts the time series of CDS spreads averaged within each rating group. Vertical lines indicate

two key recent events. The first line is in August 2007, when BNP Paribas suspended funds because of

subprime problems. The second line indicates the Lehman Brothers collapse in September 2008. Figure 1

shows that investment grade companies have lower spreads on average and are less volatile relative to non-

investment grade ones. It also reveals two noticeable peaks in the time series of CDS spreads: the first one

is attributed to the bankruptcy of WorldCom in July 2002, a highly volatile period in the credit markets.

The other peak corresponds to the period from August 2007 and upwards, and is associated with the recent

financial crisis.

[INSERT FIGURE 1 ABOUT HERE]

Table 3 provides summary statistics of our CDS spreads. The average spread increases both across ratings

and maturities for the overall sample. Similar results apply to the median spread.

[INSERT TABLE 3 ABOUT HERE]

To examine the commonality in CDS spreads we carry out a principal component analysis (PCA). More

specifically, we compute the first two principal components of each CDS term structure. Table 4 displays the

percentiles of aggregate results both in levels and first differences. Table 4 shows that on average the first

PC explains about 96% (92%) of the variation of a CDS term structure in levels (differences). These results

suggest a strong pattern of commonality in each individual CDS term structure.

[INSERT TABLE 4 ABOUT HERE]

3 The Liquidity of CDS spreads

This section describes the liquidity proxies employed throughout the article. Then, we run some panel data

regressions to analyze the relationship between our liquidity proxies and CDS spreads.

8

3.1 Liquidity Proxies

CDS liquidity can be broadly defined as the ease with which one can initiate or unwind a CDS position at a fair

price. Each CDS trade has certain costs associated with it, such as search costs, broker/dealer commissions,

and asymmetry of information costs. The higher these costs, the higher the illiquidity of the corresponding

CDS contract.

We consider the number of contributors (NOC) and bid-ask spreads as our two proxies for CDS liquidity.

The NOC variable is the number of licensed market makers that submit to Markit the 5-year CDS quotes. As

market makers are liquidity providers in financial markets, their concentration can reflect the degree of com-

petitiveness in CDS markets. Less competitive markets can lead to reduced liquidity provision. Hence, with

this measure we intend to capture the aspect of liquidity that is associated with the size and competitiveness

of CDS markets.

For each CDS name we compute the average number of market makers in a month as our proxy for

liquidity associated with NOC. A positive change in NOC is interpreted as a sign of growing interest by

market participants in buying or selling credit protection for a particular CDS. Consequently, positive changes

in NOC can be attributed to increased liquidity in CDS markets, which should be associated with a drop in

the price for credit protection. In this context, we expect to find a negative relationship between changes in

NOC and changes in CDS spreads. Data on NOC has also been obtained from Markit.

Bid-ask spreads are one of the most widely used measure of liquidity in finance. According to the lit-

erature, bid-ask spreads reflect order processing, inventory holding and information asymmetry costs (see

Venkatesh and Chiang (1986), Stoll (1989) or Krinsky and Lee (1996), among others). We construct the

bid-ask measure of liquidity for CDS spreads on a monthly basis. More specifically, we do it by averaging

the daily bid-ask spreads over a month. As liquidity dries up, the size of bid-ask spread increases. Hence, we

expect a positive relationship between changes in CDS spreads and changes in the bid-ask spread.

Our sample of bid-ask spreads is composed of daily spreads for 5-year maturity CDS names and its taken

from CMA Datastream. The data on bid-ask spreads is available from January 1, 2004. When transforming

the data to a monthly frequency, there are at most 72 observations available for each CDS name.

Figure 2 and 3 display the time series of our liquidity proxies averaged within each rating group. The

graph for number of contributors shows that the NOC variable does not vary much across ratings. Only

9

NOC in rating category B seems to be lower compared to the rest. Additionally, the graph reveals that NOC

increased from 2001 till the beginning of 2006. Since then, NOC started decreasing.

As for the graph of bid-ask spreads, we can observe that the higher the rating, the thinner the bid-ask

spread. Bid-ask spreads remained relatively flat until mid 2007, increasing considerably afterwards.

[INSERT FIGURE 2 and 3 ABOUT HERE]

Tables 5 and 6 provide summary statistics for the two liquidity measures, respectively. Table 5 shows that

the average NOC over the entire sample is approximately 10. Moreover, there are at least two contributors

providing quotes. Table 6 shows that the average bid-ask spread for 5-year maturity is 10 basis points over

the entire sample. It is lower than the bid-ask spreads of other maturities for the overall sample. The same

pattern applies to other rating groups. This could reflect the fact that 5-year CDS contracts are the most traded

contracts. Hence, they have the narrowest bid-ask spread compared to CDS spreads with other maturities.

[INSERT TABLE 5 and 6 ABOUT HERE]

3.2 Control Variables

In addition to the liquidity proxies described above, we control for factors that can be related to the credit risk

of CDS names. We follow Collin-Dufresne et al. (2001) and consider the following variables that can drive

the default probabilities of underlying CDS companies:

1. Changes in the spot interest rate. A higher spot rate can increase the risk neutral drift of the firm value

process. A higher drift reduces the probability of default, hence should reduce credit spreads or CDS spreads.

As a proxy for the spot interest rate we use the 10-year yields (end of month) on US Treasury bonds. The

data on spot interest rates in downloaded from Datastream.

2. Changes in the slope of the yield curve. Though the spot rate is the only interest rate relevant for firm value

process in structural models, the spot rate can itself depend on other factors, such as the slope of its term

structure. The slope of the interest rate term structure is constructed by taking the difference between 10 year

and 2 year bond yields (end of month) on US Treasury bonds. The data in downloaded from Datastream.

3. Changes in equity prices. In structural default models, default happens when the leverage ratio gets close

to one. To construct the leverage ratio, data on a firm’s debt value is needed. We have access to book debt

10

value in Compustat with quarterly frequency whereas the frequency of our CDS spreads in monthly. Previous

empirical research has often considered changes in the firm’s equity return as a proxy for the financial health

of a company. Hence, instead of changes in the leverage ratio, we use equity returns of a CDS reference

entity. We use the data on monthly equity returns downloaded from CRSP.

4. Volatility. We do not have access to the implied equity volatility of a CDS reference entities. To capture

the changes in market wide volatility, we use the changes in the VIX index.

5. Overall business climate. As a proxy for the overall state of the economy we use the monthly return on the

S&P500 index.

Besides the variables considered above, we include KMV’s expected default frequency (EDF) with one year

maturity as another control variable for CDS default probabilities. Note, that EDF is a measure of the proba-

bility that a firm will default over a specified period of time. It is also a measure of real probability of default.

For that reason, EDF data can serve as a base for backing out the default event risk premium embedded in

excess bond yields or CDS spreads (Jarrow et al. (2005)). EDF data has been previously employed in Berndt

et al. (2005) and Bharath and Shumway (2008).

3.3 Panel Data analysis

To assess the relationship between our two liquidity proxies and CDS spreads, we estimate the following

panel data model,

∆CDS5i,t = α +φ ·∆CDS5

i,t−1 +∑j

β j ·∆Liquidityi,t− j +∑k

γk ·∆Controlk,t + εi,t . (2)

Liquidityi,t is the vector of liquidity measures including the number of contributors and bid-ask spreads.

Controli,t is the vector of control variables introduced in subsection 3.2. We estimate the model by OLS

controlling for rating-, sector-, month- and company fixed effects. The robust standard errors are adjusted for

issuer-clustering. We do the estimation for two periods: before and after August 2007.

The results of the estimation for the two periods are provided in Table 7. The results reveal that changes

in bid-ask spreads are a significant determinant for changes in 5-year CDS spreads. These results hold both

for the period before and after August 2007. When the bid-ask spread variable is added to the panel data

regression, the R squared statistics increases from 24 to 32 percent before August 2007, and from 24 to 36

11

% after August 2007. The sign of the coefficient on bid-ask spreads is positive. In other words, growing

illiquidity increases CDS prices.

Changes in NOC is a significant factor for changes in CDS spreads before August 2007. Contrary to our

conjecture, the sign of NOC is positive. When both NOC and bid-ask spreads are included in the regression,

they are both significant for the time period before August 2007. For the time period after August 2007,

only the bid-ask spread is positively and significantly related to changes in CDS spreads. The NOC has the

expected negative sign, but it is not significant.

