Determinants of CDS premium and bond yield spread

Transcription

1 Determinants of CDS premium and bond yield spread Yusho KAGRAOKA Musashi University, Toyotama-kami, Nerima-ku, Tokyo , Japan tel: , fax: Abstract A reduced-from model for credit risk is applied to evaluation of credit default swaps (CDSs) and corporate bond spreads. For each reference entity, the term structure of default intensity in the reduced-form model is estimated from CDS premiums. The CDS-implied bond spread of a market-traded corporate bond is calculated by using the term structure of default intensity. The market and CDS-implied bond spreads are examined by fixed-effects panel data analysis. As a byproduct, a new method to estimate the risk-free interest rate is developed. The method is appealing to practitioners since the resultant term structure of the risk-free rate is consistent with both sovereign CDS premiums and government bond spreads. Empirical study on Japanese market is conducted based on a quarterly dataset from 2005 to Empirical study unveils the following facts: (i) CDS-implied bond spread comprises of credit and firm-specific liquidity premiums, (ii) market bond spread comprises of credit, firm-specific and bond-specific liquidity premiums. Preprint submitted to Financial Markets and Portfolio Management October 28, 2012

2 1. Introduction Growing credit derivatives market shows strong demand by financial market participants for credit-risk management vehicles because many investors are exposed to credit risk resulting from corporate bonds in their portfolios. Investing in corporate bonds is definitely a long-position in credit risk. Investors were not able to take a short-position in credit risk until the advent of credit derivatives in early 1990 s. Credit default swaps (CDSs) are one of the most popular instruments among the credit derivatives. Brokers constantly quote CDSs premiums and one can observe current premiums on financial information terminals such as Bloomberg. In this paper we use the terms default risk and credit risk interchangeably. Credit risk of an issuing company are reflected in CDS premium as well as yield spread. Hull, Predescu and Vorst (2004) and Blanco, Brennan and Marsh (2005) compared CDS premiums and corporate spreads and concluded that CDS premium was consistent with corporate bond spreads. Their results can be biased since they employed fixed-rate corporate bonds in place of floating-rate corporate bonds. Cashflows from CDS are replicated by a long position in a par default-free floating-rate note (FRN) and a short position in a par defaultable FRN issued by the reference entity. Duffie and Liu (2001) show that if a issuer s default risk is risk-neutrally independent of interest rates, floating-fixed spreads are determined by a term structure of the risk-free forward rate. Credit risk models are useful to compare CDS premiums and corporate bond spreads on a comparative basis 1. The models are categorized into two types, structural and reduced-form models. Structural model is first developed by Black and Scholes (1973) and practically applied by KMV (Vasicek (2001)). The structural model requires information on the current financial structure of a firm. It is difficult to apply the structural model for timely valuation of credit risk since financial reports are disclosed only quarterly. Reduced form models are developed by Jarrow, Lando and Turnbull (1997), Duffie and Singleton (1999), Jarrow (2001), Madan, Guntay, and Unal (2003), and Das and Sundaram (2007). The reduced-form models are more appropriate for evaluation of the credit risk than the structural one since model parameters in the reduced-form models can be estimated from market 1 Credit risk models are reviewed in many textbooks such as Duffie (2003), Lando (2004), and Schonbucher (2003), Bielecki and Rutkowski (2010), and so forth. 2

