DBJ Discussion Paper Series, No.1210

What Determines CDS Prices?
Evidence from the Estimation of Protection Demand and Supply

Daisuke Miyakawa(Development Bank of Japan)
And
Shuji Watanabe(Nihon University)

December

2012

Discussion Papers are a series of preliminary materials in their draft form. No quotations,reproductions or circulations should be made without the written consent of the authors inorder to protect the tentative characters of these papers. Any opinions, findings,
conclusions or recommendations expressed in these papers are those of the authors and do
not reflect the views of the Institute.

白紙

What Determines CDS Prices?
Evidence from the Estimation of Protection Demand and Supply

December 2012

Daisuke Miyakawa† and Shuji Watanabe‡
Development Bank of Japan and Nihon University

Abstract
This paper examines the determinants of Credit Default Swap (CDS) premiums by applying alimited dependent variable simultaneous equation system to a unique set of time-series data for theJapanese credit market. The estimation results indicate that CDS premiums decrease as a result of anincrease in the supply of protection due, for example, to fewer opportunities for investment in otherassets (e.g., loans). We also find that premiums increase when the demand for protection increases
due, for example, to larger short cover needs. Further, the quantitative impact of factors accounting
for the supply and demand of protection is likely to be misestimated unless the simultaneous
determination of supply and demand is taken into account. This indicates that it is necessary toinclude demand and supply factors to understand fluctuations in CDS premiums.

Key words: Credit Default Swap; Demand and Supply; Simultaneous Equation; Credit Link Note
JEL Classification: G12, C34, C36,

We thank would like to thank Tatsuyoshi Okimoto (Hitotsubashi University), Takayoshi Kitaoka (Meiji University),
Kentaro Akashi (Gakushuin University), Hiroaki Yamauchi (MTEC), Masazumi Hattori (Bank of Japan), Toyoichiro
Shirota (Bank of Japan), Robert Dekle (University of Southern California), and seminar participants at the ResearchInstitute of Capital Formation, the Development Bank of Japan (RICF-DBJ), the Japan Society of Monetary
Economics 2012 spring meeting, the Nippon Finance Association 2012 annual meeting, and the Bank of Japan
Institute of Monetary and Economic Studies Seminar for helpful suggestion. We are also grateful to Takeshi Moriya
for excellent research assistance.
†
Corresponding Author, Associate Senior Economist, Research Institute of Capital Formation, Development Bank ofJapan, 1-9-3 Otemachi Chiyoda-ku, Tokyo, 100-0004 Japan. Phone: +81-3-3244-1917. E-mail: damiyak@dbj.jp.
‡
Professor, College of Economics, Nihon University, 1-3-2 Misaki-cho, Chiyoda-ku, Tokyo 102-8360 Japan. E-mail:watanabe.shuji@nihon-u.ac.jp.
-1-1. Introduction
Credit default swaps (CDS) are a type of credit derivatives written against the default of a
specific firm, security, country, or a basket of these. They function as an insurance against default
events and have been widely used as a hedging tool as well as a speculation tool in recent years.
However, during the recent financial crisis, substantial turmoil in CDS markets could be observed.
Indexes of CDS spreads (i.e., the premium paid for protection) in the United States, Europe, andJapan show large jumps from early 2008 onward in response to the financial crisis triggered by the
malfunctioning of U.S. credit markets, which was accompanied by a sharp decline in the prices of
securitized products based on various underlying assets.
Given the growing presence of CDSs in financial markets and such large fluctuations in
CDS premiums, many academic researchers and practitioners have been trying to establish thedeterminants of such premiums. The list of candidates includes macro and micro credit factors (e.g.,stock prices and bond prices) directly affecting the default probability of the entities referenced by
CDSs as well as factors relatively specific to credit markets (e.g., counter-party risk, market
segmentation, illiquidity). Thanks to the research effort into the mechanisms governing CDS markets,the role of the various determinants is now largely understood. However, an issue that has received
surprisingly little attention in this context so far is the role played by the demand for and supply ofprotection through CDSs. Against this background, the aim of the present paper is to examine thedeterminants of CDS premiums explicitly taking such demand and supply into account.
The empirical strategy employed in the large majority of extant studies has been to regress
the CDS premium on various covariates representing factors accounting for credit and liquidity in asingle equation (e.g., Huang et al. 2003; Blanco et al. 2005; Scheicher 2008; Ericsson et al. 2009). In
other words, CDS premiums have been considered as a measure of the default risk and assumed not
be affected by the demand for and supply of CDSs. In contrast, the present study explicitly
introduces the notion of demand and supply, which has been widely considered as a key determinantof prices in other financial markets such as stock, government and corporate bond, and foreignexchange markets. Specifically, we examine how the interaction of the demand for and supply ofprotection affects an index of CDS premiums in the Japanese credit market.
While it is relatively easy to measure the price of protection using indexes of premiums in
CDS markets (e.g., the various indexes provided by Markit Group Ltd. such as the iTraxx Japan for
the Japanese credit market), the quantity of CDS transactions is more difficult to observe. It isparticularly difficult to obtain information on the volume of each transaction, mainly due to the lackof a central clearing system. This is the biggest reason making it difficult to study the demand forand supply of protection. We should note, however, that most of the transactions among market
makers, which account for the majority of transactions, are offset in a relatively short period bytransactions in the opposite direction. This reflects the intention of market makers to “square” their-2-