From the control variables, company specific variables (i.e. Moody’s EDF and individual company equity

returns) are significant with the right sign for both time periods.

[INSERT TABLE 7 ABOUT HERE]

In conclusion, the results of the panel data analysis indicate that the coefficient of the measure of bid-ask

spreads is statistically significant for the time periods before and after August 2007, while the coefficient of

NOC is positive and significant for changes in CDS spreads only before August 2007.

4 Components of CDS spreads

In this section we use the methodology of Pan and Singleton (2008) and Longstaff et al. (2008) in order to

decompose CDS spreads into a default risk and a risk premium component. We also provide details on the

risk premium component we estimate, emphasizing its relationship with liquidity factors.

4.1 Default Intensity of CDS spreads

The intensity modelling framework has it roots in Duffie and Singleton (1999) and Lando (1998). Within this

methodology, the default event is specified as the first jump of a Poisson process, where the intensity of the

process evolves stochastically in time. The survival probability p of a firm is given by

p(t,T ) = E[e−

∫ Tt λsds

], (3)

where λ is the stochastic intensity of the Poisson process.

This formulation permits us to compute the expectations in equation (1) using the same machinery as that of

12

the risk-free term structure models (Duffie et al. (2000)).

Since default and liquidity are not easily discernible events, we hypothesize that the intensity process

accounts for both default and liquidity factors, as in Longstaff (2011). Thus, the dynamics of the de-

fault/liquidity process λQt under the physical measure P is given as a CIR process,

dλQt = κ

P(θ P−λQt )dt +σ

√λ

Qt dW P

t , (4)

where κP and θ P are the mean-reversion speed and long-run mean, respectively, and σ accounts for the

volatility of the process. This CIR process allows for both mean reversion and conditional heteroskedasticity

of CDS spreads, and ensures the positiveness of the default intensity. This specification has been previously

employed by Duffee (1999) or Longstaff et al. (2005). Moreover, under the CIR specification, the expecta-

tions can be calculated in closed form (Duffie et al. (2000)).

For the purpose of CDS pricing, we need to specify the process (4) under the risk neutral measure Q. The

change of measure from P to Q implies that

dλQt = κ

Q(

θQ−λ

Qt

)dt +σ

√λ

Qt dW Q

t , (5)

where κQ = κP + δ0σ and κPθ P = κQθ Q. Additionally, δ0 is the parameter governing the market price of

risk η , where

dW Q = ηdt +dW P

= δ0√

λ Qdt +dW P.

On the one hand, the market price of risk allows the mean reversion rate of λ Q to be different under the

P and Q measures. On the other hand, the dynamics of the default intensity is the same under both measures.

Finally, note that we specify the risk neutral default intensity process λ Q under two different measures. The

default intensity under the historical measure λ P does not play any role in our analysis.

13

4.2 Risk premium

Jarrow et al. (2005) provides the basic results on risk premium under an intensity framework. Within this

context, two types of compensation can be differentiated: first, the compensation for changes in the default

environment (changes in liquidity supply, changes in monetary policy, etc.), or distress premium (see Pan and

Singleton (2008) or Longstaff et al. (2008)). Second, the compensation for default itself, named default event

(Yu (2002)) or jump-to-event premium (Pan and Singleton (2006)). The jump-to-event premium measures

a certain distance between actual and risk-neutral default probabilities, and it has been analyzed in Pan and

Singleton (2006) or Berndt et al. (2005).

We focus on the distress risk premium, as Pan and Singleton (2008) and Longstaff et al. (2008) do for

sovereign CDS markets. To quantify the risk premium embedded in CDS spreads, we first compute CDS

spreads using the risk neutral parameter values of λ Q by means of equation (1) and (5). By restricting the

parameter of the market price of risk to be zero (δ = 0), we are able to calculate the CDS spreads under the

physical measure,

CDSPt (M) =

4LQ ∫ t+Mt EP

t

[λQ

u e−∫ u

t (rs+λQs )ds

]du

∑4Mi=1 EP

t

[e−

∫ t+.25it (rs+λ

Qs )ds

] , (6)

where the default intensity is given by (4).

Note that if the market price of risk ηt is zero, then the risk neutral and objective intensity of λ Q will

be the same. This then implies that CDSQ = CDSP. However, if ηt is not zero, the parameters of the λ Q

process under both measures will be different. Hence, CDS spreads calculated under P and Q measures

will be different. By subtracting CDSP from CDSQ we obtain an estimate of the distress default premium.

Sometimes this premium is also known as the market price of risk, which we will denote by RP.

5 Estimation procedure

This section describes the estimation methodology, presenting some results. We also explore the relationship

between our liquidity proxies and the distress risk premium.

14

5.1 Econometric Framework

Pan and Singleton (2008) and Longstaff et al. (2008) specify the arrival rate of default as a log Ornstein-

Uhlenbeck (OU) process, and estimate the parameters of the process via Maximum Likelihood. This tech-

nique has been also employed in Duffie and Singleton (1997) and Duffie et al. (2003) with CIR-type models.

We propose an alternative estimation strategy using the Generalized Method of Moments (GMM). This ap-

proach permit us to work with an ample variety of models by using a simple discretization of the default

process. This strategy follows the work by Chan et al. (1992) on interest rates.

For ease of notation, we denote λ Q as λ . To be able to identify the λ process and the parameters governing

it, we need a term structure of CDS spreads for each name. Thus, we employ the CDS spread term structure

using 1y-, 3y-, 5y- 7y- and 10y- maturities. We assume that the 5 year CDS contracts are priced perfectly

so that the theoretical pricing function (1) can be inverted to get the time series for λ ’s. Additionally, we

also assume that the 1-, 3-, 7- and 10-year CDS contracts are priced with error, denoted by εt(M), that are

normally distributed with zero means and standard deviations σε(M) and M = 1,3,7,10. For simplicity,

εt(M) will be assumed to be uncorrelated across maturity, and not autocorrelated individually. Finally, we

impose a constant risk-free term structure similarly to Pan and Singleton (2008), since they argue that CDS

spreads are not highly sensitive to the level of interest rates.

To explain our procedure, let CDSt(5) denote the observed time series of 5-year CDS spreads assumed to

be observed without error at time t for a given company. Additionally, let CDSt(1), CDSt(3), CDSt(7) and

CDSt(10) denote the remaining four observed CDS spreads with 1-, 3-, 7- and 10-year maturity, respectively.

As a first step, we extract the λt time series from the 5-year CDS spreads

CDSt(5) = f (λt ;κQ,θ Q,σ) (7)

λt = f−1(CDSt(5);κQ,θ Q,σ). (8)

Given λt and the (κP,θ P,σ) parameters under the objective measure, the Euler discretization of λt process

15

of expression (4) yields,

λt+1−λt = κP(θ P−λt)∆t + εt+1 (9)

E [εt+1] = 0, E[ε2

t+1]= σ2λt∆t. (10)

with ∆t = ti− ti−1 equal to 1/12 because of the monthly frequency of our data.

As a second step, we calculate differences between the observed values of CDS spreads and the values

implied by the model for the remaining CDS maturities. If we denote the pricing error by εt(M) then,

εt(M) = CDSt(M)−CDSQt (M), M = 1,3,7,10 (11)

CDSQt (M) = f (λt ;κ

Q,θ Q,σ). (12)

where CDSt(M) is the market observed CDS spread with M year maturity, and the model implied spread

CDSQt (M) is calculated using equation (1) for a given set of (κQ,θ Q,σ) parameters and the implied values of

λt from the first step. According to the assumptions we made earlier,

εt(M) ∼ iid N(0,σ2

ε (M)), M = 1,3,7,10. (13)

The final step consists of finding the parameters of the model using GMM estimation. This approach

finds the parameters that match the population moments with their sample counterparts. The parameter space

of the model is Θ = (κQ,κQθ Q,κP,σ ,σε(1),σε(3),σε(7),σε(10)). Letting ft(Θ) be the vector that matches

sample and population moments,

ft(Θ) =

εt+1

εt+1λt

ε2t+1−σ2λt∆t(

ε2t+1−σ2λt∆t

)λt

εt(M)

ε2t (M)−σ2

ε (M)

(14)

16

where, under the previous specifications, E[ ft(Θ)] = 0. The sample counterpart of the latter equation is:

g(Θ) =1T

T

∑t=1

ft(Θ). (15)

The matching is done by minimizing the following quadratic form

JT = minΘ

[g(Θ)]′WT [g(Θ)] , (16)

where g(Θ) is a vector that contains both the set of moments and the unknown parameter vector θ which we

are optimizing over. WT is the weighting matrix and it is defined as WT = S−1

S =1T

T

∑t=1

[ft(Θ) f ′t (Θ)

].