3 prices of CDSs or corporate bonds. Longstaff, Mithal, and Neis (2005) apply a reduced-form model to valuation of CDS premiums and corporate bond spreads and study their relationship empirically. They regard that CDS is very liquid and its risk premium contains mainly credit risk; if an investor want to liquidate a CDS position, it is easy to enter into a new swap in the opposite direction. The difference between CDS premiums and corporate bond spreads comprises of a liquidity risk of corporate bonds. They report that the default component represent 51% of the spread for AAA/AA-rated bonds, 56% for A-rated bonds, 71% for BBB-rated bonds, and 83% for BB-rated bonds. Houweling and Vorst (2005) apply a reduced-form model and investigate relationship between CDS premiums and corporate bond prices. They parametrize the default intensity as constant, linear, quadratic or cubic function of term to maturity, and consider three types of interest rates as the risk-free rate; government, swap, and repo curves They conclude that a quadratic model that use the repo curve works well for investment grade issuers and the underestimation of CDS premiums for speculative grade issuers is substantial. Our objective is two-fold. Firstly, we empirically examine a relationship between CDS premium and corporate bond spread by applying a reducedform of credit risk model. Secondly, we identify the determinants of CDS premium, corporate bond spread, and the difference between them by investigating the default intensity in the reduced-form model. We calculate CDS-implied bond spread from the default intensity which is estimated from CDS premium. We have a large data set of quarterly market quotes on Japanese CDSs from 2005Q3 to 2011Q3 at our disposal. We expect that the difference between the CDS-implied and market spread of corporate bond arising from liquidity risk as Longstaff, Mithal, and Neis (2005). Our study expands Houweling and Vorst (2005) in three ways. Firstly we use premiums of CDSs with various maturities and estimate term structure of the default intensity. Secondly we simultaneously estimate the risk-free rate and the default intensity from the government from sovereign CDS premiums and government bond prices. They recommend repo rate as proxy for the riskfree rate, however, it is impossible to get long-term repo rate. Thirdly we estimate CDS-implied bond spreads from CDS premiums while they estimate CDS premiums using bond spreads. The remainder of the paper is organized as follows. In section 2, a reduceform model of credit risk is presented. In section 3, our data sets on CDS and corporate bonds are explained. In section 4, our empirical study is 3

4 conducted. The default intensity in the credit risk model is estimated from CDS and corporate bond. The determinants of CDS premium, corporate bond spread, and the difference between them are investigated. Section 5 summarizes the paper and includes discussions on our model. 2. Model 2.1. Reduced-form model of credit risk We review Houweling and Vorst (2005) to introduce our notations and to explain our extension. We assume that default event of a reference entity is modelled by a point process with deterministic intensity. Let p(t, T ) denote for the time-t value of default-free discount bond maturing at time T with face value 1. Let λ(t) and Pr(t, T ) denote default intensity at time t and martingale survival probability at time t up to time T, respectively. The following relationship holds for them, ( T )] Pr(t, T ) = E t [exp ds λ(s). (1) t Houweling and Vorst (2005) assume default intensity as constant, linear, quadratic, or cubic function with respect to term-to-maturity. We assume that the default intensity λ(t) is expressed by a piecewise constant function which is discontinuous at simple knots [ 0, 1, 2, 3, 4, 5, 7, 10 ]. Our parametrization has an advantage that we can fit theoretical CDS premiums to the corresponding market premiums. Let us investigate the value of a defaultable fixed-rate bond maturing at time t n. The defaultable bond has a stream of coupon payment c at times t = (t 1, t 2,..., t n ). The value of the bond, v(t, t, c), is given by v(t, t, c) = = n i=1 [ p(t, t i )E t c1{τ>ti }] + p(t, tn )E [ ] 1 {τ>tn } [ ] + E t p(t, τ)δ1{τ tn } n p(t, t i )c Pr(t, t i ) + p(t, t n ) Pr(t, t n ) i=1 tn + t ds p(t, s)δφ(s), (2) 4