The minimum value of the quadratic form given by (16) provides a goodness-of-fit test for the model.

Under the null hypothesis that the model is true, Hansen (1982) shows that T JT statistics follows a χ2p dis-

tribution, where p is the difference between the number of orthogonality conditions and the number of pa-

rameters to be estimated. Statistical significance of the parameters can be assessed based on the asymptotic

covariance matrix of the GMM estimate of Θ, which is given by:

S =1T

(D′(Θ)W−1(Θ)D(Θ)

)−1.

D(Θ) is the Jacobian matrix of g(Θ) with respect to Θ.

Once the parameters of the model are estimated by minimizing (16), we can calculate the parameter of

the market price of risk as,

δ0 =κQ−κP

σ.

5.2 Estimation results

Table 8 reports the results of the GMM estimation. We find considerable differences between the parame-

ters estimated under P and Q measures. On average, the median value of the mean reversion rate under the

17

risk-neutral measure is higher than under the objective measure, implying that the risk-neutral environment

worsens as time goes by. This can indicate that there is a considerable risk premium in the CDS spread asso-

ciated with uncertainty over the future credit event arrival rates.

[INSERT TABLE 8 ABOUT HERE]

The magnitude of CDS spread mispricing for maturities other than 5 years can be judged by the σε(M)

parameters for M = 1,3,7,10. The results show that mispricing is highest for 1-year and 10-year maturity

CDS spreads. The mean values of σε(1) and σε(10) are 22.6 and 14.1 basis points respectively, which are

higher than the mispricing parameters for other maturity CDS spreads.

Table 9 gives the summary statistics for the risk premium. The results reveal that higher risk premia

(on average) are demanded to lower-rated firms4. This view is confirmed by the standard deviation of the

premia which increases (on average) as the credit quality worsens. Additionally, compensation does not

seem to follow a linear pattern: investors on BB or B ratings (non-investment grade) demand much higher

compensation than investment ones.

[INSERT TABLE 9 ABOUT HERE]

We conduct a principal component analysis to examine the existance of common factors driving the

dynamics of risk premia. Table 10 summarizes the results of the PCA analysis. We observe that there is a

strong source of commonality driving the risk premia. The first principal component explains around 75%

(50%) of the variation of the level (first differences) of risk premia. The total variance increases to around

80% (55%) when the second component is included. These results seem to be robust across all rating groups.

[INSERT TABLE 10 ABOUT HERE]

Concerning the identity of these two factors, we follow Pan and Singleton (2008), and project the first

and second principal components on different financial variables. Table 1 displays the OLS results for the

spot interest rate, the slope of the interest term-structure, the VIX and S&P indices, respectively. We also do

our regression analysis for two subperiods, corresponding to the periods before and after August 2007.

4The conflicting result in rating BB might be due to the scarcity of these firms, which represent a 12.5% of our total sample

18

[INSERT TABLE 1 ABOUT HERE]

Table 1 shows that the information content of the first principal component relies on the stock index. This

result is robust across subsamples and other variables (VIX is not significant when it is considered together

with the S&P index). Moreover, the explanatory power of the stock index increases from 37% to 57% during

the crisis period. Additionally, S&P also explains part of the variation in the second principal component for

the pre-crisis sample, although its explanatory power vanishes at the expense of long-run spot interest rates.

Finally, spot rates seem to explain around 22% of the variation in the second principal component for the

whole sample.

5.3 Panel data analysis

After obtaining the risk premium series from CDS spreads, we run panel data regressions to examine the

relationship between the risk premium and our two proposed measures of liquidity. Table 11 provides the

results for CDS risk premia. We observe that neither the bid-ask spread nor the NOC measure are significant

determinants for changes in CDS spreads before August 2007. When we consider the time period after

August 2007, contemporaneous changes in bid-ask spreads have a positive and significant effect on changes

in CDS risk premia. This result holds both for cases when the bid-ask spread is considered separately in the

regressions, and when it is included together with the NOC variable in the regression. The positive sign of

the bid-ask spread variable after August 2007 implies that illiquidity increases the premium that the market

participants ask for providing credit protection after the start of the financial crisis. As for the number of

contributors, the lag of changes in NOC is a negative and statistically significant factor for changes in the

CDS risk premium after August 2007. As for the control variables, changes in EDF have a positive and

statistically significant effect on changes in risk premiums for all regressions and time periods.

[INSERT TABLE 11 ABOUT HERE]

In conclusion, the results of the panel data analysis indicate that the measure of bid-ask spreads is a

positive and statistically significant factor for changes in CDS risk premiums after August 2007. The lag

of changes in NOC is a negative and statistically significant determinant for changes in risk premium after

August 2007.

19

6 Robustness Check

As a robustness check, we analyze alternative stochastic models for the CDS default intensity, as previously

used in the literature. We complement our results on the CIR model with those of Ornstein-Uhlenbeck

(OU) and log-OU processes. The CIR specification for default intensity has been employed, for instance, in

Longstaff et al. (2005). A one-factor version of the OU process for corporate CDS markets is employed, for

example, in Berndt et al. (2005). The log-OU approach for the sovereign CDS markets has been considered

in Pan and Singleton (2008) and Longstaff et al. (2008).

We employ two different criteria to compare the performance of the three models mentioned above: first,

we regress the sample CDS spread increments onto their theoretical counterparts, in line with Duffie and

Singleton (1997). Second, we track the evolution of averaged pricing errors through time.

We start by analyzing the projections of sample CDS spreads (increments) onto those obtained from

the three different models. According to this criterion, if the performance of a model is good, we should

expect an intercept equal to zero and a slope coefficient close to one. Results are displayed in Table 12. In

general, the regression analysis of all three models seem to produce beta coefficients with the expected size

in magnitudes. The regression analysis of mispricing for maturities close to 5-years exhibit better results

in terms of slope and determination coefficients. The log-OU model produces higher standard deviation in

the residuals, which possibly indicates a poor performance of the model. Finally, Durbin-Watson tests do

not reject autocorrelation in residuals, a result also documented by Duffie and Singleton (1997) and Pan and

Singleton (2008).

[INSERT TABLE 12 ABOUT HERE]

Second, Figure 4 shows the evolution of the averaged pricing errors of all three models for different

maturities. Pricing errors are measured as the difference between the sample and theoretical CDS values.

According to this criterion, the log-OU model exhibits the lowest performance independently of the maturity

considered. It is important to notice that the log-OU model is computed numerically since there is no closed-

form for the CDS expectations in (1). This results is surprising. Although applied to the sovereign CDS

market, Pan and Singleton (2008) found that the log-OU model is superior to the CIR.

[INSERT FIGURE 4 ABOUT HERE]

20

In conclusion, the CIR model seems to provide the best fit under the two criteria considered. Additionally,

it is a parsimonious version of the log-OU model.

7 Conclusions

This paper examines the relationship between CDS spreads and their liquidity. We proxy liquidity by the

number of contributors and bid-ask spreads. We conduct two analysis. First, we run panel data regressions

to study the relationship between liquidity measures and CDS spreads. Second, we extract the risk premium

component from CDS spreads and analyze its relationship with the proposed liquidity proxies.

Our findings reveal that changes in bid-ask spreads have a positive and significant effect on CDS spreads

before and after August 2007. The positive sign of bid-ask spreads indicates that CDS illiquidity contributes

to the increase of CDS spreads. Changes in the number of contributors have a positive and significant effect

on CDS spreads before August 2007. The positive sign for NOC is still puzzling for us.

Concerning the analysis of the risk premium, we provide an alternative estimation of the distress premium

via the GMM methodology. Our estimation results show considerable differences in the estimated parameters

for credit event arrival rates under P and Q measures. This indicates that there is a considerable risk premium

in the CDS spreads associated with uncertainty over the future credit risk environment. These results are in

line with Pan and Singleton (2008) or Longstaff et al. (2008) for sovereign CDS markets.

Our panel data estimations of risk premia show that bid-ask spreads are positive and statistically signifi-

cant determinants for changes in CDS risk premia after August 2007. The lag of changes in NOC is a negative

and statistically significant factor for changes in risk premium after August 2007.

In conclusion, our results seem to indicate that bid-ask spreads constitute an important factor for ex-

plaining illiquidity of both CDS spreads and CDS implied risk premia, while the results for the number of

contributors are surprising and generally weak.

21

References

Acharya, V. V. and Johnson, T. C. (2007), ‘Insider trading in credit derivatives’, Journal of Financial Eco-

nomics (84), 110–141.

Bao, J., Pan, J. and Wang, J. (2011), ‘The illiquidity of corporate bonds’, Journal of Finance 66(3), 911–946.

Berndt, A., Douglas, R., Duffie, D., Ferguson, M. and Schranz, D. (2005), Measuring default risk premia

from default swap rates and EDFs. Working Paper.

Bharath, S. T. and Shumway, T. (2008), ‘Forecasting default with the merton distance to default model’, The

Review of Financial Studies 21(3), 1339–1369.

Blanco, R., Brennan, S. and Marsh, I. W. (2005), ‘An empirical analysis of the dynamic relation between

investment-grade bonds and credit default swaps’, The Journal of Finance 60(5), 2255–2281.

Bongaerts, D., Jong, F. D. and Driessen, J. (2011), ‘Derivative pricing with liquidity risk: Theory and evi-

dence from the credit default swap market’, Journal of Finance 66(1), 203–240.

Brockman, P. and Chung, D. Y. (2003), ‘Investor Protection and Firm Liquidity’, The Journal of Finance

58(2), 921–938.

Brunnermeier, M. and Pedersen, L. (2009), ‘Market liquidity and funding liquidity’, Review of Financial

Studies 22(6), 2201–2238.

Chan, K. C., Karolyi, G. A., Longstaff, F. A. and Sanders, A. B. (1992), ‘An empirical comparison of alter-

native models of the short-term interest rate’, The Journal of Finance 47(3), 1209–1227.

Collin-Dufresne, P., Goldstein, R. S. and Martin, J. S. (2001), ‘The determinants of credit spread changes’,

The Journal of Finance 56(6), 2177–2207.

Driessen, J. (2005), ‘Is default event risk priced in corporate bonds?’, The Review of Financial Studies

18(1), 165–195.

Duffee, G. R. (1999), ‘Estimating the price of default risk’, The Review of Financial Studies 12(1), 197–226.

22

Duffie, D., Garleanu, N. and Pedersen, L. H. (2007), ‘Valuation in over-the-counter markets’, The Review of

Financial Studies 20(5), 1865–1900.

Duffie, D., Pan, J. and Singleton, K. (2000), ‘Transform analysis and asset pricing for affine jump-diffusions’,

Econometrica 68(6), 1343–1376.

Duffie, D., Pedersen, L. and Singleton, K. J. (2003), ‘Modeling Sovereign Yield Spreads: A Case Study of

Russian Debt’, The Journal of Finance LVIII(1), 119–160.

Duffie, D. and Singleton, K. J. (1997), ‘An econometric model of the term structure of interest-rate swap

yields’, The Journal of Finance 52(4), 1287–1321.

Duffie, D. and Singleton, K. J. (1999), ‘Modeling term structures of defaultable bonds’, The Review of Fi-

nancial Studies 12(4), 687–720.

Easley, D., Kiefer, N. M., O’Hara, M. and Paperman, J. B. (1996), ‘Liquidity, Information, and Infrequently

Traded Stocks’, The Journal of Finance LI(4), 1405–1436.

Ericsson, J. and Renault, O. (2006), ‘Liquidity and credit risk’, Journal of Finance 61(5), 2219–2250.

Forte, S. and Peña, J. I. (2009), ‘Credit spreads: An empirical analysis on the informational content of stocks,

bonds, and CDS’, Journal of Banking & Finance 33(11), 2013–2025.

Fulop, A. and Lescourret, L. (2007), ‘How liquid is the CDS market?’, Working Paper.

Hansen, L. P. (1982), ‘Large sample properties of generalized method of moment estimators’, Econometrica

50(4), 1029–1054.

Jarrow, R. A., Lando, D. and Yu, F. (2005), ‘Default risk and diversification: theory and empirical implica-

tions’, Mathematical Finance 15(1), 1–26.

Krinsky, I. and Lee, J. (1996), ‘Earnings announcements and the components of the bid-ask spread’, The

Journal of Finance 51(4), 1523–1535.

Lagos, R., Rocheteau, G. and Weill, P.-O. (2011), ‘Crisis and liquidity in over the counter markets’, Journal

of Economic Theory .

23

Lando, D. (1998), ‘On Cox processes and credit risky securities’, Review of Derivatives Research 2, 99–120.

Lin, H., Wang, J. and Wu, C. (2011), ‘Liquidity risk and the cross-section of expected returns’, Journal of

Financial Economics 99, 628–650.

Longstaff, F. A. (2011), ‘Municipal debt and marginal tax rates: is there a tax premium in asset prices?’, The

Journal of Finance .

Longstaff, F. A., Mithal, S. and Neis, E. (2005), ‘Corporate yield spreads: Default risk or liquidity? new

evidence from the credit default swap market’, The Journal of Finance 60(5), 2213–2253.

Longstaff, F. A., Pan, J., Pedersen, L. H. and Singleton, K. J. (2008), How sovereign is sovereign credit risk?

Working Paper.

O’Kane, D., Pedersen, C. M. and Turnbull, S. M. (2003), ‘The restructuring clause in credit default swap

contracts’, Fixed Income Quantitative Credit Research - Lehman Brothers.

Pan, J. and Singleton, K. J. (2006), ‘Interpreting recent changes in the credit spreads of Japanese banks’,

Monetary and Economic Studies pp. 129–150.

Pan, J. U. N. and Singleton, K. J. (2008), ‘Default and recovery implicit in the term structure of sovereign

CDS spreads’, The Journal of Finance 63(5), 2345–2384.

Stoll, H. R. (1989), ‘Inferring the components of the bid-ask spread: Theory and empirical tests’, The Journal

of Finance 44(1), 115–134.

Tang, D. Y. and Yan, H. (2007), Liquidity and credit default swap spreads. Working Paper.

Tang, D. Y. and Yan, H. (2010), ‘Market conditions, default risk and credit spreads’, Journal of Banking &

Finance 34(4), 743–753.

Venkatesh, P. C. and Chiang, R. (1986), ‘Information asymmetry and the dealer’s bid-ask spread: A case

study of earnings and dividend announcements’, The Journal of Finance 41(6), 1089–1102.

Yu, F. (2002), Modeling expected return on defaultable bonds. Working Paper.

24

Tabl

e1:

OL

SR

egre

ssio

nsof

the

first

two

Prin

cipa

lCom

pone

nts

ofth

e5

year

CD

SR

isk

Prem

ia

The

depe

nden

tvar

iabl

ein

the

uppe

rpan

elis

the

diff

eren

ceof

the

first

prin

cipa

lcom

pone

nt(P

C)c

alcu

late

dov

erth

eC

DS

risk

prem

iata

ken

inle

vels

,whi

leth

ede

pend

entv

aria

ble

inth

elo

wer

pane

lis

defin

esan

alog

ousl

yfo

rthe

seco

ndPC

.∆r10 t

deno

tes

chan

ges

inth

esp

otin

tere

stra

tew

here

the

spot

inte

rest

rate

ism

easu

red

asth

e10

year

trea

sury

yiel

d,∆

slop

e tde

note

sch

ange

sin

the

slop

eof

the

inte

rest

rate

curv

em

easu

red

asth

edi

ffer

ence

betw

een

10-a

nd2-

year

trea

sury

yiel

ds,∆

VIX

tde

note

sch

ange

sin

the

VIX

vola

tility

inde

x,an

dS&

P tde

note

sth

ere

turn

onS&

P50

0in

dex.

The

PCan

alys

isof

the

dist

ress

risk

prem

iais

done

over

the

corr

elat

ion

mat

rix.

All

the

righ

than

dsi

deva

riab

les

are

furt

hern

orm

aliz

ed.