5 where τ is a stopping time at which default occurs and φ is a probability density function of Pr(t, T ). The last term in eq. (2) is approximated by discretizing the time interval [t, t n ] into series of time {s 0, s 1,..., s m } (s j 1 < s j ) so as to s 0 = t and s m = t n. We finally obtain a valuation formula, n v(t, t, c) = p(t, t i )c Pr(t, t i ) + p(t, t n ) Pr(t, t n ) i=1 + m p(t, s i )δ (Pr(t, s i 1 ) Pr(t, s i )). (3) i=1 Next let us evaluate a CDS with payment dates T = (T 1, T 2,..., T N ), premium p, notional 1, and cash settlement at time t. We discretize the time interval [t, T n ] into series of time {S 0, S 1,..., S M } (S j 1 < S j ) so as to S 0 = t and S M = T N. The value of a fixed leg is given by V (t, T, p) = = = N i=1 [ [ ] p(t, T i )α(t i 1, T i )pe t 1{τ>Ti }] + E p(t, τ)α(t (τ), τ)p1{τ TN } N p(t, t i )α(t i 1, T i )p Pr(t, T i ) + i=1 N p(t, t i )α(t i 1, T i )p Pr(t, T i ) i=1 + TN t ds p(t, s)α(t (s), s)pφ(s) M p(t, S i )α(t (s i ), S i )p (Pr(t, S i 1 ) Pr(t, S i )), (4) i=1 where α(t, S) is the year fraction between time t and S, and T (S) = max i=0,...,n (T i : T i < S). The last term corresponds to an accrual payment; the holder of CDS is required to pay the part of the premium payment that has accrued since the last payment date. The value of a floating leg is expressed as V (t, T [ ] ) = E t p(t, τ)(1 δ)1{τ Tn } = = TN t ds p(t, s)(1 δ)φ(s) M p(t, S i )(1 δ) (Pr(t, S i 1 ) Pr(t, S i )). (5) i=1 The CDS premium is set to the level at which it holds V (t, t, p) = V (t, T ). 5

6 2.2. Risk-free rate Traditionally practitioners and academics have taken it for granted that the interest rate estimated from the government bonds corresponds to the risk-free rate, however, non-zero sovereign CDS premiums imply that the government bonds are risky. The Japanese Governmental Bonds (JGBs) are traded very actively in the OTC market, and they are highly liquid. We assume that the JGBs have no liquidity risk. We simultaneously estimate the risk-free rate and the default intensity of the government by applying the reduced-form model of credit risk. Denote instantaneous forward rate at time t maturing at time T by f(t, T ). We assume that the instantaneous forward rate is expressed by a piecewise constant function with discontinuities at simple knots [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]. The time-t value of default-free discount bond maturing at time T with face value 1 is expressed as ( T ) p(t, T ) = exp ds f(t, s). (6) t 2.3. Explanatory variables for the spread We investigate the CDS-implied and market spread of corporate bond. The CDS-implied bond prices are calculated by using the reduced-form model whose parameters are estimated from CDS premiums, and the CDS-implied bond prices are converted into spreads over the risk-free rate. We identify the risk factors generating the CDS-implied and market spread, and investigate the differences between the CDS-implied and market spreads. We assume that risk factors are additive. Credit risk is traditionally evaluated by credit rating, and we use an ordinal number to express credit rating; 1 for AAA, 2 for AA, 3 for A, and so forth. We assign 9 to the worst rating of C. We adopt logarithm of the issue amount and yield discrepancy as liquidity measure. The yield discrepancy is proposed as a liquidity measure by Kagraoka (2010). it is a difference in yields of a corporate bond between the highest and the lowest of quoted yields by brokerage firms. If a corporate bond is liquid, quoted prices by brokerage firms are very close to each other. If a bond is illiquid, quoted prices by brokerage firms vary widely. Therefore, we expect that the yield discrepancy is greater for less liquid bonds. We include a dummy variable for firms belonging to a financial sector. We summarize our regression model for the spreads and their difference 6