02/2

004

-08/

2007

08/2

007

-12/

2009

02/2

004

-12/

2009

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

∆r10 t

-0.4

5∗∗

-0.3

9∗∗

-1.5

8∗-1

.64∗∗

-1.1

9∗∗

-1.0

6∗∗∗

(-2.

24)

(-2.

34)

(-1.

88)

(-2.

62)

(-2.

08)

(-2.

71)

∆sl

ope t

0.30

0.38∗

0.86

0.42

0.72

0.18

(0.9

5)(1

.81)

(0.7

6)(0

.64)

(0.8

9)(0

.39)

∆V

IXt

1.05∗∗

0.18

1.91∗∗∗

0.36

1.79∗∗∗

0.41

(2.1

7)(0

.33)

(2.7

7)(0

.40)

(3.0

2)(0

.57)

S&P t

-1.1

6∗∗∗

-0.9

3∗∗∗

-2.6

8∗∗∗

-2.1

7∗∗∗

-2.4

3∗∗∗

-1.9

7∗∗∗

(-3.

19)

(-3.

00)

(-4.

79)

(-3.

04)

(-4.

88)

(-3.

12)

N42

4242

4242

2929

2929

2971

7171

7171

adj.

R2

0.09

70.

002

0.23

40.

297

0.37

10.

106

0.01

00.

243

0.49

70.

572

0.10

20.

028

0.25

00.

472

0.53

4

02/2

004

-08/

2007

08/2

007

-12/

2009

02/2

004

-12/

2009

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

∆r10 t

-0.3

7∗∗∗

-0.3

9∗∗∗

-0.6

7∗∗∗

-0.8

4∗∗

-0.5

8∗∗∗

-0.6

4∗∗∗

(-3.

10)

(-2.

87)

(-2.

87)

(-2.

60)

(-3.

64)

(-3.

33)

∆sl

ope t

0.10

0.42∗∗

0.06

0.40

0.11

0.31

(0.5

6)(2

.70)

(0.1

8)(1

.13)

(0.4

3)(1

.31)

∆V

IXt

0.37

-0.5

9∗∗

0.07

-0.0

30.

10-0

.11

(1.6

5)(-

2.33

)(0

.37)

(-0.

09)

(0.6

5)(-

0.43

)S&

P t-0

.77∗∗∗

-1.0

4∗∗∗

-0.1

60.

01-0

.26

-0.1

6(-

3.55

)(-

3.94

)(-

0.65

)(0

.04)

(-1.

22)

(-0.

60)

N42

4242

4242

2929

2929

2971

7171

7171

adj.

R2

0.12

8-0

.019

0.03

10.

224

0.35

80.

194

-0.0

35-0

.034

-0.0

210.

170

0.18

8-0

.007

-0.0

080.

026

0.21

7ts

tatis

tics

inpa

rent

hese

s∗

p<

0.1,∗∗

p<

0.05

,∗∗∗

p<

0.01

25

Table 2: Distribution of CDS names across Sector and Rating

AA A BBB BB B TotalBasic Materials 0 10 0 0 0 10Consumer Goods 0 19 0 0 0 19Consumer Services 5 6 0 3 20 34Financials 0 0 4 15 0 19Health Care 0 0 9 0 0 9Industrials 0 0 27 0 0 27Oil & Gas 0 0 11 0 0 11Technology 0 0 6 0 0 6Telecommunications 0 0 2 0 0 2Utilities 0 0 6 0 0 6Total 5 35 65 18 20 143

This table shows the distribution of 143 CDS names in our database by S&P letter rating group and ICBIndustry category.

26

Table 3: Summary statistics of CDS spread term structure

mean sd skew kurt min 25% med 75% max countAAspread1y 34.15 95.35 6.30 48.61 1.06 3.90 9.62 23.50 950.53 503spread3y 39.89 88.70 5.62 39.54 1.54 7.55 15.51 31.06 811.87 498spread5y 44.80 82.54 5.29 36.25 2.94 11.49 21.62 40.00 737.96 507spread7y 47.20 76.31 5.14 34.87 4.68 15.70 26.31 43.57 680.53 493spread10y 51.07 72.33 5.07 34.40 5.05 21.27 31.62 51.10 652.67 481Aspread1y 50.64 178.99 19.31 563.34 1.36 6.66 17.84 42.79 6524.64 3566spread3y 57.56 145.10 14.45 318.87 3.89 15.05 28.02 54.92 4391.16 3565spread5y 65.15 128.19 12.74 253.75 6.93 23.57 37.41 65.93 3606.86 3592spread7y 68.57 115.52 11.93 225.85 10.08 29.47 43.51 69.39 3132.83 3578spread10y 73.95 105.94 11.00 194.29 12.87 36.82 50.53 75.33 2714.45 3518BBBspread1y 62.76 128.49 8.92 137.88 1.78 10.16 26.87 65.18 3274.88 6471spread3y 75.78 112.16 5.91 60.90 4.51 23.40 41.65 82.73 2212.41 6519spread5y 87.87 104.30 5.21 48.12 8.59 36.84 57.27 96.10 1951.96 6567spread7y 93.26 96.52 4.81 40.14 12.80 45.14 65.13 100.62 1652.45 6503spread10y 100.23 90.50 4.56 36.04 17.20 53.78 74.97 110.00 1486.07 6365BBspread1y 205.76 326.77 4.75 39.92 4.17 32.93 94.57 246.20 4684.17 1709spread3y 241.55 296.12 3.85 27.79 11.83 66.95 143.71 307.97 3625.62 1733spread5y 267.34 276.78 3.88 32.62 19.67 98.42 177.07 347.22 3984.59 1758spread7y 270.19 255.04 3.51 26.89 25.25 111.00 189.20 348.00 3370.00 1728spread10y 275.56 241.54 3.66 31.92 29.36 123.17 200.94 354.59 3516.67 1655Bspread1y 377.77 662.30 6.28 62.82 4.36 86.22 190.43 424.56 9912.60 1760spread3y 453.62 562.76 5.15 47.73 7.42 163.52 293.70 544.01 8006.59 1796spread5y 498.91 520.74 4.41 34.61 13.26 217.29 368.21 613.51 6626.99 1830spread7y 492.58 461.62 4.64 41.12 16.67 236.45 384.17 618.35 5824.42 1764spread10y 493.12 426.04 4.75 43.45 20.00 255.95 406.33 618.38 5600.00 1703Totalspread1y 115.67 310.54 11.11 215.04 1.06 11.09 32.82 98.79 9912.60 14009spread3y 138.36 283.23 8.23 131.97 1.54 23.10 49.17 130.88 8006.59 14111spread5y 155.52 273.71 6.89 90.58 2.94 34.74 64.11 156.75 6626.99 14254spread7y 157.18 250.18 6.61 91.41 4.68 42.13 71.20 161.76 5824.42 14066spread10y 161.68 236.13 6.41 89.01 5.05 49.89 79.05 169.00 5600.00 13722

This table gives the summary statistics for the pooled time series of CDS spreads across rating group and maturity. The date is collectedfrom Markit. The CDS spreads are in basis points (bp) with monthly frequency. The sample spans from January 2001 until December2009

27

Table 4: CDS Term Structure Principal Component Analysis.

Levelcumulative R2 min 10% median mean 90% max

1st factor 0.7339 0.9069 0.9794 0.9615 0.9921 0.99622nd factor 0.9714 0.9877 0.9965 0.9944 0.9990 0.9997

First Differencecumulative R2 min 10% median mean 90% max

1st factor 0.6917 0.8540 0.9321 0.9230 0.9777 0.99372nd factor 0.8859 0.9446 0.9809 0.9742 0.9952 0.9994

This table presents the summary statistics on the distribution of the variance explained by the first two principalcomponents of all CDS names in our database. The principal components for each CDS name are calculatedfrom the CDS spread term structure with 1-, 3-, 5-, 7- and 10-year maturity.

28

Table 5: Summary statistics of number of contributors(NOC)

mean sd skew kurt min 25% med 75% max countAA 10.21 5.03 0.65 3.58 2.00 5.82 10.40 12.96 27.64 507A 10.13 4.51 0.27 2.79 2.00 6.36 10.60 12.91 25.00 3592BBB 10.30 5.01 0.35 2.66 2.00 5.77 10.61 13.35 26.71 6567BB 8.99 5.37 0.94 3.12 2.00 4.78 7.27 12.76 26.05 1758B 6.35 3.54 2.00 8.24 2.00 4.15 5.40 7.50 25.70 1830Total 9.59 4.95 0.56 2.82 2.00 5.19 9.33 12.86 27.64 14254

This table gives the summary statistics for the pooled time series of contributors providing quotes for 5 year CDSspreads. The sample spans from January 2001 until December 2009.