7 in the following, (market spread) = β 1 (rating) + β 2 log(issue amount) + β 3 (yield discrepancy) + β 4 (financial sector) + β 5, (7) (CDS-implied spread) = β 1 (rating) + β 2 log(issue amount) + β 3 (yield discrepancy) + β 4 (financial sector) + β 5, (8) (market spread) (CDS-implied spread) = β 1 (rating) + β 2 log(issue amount) + β 3 (yield discrepancy) + β 4 (financial sector) + β 5, (9) The coefficient parameters are estimated by panel analysis with time-fixed effect 3. Data Our database records quarterly CDS premiums and bond prices from 2005Q3 to 2011Q3. The numbers of observations of CDSs and corporate bonds are given in Table 1. CDS maturity ranges from one to ten year; every one year up to five year, seven and ten year. Time series of CDS premium of Japan and that of recovery rate of Japan are depicted in Fig. 1. Time series of average CDS premium of Japanese firms by rating class are depicted in Fig JGB and corporate bond data are provided by the Japan Securities Dealers Association (JSDA). The JSDA has published the reference yields for over-the-counter bond transactions from August The reference yields are calculated by the JSDA, based on quotations reported by the designatedreporting members of the JSDA. The yield discrepancy is calculated from the highest and lowest quotation by the designated-reporting members of the JSDA. We select corporate bonds by the following criterion; their coupon rates are fixed, coupons are paid semi-annually, principal amount is fully repaid at the maturity, without call or put provisions, and remaining term to maturity of a bond is greater than one year. 7

8 4. Empirical result 4.1. Estimation of the CDS-implied spread We regard that the JGBs are not risk-free and sovereign CDS premiums of Japan reflect its credit risk. We simultaneously estimate the term structure of the risk-free rate and the term structure of the default intensity of Japan by minimizing sum of squared pricing errors of the JGBs under constraints that theoretical premiums of the sovereign CDS exactly coincide with the corresponding market premiums. The sum of squared pricing errors is defined as ( ) 2 PJGB,i P JGB,i, (10) i P JGB,i where P JGB,i and P JGB,i are the CDS-implied and market price of i-th JGB, respectively. The CDS-implied price of the JGB is calculated from eq. (3) with the default intensity estimated from the sovereign CDS premiums of Japan. The theoretical premium of CDS is calculated from eqs. (4) and (5). Time series of the estimated term structure of the forward rate and that of the default intensity of Japan are shown in Fig. 6 and Fig. 7, respectively. We assume that default risk of a firm is perfectly reflected in CDS premium. We estimate term structure of the default intensity for each reference company so that the theoretical premiums of CDS exactly coincide with the corresponding market premiums. Then CDS-implied price of a corporate bond is calculated by using eq. (3) 2. CDS-implied price of a corporate bond is estimated by using the risk-free rate and the default intensity of the issuing company. The CDS-implied and market spread of a corporate bond is calculated from the corresponding CDS-implied and market bond price, respectively. We calculate non-credit spread by subtracting the CDS-implied spread from the market spread. Scatter plots of the CDS-implied and market spread are provided in Fig Histograms of the non-credit spread are given in Fig We verify that recovery rate does not affect our result. We set the recovery rate depending on the credit rating. We also estimate the default intensity by taking the common recovery rate at 0.35, and we obtain similar result for the CDS-implied price of corporate bond. This is because the fact that lower recovery rate is compensated by higher level of default intensities and vice versa. Das and Hanouna (2009) discuss how to estimate the recovery rate from the market data. 8

9 4.2. Panel data analysis We apply panel data model to three kinds of spreads; the market spread, the CDS-implied spread, the non-credit spread defined as a difference between the market and CDS-implied spread. If CDS has no liquidity risk, the CDSimplied spread purely arises from credit risk, and the difference between the market and CDS-implied spread corresponds to non-credit risk, which consists of liquidity and other risk factors. Panel data model has many versions, and we employ fixed-effects for time variable since CDS premiums fluctuate wildly in the period as seen in Fig After the turmoil of the sub-prime loan crisis, CDS premiums are very high and corporate bonds are over-priced compared to CDS. Empirical results of the panel analysis are summarized in Table 2-4. We first examine the result for the market spread shown in Table 2. The empirical result shows that all of the explanatory variables are statistically significant. The adjusted R 2 for the market spread is The credit spread is well explained by the credit rating; the coefficient to the credit rating is , and it implies that spread widen as credit rating deteriorates. The coefficient to the logarithm of issue amount is , and it means that the larger issue amount has the tighter spread. Among the explanatory variables, the yield discrepancy is the most statistically significant, and the coefficient to the yield discrepancy is This is another evidence that the yield discrepancy is an effective measure for liquidity risk. The coefficient to the financial sector is , and it captures the fact that corporate bond spread for financial firm is higher than other firms. Next we examine the result for the CDS-implied spread. The empirical result shows that all of the explanatory variables are statistically significant. The adjusted R 2 for the CDS-implied spread is , and it is comparable to the result for the market spread. All of the magnitude of the regression coefficient for the CDS-implied spread is greater than that for the market spread. The credit spread is well explained by the credit rating; the coefficient to the credit rating is , and it is slightly greater than the coefficient for the market spread. It means that the CDS-implied spread reflect bond credit rating stronger than the market spread. On contrary to our assumption that CDS has no liquidity risk, the result suggests that CDS premium reflects the liquidity risk. The coefficient to the yield discrepancy is The coefficient to the logarithm of issue amount is , however, it is not statistically significant at 95% confidence level. It is interesting to notice that one of the liquidity measure, the yield discrepancy, is 9

10 statistically significant while another measure, the logarithm of issue amount is not. This distinction is interpreted as follows. There exist two type of liquidity risk for corporate bonds, firm-specific and bond-specific ones. The yield discrepancy is attributed to firm-specific liquidity risk, and the logarithm of issue amount is directly related to bond-specific liquidity risk. The coefficient to the financial sector is , and it is also greater than the market spread. We investigate the results on liquidity proxies, yield discrepancy and logarithm of issue amount. We conjecture that there exists two types of liquidity risk, company-specific liquidity and bond-specific one. The yield discrepancy reflects the company-specific liquidity, and it is statistically significant in the market and CDS-implied spreads. The logarithm of issue amount is the bond-specific liquidity, and is statistically significant for the market spreads but the CDS-implied spread. Finally, we examine the result for the non-credit spread. The result for the CDS-implied spread suggests that it is not appropriate to call the difference between the market and CDS-implied spread as the non-credit spread, however, we continue to use the term non-credit spread for backward consistency. The adjusted R 2 is , and it is quite low compared to the results for the market and CDS-implied spread. Except the coefficient to the logarithm of the issue amount, signs of the coefficient for the non-credit spread are opposite to that for the market and CDS-implied spread. The coefficient to the logarithm of issue amount is and it is statistically significant. Regarding the fact that the CDS-implied spread does not reflect the bond-specific liquidity risk, this is consistent with the result for the market and CDS-implied spread. The coefficient to the credit rating, the yield discrepancy, and dummy variable for financial sector are , , and , respectively. It is difficult to interpret these result, and further investigation is needed. 5. Conclusion Combining data on CDS premiums and corporate bond spreads, we study credit risk embedded in the market and CDS-implied spreads of corporate bonds. The CDS-implied spreads are calculated by applying the reducedform model for default risk and estimating the default intensity from CDS premiums. Both spreads as well as their difference are investigated by panel data analysis with time-fixed effects. Empirical study unveils that the market 10

11 and CDS-implied spreads are well explained by the credit and liquidity measures. It is found that CDS does not bear only credit risk but also liquidity risk. The CDS-implied spread is explained by one of the liquidity measure, the yield discrepancy. The yield discrepancy is comparable for a firm, and the yield discrepancy is a useful measure for firm-specific liquidity. In our future study, we investigate the firm-specific liquidity risk in detail. 11