29

Table 6: Summary statistics of Bid/Ask spread term structure:

mean sd skew kurt min 25% med 75% max countAACDSba1y 9.38 16.60 7.72 79.48 0.39 3.15 5.65 9.43 204.36 338CDSba3y 6.93 7.57 5.80 50.29 1.52 3.84 4.32 7.35 87.73 338CDSba5y 4.58 3.81 4.41 32.03 1.05 2.59 3.61 5.09 40.14 360CDSba7y 5.96 4.87 3.26 16.24 2.00 3.30 4.14 7.00 39.68 356CDSba10y 6.24 4.67 2.99 13.15 2.29 3.74 4.34 7.19 33.64 356ACDSba1y 11.79 26.32 9.22 105.93 0.70 5.71 6.30 8.70 422.07 2276CDSba3y 8.40 12.48 9.41 118.68 2.14 4.86 5.63 7.55 237.09 2276CDSba5y 5.95 7.82 11.68 206.23 1.45 3.65 4.60 5.18 196.30 2520CDSba7y 6.99 7.23 11.64 203.20 2.28 4.67 5.45 7.29 175.59 2474CDSba10y 6.99 6.54 12.00 217.22 2.52 4.73 5.57 7.54 162.14 2474BBBCDSba1y 12.70 21.90 9.61 124.94 1.54 6.12 7.27 11.22 437.35 4178CDSba3y 9.40 9.80 7.67 88.00 2.38 5.48 6.90 9.56 188.65 4178CDSba5y 6.44 5.65 6.19 60.74 1.77 4.10 4.91 6.68 95.80 4636CDSba7y 7.96 5.48 6.46 71.97 2.69 5.30 6.60 8.76 114.90 4540CDSba10y 8.09 4.93 6.19 68.98 2.68 5.57 7.04 9.00 103.95 4540BBCDSba1y 31.38 43.76 4.07 23.20 4.83 9.58 18.54 34.55 404.45 1132CDSba3y 21.17 19.21 3.10 15.15 4.45 9.71 16.31 25.12 152.00 1132CDSba5y 13.88 12.15 2.80 14.33 2.71 5.74 10.00 18.34 106.95 1280CDSba7y 16.40 11.07 2.84 15.89 3.88 9.33 14.03 19.83 102.48 1239CDSba10y 16.34 9.99 2.65 14.54 4.31 9.87 14.23 19.70 92.29 1239BCDSba1y 59.98 84.91 3.58 23.43 5.39 17.66 28.17 53.19 1012.91 1127CDSba3y 38.76 37.23 2.62 12.20 5.04 18.13 25.73 39.50 336.00 1127CDSba5y 27.26 26.97 3.65 24.52 2.68 11.82 20.09 29.83 323.91 1361CDSba7y 28.35 21.01 3.07 17.02 4.70 17.01 22.24 31.37 207.30 1260CDSba10y 27.50 19.18 3.13 17.88 4.44 17.17 22.30 30.78 193.20 1260TotalCDSba1y 20.57 42.46 6.74 73.56 0.39 6.09 8.07 17.89 1012.91 9051CDSba3y 14.18 20.16 5.09 39.56 1.52 5.41 7.48 14.35 336.00 9051CDSba5y 9.98 14.10 6.30 71.42 1.05 4.17 5.09 9.95 323.91 10157CDSba7y 11.31 12.27 4.93 42.65 2.00 5.25 7.21 12.19 207.30 9869CDSba10y 11.26 11.36 4.83 42.15 2.29 5.44 7.60 12.15 193.20 9869

This table gives the summary statistics for the pooled time series of Bid/Ask spreads across rating groups and maturity. TheBid/Ask spreads are in basis points with monthly frequency. The sample spans from January 2004 until December 2009.

30

Table 7: Panel data regression for CDS spreads

This table reports the results for the following panel data regression:

∆CDS5i,t = α +φ ·∆CDS5

i,t−1 +∑j

β j ·∆Liquidityi,t− j +∑k

γk ·∆Controlk,t + εi,t

CDS5i,t is the CDS spread of issuer i at time t with 5 year maturity. Liquidityi,t is the vector of liquidity proxies including NOC5

i,t and BA5i,t .

NOC5i,t is the number of contributors providing quotes to Markit for 5 year CDS spreads, and BA5

i,t is the 5 year bid-ask spread for thecorresponding CDS name. ∆Controlt includes changes in one year EDF from Moody’s, changes in the spot interest rate (∆r10

t ) measured asthe 10 year treasury yield, changes in the slope of the interest rate curve (∆slopet ) measured as the difference between 10- and 2-year treasuryyields, the equity return of the CDS reference entity (rett ), changes in the VIX volatility index (∆V IXt ), and the return on S&P 500 index(S&Pt ). The coefficients are estimated by OLS; robust standard errors are adjusted for issuer-clustering.

Before August 2007 After August 2007

(1) (2) (3) (4) (5) (6) (7) (8)∆BA5

t 2.82∗∗∗ 2.83∗∗∗ 7.55∗∗ 7.58∗∗

(4.47) (4.48) (2.51) (2.55)∆BA5

t−1 0.02 0.03 0.30 0.27(0.17) (0.23) (0.54) (0.49)

∆NOC5t 0.35∗ 0.56∗∗∗ -3.89 -0.25

(1.91) (3.26) (-1.04) (-0.14)∆NOC5

t−1 0.03 0.21 -1.81 -4.31(0.11) (1.28) (-0.44) (-0.84)

∆CDS5t−1 0.00 -0.05 0.00 -0.06 -0.08 -0.22∗∗∗ -0.08 -0.22∗∗∗

(0.09) (-0.95) (0.08) (-0.99) (-1.10) (-3.11) (-1.12) (-3.11)∆EDF1

t 21.11∗∗∗ 21.45∗∗∗ 21.11∗∗∗ 21.50∗∗∗ 29.53∗ 30.56∗ 29.44∗ 30.50∗

(6.39) (10.07) (6.39) (10.06) (1.88) (1.94) (1.87) (1.94)∆r10

t -24.73∗∗∗ -7.24∗∗∗ -24.94∗∗∗ -7.71∗∗∗ -84.18∗ -63.31 -79.22∗ -61.29(-6.40) (-2.68) (-6.50) (-2.94) (-1.93) (-1.55) (-1.75) (-1.50)

∆slopet 29.61∗∗∗ 0.00 29.88∗∗∗ 0.00 38.87 30.13 29.84 28.36(5.40) (.) (5.44) (.) (1.11) (0.97) (0.78) (0.89)

ret -0.58∗∗∗ -0.48∗∗∗ -0.58∗∗∗ -0.47∗∗∗ -3.23∗∗∗ -2.15∗∗∗ -3.23∗∗∗ -2.16∗∗∗

(-3.70) (-3.26) (-3.68) (-3.22) (-2.89) (-2.92) (-2.88) (-2.91)∆V IXt 0.30 5.92∗∗∗ 0.29 5.89∗∗∗ 0.61 0.14 0.76 0.01

(0.37) (7.53) (0.35) (7.48) (0.38) (0.09) (0.45) (0.00)S&Pt -0.36 1.65∗∗∗ -0.37 1.67∗∗∗ 3.95 2.40 3.71 2.24

(-0.63) (3.94) (-0.64) (3.87) (0.91) (0.60) (0.85) (0.56)Constant 9.20∗∗∗ -9.09∗∗∗ 9.06∗∗∗ -8.91∗∗∗ -107.21∗∗∗ -49.66∗∗∗ -116.16∗∗∗ -58.23∗∗∗

(4.37) (-5.93) (4.27) (-5.79) (-5.51) (-4.63) (-4.09) (-7.57)company dummy Yes Yes Yes Yes Yes Yes Yes Yessector dummy Yes Yes Yes Yes Yes Yes Yes Yesrating dummy Yes Yes Yes Yes Yes Yes Yes Yesmonthly dummy Yes Yes Yes Yes No No No NoN 8172 4863 8172 4863 3416 3363 3416 3363adj. R2 0.237 0.329 0.237 0.329 0.243 0.365 0.243 0.365t statistics in parentheses∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01