12 References Bielecki, Tomasz R., and Marek Rutkowski, 2010, Credit Risk: Modeling, Valuation and Hedging, Springer, Springer Finance. Black, Fischer, and Myron Scholes, 1973, The pricing of options and corporate liabilities, Journal of Political Economy 81, Roberto Blanco, Simon Brennan, and Ian W. Marsh, 2005, An Empirical Analysis of the Dynamic Relation between Investment-Grade Bonds and Credit Default Swaps, The Journal of Finance 60, Das, Sanjiv R., and Paul Hanouna, 2009, Implied recovery, Journal of Economic Dynamics & Control 33, Das, Sanjiv R., and Rangarajan K. Sundaram, 2007, An integrated model for hybrid securities, Management Science 53, Duffie, Darrell, 2003, Credit Risk: Pricing, Measurement, and Management, Princeton University Press, Princeton Series in Finance. Duffie, Darrell, and Jun Liu, 2001, Floating-fixed credit spreads, Financial Analysts Journal 57-3, Duffie, Darrell, and Kenneth J. Singleton, 1999 Modeling term structures of defaultable bonds, The Review of Financial Studies 12, Houweling, Patrick, and Ton Vorst, 2005, Pricing default swaps: Empirical evidence, Journal of International Money and Finance 25, Hull, John, Mirela Predescu, and Alan White, 2004, The relationship between credit default swap spreads, bond yields, and credit rating announcements, Journal of Banking and Finance 28, Jarrow, Robert, 2001, Default parameter estimation using market prices, Financial Analysts Journal 57-5, Jarrow, Robert A., David Lando, and Stuart M. Turnbull, 1997, A Markov model for the term structure of credit risk spreads, The Review of Financial Studies 10,

13 Kagraoka, Yusho, 2010, A time-varying common risk factor affecting corporate yield spreads, The European Journal of Finance 16-6, Lando, David, 2004, Credit Risk Modeling: Theory and Applications, Princeton University Press, Princeton Series in Finance. Longstaff, Francis A., Sanjay Mithal, and Eric Neis, 2005, Corporate yield spreads: Default risk or liquidity? New evidence from the credit default swap market, The Journal of Finance 60, Unal, Haluk, Dilip Madan, and Levent Güntay, 2003, Pricing the risk of recovery in default with absolute priority rule violation, Journal of Banking & Finance 27, Schonbucher, Philipp J., 2003, Credit Derivatives Pricing Models: Model, Pricing and Implementation, Wiley. Vasicek, Oldrich Alfons, 2001, EDF TM credit measure and corporate bond pricing, Moody s Analytics, working paper. 13

14 Table 1: Description of observations. date CDS bond 2005Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q The numbers of observations of CDSs and corporate bonds are given. The second and third column are the number of CDS and that of corporate bonds, respectively. We select firms which are assigned as reference entities of CDSs and issue corporate bonds. 14

15 Table 2: Panel analysis for the market spread. Coefficient Std. Error t-statistic Prob. rating log(amount) yield discrepancy financial interception R Adjusted R The result of panel analysis with period-fixed effect is given. The market spread of a corporate bond is regressed by (market spread) = β 1 (rating) + β 2 log(issue amount) + β 3 (yield discrepancy) + β 4 (financial sector) + β 5, 15

16 Table 3: Panel analysis for the CDS-implied spread. Coefficient Std. Error t-statistic Prob. rating log(amount) yield discrepancy financial interception R Adjusted R The CDS- The result of panel analysis with period-fixed effect is given. implied spread of a corporate bond is regressed by (CDS-implied spread) = β 1 (rating) + β 2 log(issue amount) + β 3 (yield discrepancy) + β 4 (financial sector) + β 5, The CDS-implied price is estimated from CDS premiums. 16

17 Table 4: Panel analysis for the non-credit spread. Coefficient Std. Error t-statistic Prob. rating log(amount) yield discrepancy financial interception R Adjusted R The result of panel analysis with period-fixed effect is given. The non-credit spread which is defined as a difference of the market and CDS-implied spread is regressed by (market spread) (CDS-implied spread) = β 1 (rating) + β 2 log(issue amount) + β 3 (yield discrepancy) + β 4 (financial sector) + β 5, 17

18 Figure 1: CDS premium of Japan. CDS premium and recovery rate of Japan. 18

19 Figure 2: CDS premium of Japanese company. CDS premium of Japanese firm is averaged by rating class. The symbol NR represents Not Rated. The symbol NUL means that its rating data is not fulfilled. 19

20 Figure 3: CDS premium of Japanese company. CDS premium of Japanese firm is averaged by rating class. The symbol NR represents Not Rated. The symbol NUL means that its rating data is not fulfilled. 20

21 Figure 4: CDS premium of Japanese company. CDS premium of Japanese firm is averaged by rating class. The symbol NR represents Not Rated. The symbol NUL means that its rating data is not fulfilled. 21

22 Figure 5: CDS premium of Japanese company. CDS premium of Japanese firm is averaged by rating class. The symbol NR represents Not Rated. The symbol NUL means that its rating data is not fulfilled. 22

23 Figure 6: Risk-free rate by regarding JGBs are risky. The risk-free rate is estimated by regarding JGBs are risky. The CDS premiums of Japan is used to estimate their credit risk. The instantaneous forward rate is a step function with discontinuities at every one year in termto-maturity. 23

24 Figure 7: Default intensity of Japan. The default intensity of Japan in the reduced-form model is estimated. The default intensity is a step function with discontinuities at every one year up to five year, seven and ten years. 24

25 Figure 8: Scatter plot for market and CDS-implied spreads Scatter plot for market and CDS-implied spread. X-axis is the market spread. Y-axis is the CDS-implied spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 25

26 Figure 9: Scatter plot for market and CDS-implied spreads Scatter plot for market and CDS-implied spread. X-axis is the market spread. Y-axis is the CDS-implied spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 26

27 Figure 10: Scatter plot for market and CDS-implied spreads Scatter plot for market and CDS-implied spread. X-axis is the market spread. Y-axis is the CDS-implied spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 27

28 Figure 11: Scatter plot for market and CDS-implied spreads Scatter plot for market and CDS-implied spread. X-axis is the market spread. Y-axis is the CDS-implied spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 28

29 Figure 12: Scatter plot for market and CDS-implied spreads Scatter plot for market and CDS-implied spread. X-axis is the market spread. Y-axis is the CDS-implied spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 29

30 Figure 13: Scatter plot for market and CDS-implied spreads Scatter plot for market and CDS-implied spread. X-axis is the market spread. Y-axis is the CDS-implied spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 30

31 Figure 14: Scatter plot for market and CDS-implied spreads Scatter plot for market and CDS-implied spread. X-axis is the market spread. Y-axis is the CDS-implied spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 31

32 Figure 15: Histogram of the non-credit spread Histogram of the non-credit spread. The CDS-implied spread is subtracted from the market spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 32

33 Figure 16: Histogram of the non-credit spread Histogram of the non-credit spread. The CDS-implied spread is subtracted from the market spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 33

34 Figure 17: Histogram of the non-credit spread Histogram of the non-credit spread. The CDS-implied spread is subtracted from the market spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 34

35 Figure 18: Histogram of the non-credit spread Histogram of the non-credit spread. The CDS-implied spread is subtracted from the market spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 35

36 Figure 19: Histogram of the non-credit spread Histogram of the non-credit spread. The CDS-implied spread is subtracted from the market spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 36

37 Figure 20: Histogram of the non-credit spread Histogram of the non-credit spread. The CDS-implied spread is subtracted from the market spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 37

38 Figure 21: Histogram of the non-credit spread Histogram of the non-credit spread. The CDS-implied spread is subtracted from the market spread. The CDS-implied price is calculated by applying the reduced-form model whose parameters are estimated from CDS premiums. 38