31

Table 8: Summary Statistics for Model Parameters

Parameter min 10% median mean 90% maxκQ 0.00000 0.00000 0.01214 0.03715 0.09481 0.49858

κQθ Q 0.00000 0.00061 0.00150 0.00378 0.00955 0.04441σ 0.00035 0.01133 0.03778 0.05189 0.11827 0.23674κP 0.00000 0.00593 0.02360 0.08752 0.16646 2.12916

σε(1) 0.00000 0.00001 0.00073 0.00226 0.00749 0.01930σε(3) 0.00000 0.00000 0.00064 0.00112 0.00296 0.01013σε(7) 0.00000 0.00001 0.00050 0.00082 0.00177 0.00956σε(10) 0.00000 0.00018 0.00099 0.00141 0.00306 0.00648δ ×σ -1.63058 -0.12481 -0.01088 -0.05037 0.03334 0.28468

JT 0.2000 0.4505 0.7025 0.6800 0.9062 0.9856

This table provides summary statistics for optimized model parameter values. κQ denotes the mean reversionrate under the Q probability measure. θ Q denotes the long run mean of default intensity processes λ Q. σ is theinstantaneous volatility of λ Q. κP is the mean reversion rate of λ Q under the objective measure P. σε (M)s arethe volatility of the mispricing of the market CDS spreads with M = 1, 3, 7, and 10 year maturity. δ denotes theparameter of the market price of risk and is calculates as δ = (κQ−κP)/σ . Finally, JT denotes the minimizedvalue of the GMM objective function.

32

Table 9: Descriptive Statistics of 5 year risk premium (MRP):

mean sd skew kurt min 25% med 75% max countAA 0.42 3.10 2.10 19.27 -12.81 -0.35 -0.07 0.63 24.75 480A 2.25 10.61 8.42 90.05 -15.29 -0.39 0.44 1.57 163.20 3510BBB 3.02 15.70 2.80 52.51 -110.05 0.28 1.40 4.92 307.30 6345BB -0.30 86.06 3.58 38.97 -398.84 -19.47 -1.53 8.35 1151.65 1646B 128.93 237.13 3.17 26.06 -521.58 10.52 58.64 221.41 2928.97 1690Total 17.90 98.60 8.28 140.37 -521.58 -0.44 1.08 5.83 2928.97 13671

This table gives the summary statistics for the pooled time series of 5 year Market Price of Risk across Rating groups and forthe overall sample. The MPR spreads are in basis points with monthly frequency. The sample spans from January 2001 untilDecember 2009.

33

Table 10: PCA analysis of Distress Risk Premium

Level (%) First Difference (%) N CountPC1 PC2 PC3 PC4 Cum. R2 PC1 PC2 PC3 PC4 Cum. R2 Nused Ntotal

Rating AA

RP1y 89.91 5.95 2.18 1.53 99.57 43.38 24.36 16.62 10.06 94.42 5 5RP3y 90.05 5.85 2.16 1.51 99.58 43.50 24.27 16.56 10.09 94.42 5 5RP5y 90.18 5.76 2.15 1.49 99.58 43.61 24.18 16.50 10.12 94.41 5 5RP7y 90.30 5.66 2.13 1.47 99.57 43.73 24.08 16.44 10.14 94.39 5 5

RP10y 90.48 5.53 2.11 1.44 99.57 43.89 23.93 16.35 10.18 94.35 5 5

Rating A

RP1y 77.94 6.85 5.10 2.21 92.10 54.93 8.28 6.95 5.58 75.74 35 35RP3y 78.06 6.85 5.08 2.18 92.18 55.03 8.29 6.92 5.53 75.77 35 35RP5y 78.18 6.85 5.06 2.16 92.25 55.12 8.28 6.90 5.48 75.77 35 35RP7y 78.28 6.85 5.04 2.14 92.31 55.20 8.27 6.86 5.43 75.76 35 35

RP10y 78.41 6.84 5.01 2.11 92.37 55.31 8.23 6.81 5.36 75.71 35 35

Rating BBB

RP1y 72.28 7.86 5.56 2.97 88.68 50.51 8.80 6.49 4.92 70.72 62 65RP3y 72.36 7.88 5.53 2.95 88.73 50.72 8.68 6.38 4.85 70.63 62 65RP5y 72.44 7.90 5.50 2.93 88.77 50.92 8.56 6.28 4.78 70.54 62 65RP7y 72.50 7.92 5.48 2.91 88.81 51.11 8.45 6.18 4.72 70.46 62 65

RP10y 72.59 7.94 5.45 2.88 88.86 51.36 8.31 6.04 4.65 70.36 62 65

Rating BB

RP1y 70.72 10.02 6.69 4.98 92.40 51.04 12.96 7.40 4.91 76.31 17 18RP3y 70.83 10.00 6.67 4.99 92.49 51.44 12.59 7.34 4.87 76.24 17 18RP5y 70.93 9.98 6.67 5.00 92.57 51.76 12.25 7.29 4.87 76.16 17 18RP7y 71.02 9.95 6.67 5.00 92.63 51.98 11.96 7.26 4.89 76.09 17 18

RP10y 71.11 9.90 6.67 5.00 92.69 52.19 11.64 7.24 4.93 76.00 17 18

Rating B

RP1y 70.12 8.70 6.21 4.96 89.99 42.61 14.38 11.72 7.40 76.11 15 20RP3y 71.16 8.76 5.97 4.81 90.69 43.89 14.20 10.92 7.40 76.41 15 20RP5y 71.79 8.76 5.85 4.74 91.14 44.70 14.16 10.37 7.45 76.69 15 20RP7y 72.14 8.75 5.79 4.73 91.40 45.14 14.17 10.03 7.51 76.86 15 20

RP10y 72.37 8.73 5.73 4.76 91.59 45.43 14.21 9.74 7.59 76.96 15 20

Overall

RP1y 72.69 6.82 5.29 2.97 87.78 47.92 7.70 5.94 5.07 66.63 134 143RP3y 72.90 6.87 5.26 2.94 87.96 48.21 7.55 5.88 5.06 66.69 134 143RP5y 73.05 6.90 5.23 2.91 88.08 48.44 7.44 5.83 5.05 66.75 134 143RP7y 73.17 6.92 5.20 2.88 88.17 48.61 7.35 5.80 5.04 66.80 134 143

RP10y 73.29 6.93 5.17 2.85 88.25 48.82 7.24 5.77 5.01 66.84 134 143

This table reports the results of PCA analysis (variance explained by the first 4 PCs) of CDS distress risk premium by maturityand rating group. The PCA analysis is done for Distress risk premia in both levels and first differences. The PCA analysis iscarrout out over sample period that spans from 01/2004 to 12/2009. The useable size of CDS names for PCA analysis is givenby Nused , whereas Ntotal denotes the total number of CDS names in the database for each rating group.

34

Table 11: Panel data regression for CDS Risk Premium

This table reports the results for the following panel data regression:

∆RP5i,t = α +φ ·∆RP5

i,t−1 +∑j

β j ·∆Liquidityi,t− j +∑k

γk ·∆Controlk,t + εi,t

RP5i,t is the CDS implied risk premium of issuer i at time t with 5 year maturity. Liquidityi,t is the vector of liquidity proxies

including NOC5i,t and BA5

i,t . NOC5i,t is the number of contributors providing quotes to Markit for 5 year CDS spreads, and BA5

i,tis the 5 year bid-ask spread for the corresponding CDS name. ∆Controlt includes changes in one year EDF from Moody’s,changes in the spot interest rate (∆r10

t ) measured as the 10 year treasury yield, changes in the slope of the interest rate curve(∆slopet ) measured as the difference between 10- and 2-year treasury yields, the equity return of the CDS reference entity(rett ), changes in the VIX volatility index (∆V IXt ), and the return on S&P 500 index (S&Pt ). The coefficients are estimated byOLS; robust standard errors are adjusted for issuer-clustering.

Before August 2007 After August 2007

(1) (2) (3) (4) (5) (6) (7) (8)∆BA5

t 0.44 0.44 0.89∗ 0.90∗∗∗

(1.05) (1.02) (1.97) (2.79)∆BA5

t−1 -0.20 -0.20 0.01 -0.01(-1.48) (-0.43) (0.09) (-0.02)

∆NOC5t -0.05 -0.07 -0.56 -0.03

(-0.66) (-0.72) (-0.57) (-0.04)∆NOC5

t−1 0.01 -0.04 -1.59∗ -1.80∗∗

(0.09) (-0.46) (-1.72) (-2.50)∆RP5

t−1 0.11∗∗∗ 0.09 0.11∗∗∗ 0.09 -0.02 -0.08 -0.02 -0.08(5.06) (1.56) (5.03) (1.02) (-0.44) (-1.34) (-0.46) (-0.78)

∆EDF1t 12.00∗∗∗ 15.61∗∗∗ 12.00∗∗∗ 15.61∗∗∗ 6.39∗∗ 6.72∗∗ 6.36∗∗ 6.69∗∗∗

(6.00) (9.18) (6.00) (4.50) (2.35) (2.39) (2.34) (3.39)∆r10

t -2.27 -2.31 -2.32 -2.24 -8.49 -6.30 -7.14 -5.54(-1.26) (-1.47) (-1.26) (-1.16) (-1.41) (-1.03) (-1.12) (-0.81)

∆slopet 4.38 0.00 4.46 0.00 10.35∗∗ 9.83∗∗ 8.68 9.26(1.05) (.) (1.05) (.) (2.05) (2.03) (1.36) (1.15)

ret -0.01 0.00 -0.01 0.00 -0.25 -0.14 -0.26 -0.14(-0.21) (0.02) (-0.22) (0.01) (-1.50) (-1.04) (-1.52) (-1.57)

∆V IXt -0.03 0.26 -0.04 0.27 -0.02 -0.05 -0.04 -0.11(-0.35) (0.69) (-0.41) (0.58) (-0.08) (-0.19) (-0.16) (-0.32)

S&Pt 0.27 0.14 0.27 0.14 0.61 0.48 0.53 0.42(1.21) (0.86) (1.22) (0.81) (0.99) (0.74) (0.82) (0.68)

Constant 6.24∗∗∗ 6.03∗∗∗ 6.23∗∗∗ 5.72 -6.01∗ -5.65∗∗∗ -9.98∗ -4.10(8.94) (12.65) (9.24) (1.27) (-1.73) (-3.80) (-1.74) (-0.14)

company dummy Yes Yes Yes Yes Yes Yes Yes Yessector dummy Yes Yes Yes Yes Yes Yes Yes Yesrating dummy Yes Yes Yes Yes Yes Yes Yes Yesmonthly dummy Yes Yes Yes Yes No No No NoN 7656 4848 7656 4848 3416 3363 3416 3363adj. R2 0.119 0.220 0.118 0.220 0.128 0.193 0.129 0.196t statistics in parentheses∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01

35

Table 12: Projections of sample values onto fitted values

∆ssamplet = β0 +β1∆stheo

t + εt

Maturity β0 β1 R2 std. res. (bps) D.W. NPanel A: CIR Model

1 Year -0.0001 1.1530 0.73 97 2.69 13782(0.0001) (0.0060) (0.00)

3 Year -0.0000 1.0429 0.86 56 3.07 13782(0.0000) (0.0036) (0.00)

7 Year 0.0000 0.9432 0.92 37 2.58 13782(0.0000) (0.0024) (0.00)

10 Year 0.0000 0.8633 0.82 53 2.59 13782(0.0000) (0.0035) (0.00)

Overall -0.0000 1.0055 0.83 59 2.68 68910(0.0000) (0.0017) (0.00)

Panel B: OU Model1 Year -0.0001 1.2094 0.74 95 2.73 13782

(0.0001) (0.0061) (0.00)3 Year -0.0000 1.0563 0.86 56 3.07 13782

(0.0000) (0.0036) (0.00)7 Year 0.0000 0.9271 0.91 39 2.62 13782

(0.0000) (0.0025) (0.00)10 Year 0.0000 0.8397 0.81 54 2.62 13782

(0.0000) (0.0035) (0.00)Overall -0.0000 1.0069 0.83 60 2.68 68910

(0.0000) (0.0017) (0.00)Panel C: LogOU Model

1 Year -0.0001 0.8141 0.68 105 2.45 13782(0.0001) (0.0048) (0.00)

3 Year -0.0001 0.9290 0.86 57 2.91 13782(0.0000) (0.0032) (0.00)

7 Year 0.0000 0.9927 0.90 41 2.64 13782(0.0000) (0.0028) (0.00)

10 Year 0.0000 0.9530 0.79 57 2.61 13782(0.0000) (0.0042) (0.00)

Overall -0.0000 0.9137 0.81 63 2.55 68910(0.0000) (0.0017) (0.00)

This Table shows the projections of CDS data increments onto their model counterparts, respec-tively. Standard deviation of the coefficients are in parenthesis. Additionally, standard deviationof residuals (std. res.) is given in basic points. Finally, Durbin-Watson statistics (D.W.) and theircorresponding P-values are in parentheses.

36

Figure 1: Time series of 5 year CDS spreads

01/01 01/02 01/03 01/04 01/05 01/06 01/07 01/08 01/09 12/090

200

400

600

800

1000

1200

1400

1600

5y C

DS

spre

ad (b

asis

poi

nts)

AAABBBBBB

This figure graphs the rating term structure of 5 year CDS spreads. The time series for each rating category is obtainedby averaging the cross-sectional 5 year CDS spreads of the companies with the given rating class. The sample frequencyis monthly, where the sample spans from January 2001 to December, 2009. Two black lines delineate the months ofAugust 2007 and September 2008, correspondingly. August 2007 is the month when the problems with subprimemortgage backed securities started becoming visible. September 2008 is the month when Lehman Brothers filed forbankruptcy protection.

37

Figure 2: Time series of Number of Contributors

01/01 01/02 01/03 01/04 01/05 01/06 01/07 01/08 01/09 12/090

2

4

6

8

10

12

14

16

18

20

Num

ber o

f Con

tribu

tors

AAABBBBBB

This figure graphs the time series of number of contributors (NOC) by rating group. The time series for each ratingcategory is obtained by averaging the cross-sectional NOC within the given rating class. The sample frequency ismonthly, where the sample spans from January 2001 to December, 2009. Two black lines delineate the months ofAugust 2007 and September 2008, correspondingly. August 2007 is the month when the problems with subprimemortgage backed securities started becoming visible. September 2008 is the month when Lehman Brothers filed forbankruptcy protection.

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Figure 3: Time series of 5 year Bid-Ask Spreads

01/04 01/05 01/06 01/07 01/08 01/09 12/090

10

20

30

40

50

60

70

80

90

100

5y B

id−A

sk S

prea

d (b

asis

poi

nts)

AAABBBBBB

This figure graphs 5 year CDS Bid/Ask spreads by rating group. The time series for each rating category is obtainedby averaging the cross-sectional 5 year Bid/Ask spreads of the CDS names within the given rating class. The samplefrequency is monthly, where the sample spans from January 2001 to December, 2009. Two black lines delineate themonths of August 2007 and September 2008, correspondingly. August 2007 is the month when the problems withsubprime mortgage backed securities started becoming visible. September 2008 is the month when Lehman Brothersfiled for bankruptcy protection.

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Figure 4: Evolution of averaged pricing errors over time

Jan2001 Jul2002 Jan2004 Jul2005 Jan2007 Jul2008 Dec2009−500

−400

−300

−200

−100

0

100

200

1 Ye

ar

CIROULogOU

Jan2001 Jul2002 Jan2004 Jul2005 Jan2007 Jul2008 Dec2009−200

−100

0

100

200

3 Ye

ar

CIROULogOU

Jan2001 Jul2002 Jan2004 Jul2005 Jan2007 Jul2008 Dec2009−200

−100

0

100

200

7 Ye

ar

CIROULogOU

Jan2001 Jul2002 Jan2004 Jul2005 Jan2007 Jul2008 Dec2009−200

−100

0

100

200

10 Y

ear

CIROULogOU

This figure depicts the difference (mispricing) between sample and theoretical CDS spreads with 1-(upper left), 3-(upperright), 7-(below left) and 10-year (below right) maturities under the CIR, OU and logOU characterization of intensityprocesses, respectively. The time series of mispricing for each maturity is obtained by averaging the cross-sectionalCDS spreads of all companies. The sample frequency is monthly. Sample period spans from January 2001 to December2009.

40