positions as soon as possible.1 Our empirical strategy in this paper is to take advantage of thisfeature and exclusively focus on the flow in trades for “outright” protection, which account for
positions held for a long period. We use the issuance volume of credit linked notes (CLNs), which
are securitized products written against CDSs, as a proxy for the trade flow in outright protection.
Due to the lack of a secondary market and high transaction costs, the standard investment strategy
for CLNs is “buy-and-hold,” which assures that the trade for protection associated with the CLN
investments tends to be held for a long period, mostly until their maturity.
An additional technical problem originating from the use of CLN data is that we observea large number of zero amounts of CLN issuance. This is partly because most of the CLNs are
tailor-made and incur time and costs to deliver. Moreover, investors in CLN are relatively limited. To
deal with such truncated data, we employ a simultaneous equation Tobit model of the type first
proposed by Nelson and Olson (1978) and refined by Amemiya (1979).
Our estimation shows that not considering the simultaneous equation system likely resultsin substantial misestimation of the impact of changes in the exogenous shift variables for theprotection supply and demand curves. This could be interpreted as a sign of simultaneity bias in the
reduced form regression. Our estimation also shows that the impact of some factors on CDS
premiums could not be identified when we do not properly take the truncated sample into account.
These results imply that, to examine the determinants of CDS spreads, it is necessary to explicitly
consider demand and supply as well as the potential bias originating from the limited dependent
variable (i.e., the truncated data on transaction volumes).
The remainder of the paper is organized as follows. The next section provides an overview
of the basic structure of CDSs and the related securitized products markets. Section 3 briefly surveys
the literature on the determinants of CDS premiums. Section 4 then describes the data and theempirical framework used for our analysis, while Section 5 discusses the results. Section 6 concludes
and highlights remaining issues.

2. Basics of Credit Default Swap Markets and Credit Linked Notes
Figure 1 provides a conceptual depiction of the CDS market. Transactions in CDSs, thatis, the selling and buying of protection, can take place between (i) outright protection sellers andmarket makers, (ii) outright protection buyers and market makers, and (iii) among market makers
themselves. Almost all the transactions are executed as over-the-counter (OTC) transactions and1

That transactions are typically largely offset within brief periods is illustrated by the following quotes from a recent
Bloomberg article: “JPMorgan purchased single-name contracts protecting $147.3 billion of debt and sold $142.4
billion related to the so-called GIIPS nations of Greece, Ireland, Italy, Portugal and Spain.” Moreover: “JPMorgan
said ‘master netting agreements’ reduced the notional amount of protection purchased to $18.5 billion and the amountsold to $13.7 billion.” (Source: Bloomberg.com, February 29, 2012, “Goldman Mirrors JPMorgan Mirrors Goldman
on Swap Exposure to European Debt,” sic).
-3-

cannot be easily tracked.2 Since most of the transactions among market makers are squared in shortperiods, however, the transaction volume in CDS markets which affects the CDS premium is likely
to be mainly affected by transactions in outright protection, which are proxied by the issuancevolume of CLNs.
CLNs are securities that resemble bonds and provide fixed coupon payments to theirholders.

3

Figure 2 illustrates how CLNs and CDSs are linked. The right-hand side showstransactions in CDSs, which take place between securities firms and outright protection buyers.
Securities firms play the role of sellers of protection against some default event and receive apremium in return. Outright buyers buy the protection and use it, for example, to hedge the credit
risk in their portfolio or to buy protection with a speculative motive.4 Next, the left-hand side showstransactions in CLNs, which are originated by the securities companies and sold to outrightprotection sellers, who receive the coupon on the CLNs, which is based on the premium associatedwith the CDSs and the return on the invested principal. In this sense, the demand for and supply of
CLNs are accompanied by protection selling and buying, respectively. The coupon payment may becontingent on a default event relating to a specific company, or a range of companies. Moreover, thecontingency may be designed in a variety of ways. 5,6 An important feature is that the CLN
investment positions are in general held for a long period due to the lack of a secondary market for
CLNs and high transaction costs. This is the reason why it is appropriate for our analysis to measure
outright transactions in CDSs based on CLN issuance data.
A graphic representation of what our empirical study seeks to examine is presented in
Figure 3. In the diagram, the volume of CDS transactions, proxied by the issuance of CLNs, isplotted on the horizontal axis, while the price, proxied by the iTraxx Japan index for CDS premiums,
is plotted on the vertical axis. Suppose that protection sellers (i.e., CLN investors = outrightprotection sellers) have a large capacity for investing in CLNs and outright protection buyers do notshow large demand for protection. Under such circumstances, the spread would be tight, since thesupply of protection is large, while the demand for protection is limited. However, if, for example,
the perceived risk of investing in CLNs increased, the protection seller curve would shift upward(i.e., t=1), since the appetite for CLN investment becomes smaller. Similarly, the protection buyer

2That being said, data on individual CDS transactions is increasingly being disclosed (e.g., by the Depository Trust& Clearing Corporation (DTCC)), but the amount of data accumulated on such transactions to date is insufficient foranalytical purposes. For Japan, the BOJ has been releasing data on CDS transaction volumes aggregated for eachsix-month period.
3
Synthetic collateralized debt obligations (CDOs) are included in the CLNs considered in this paper. Note also thatsome CLNs have floating coupon payments, but the number of such cases is limited.
4
Investors may buy CDSs for speculative purposes rather than for protection. In this case, they aim to make a profit
by buying CDSs when premiums are low and selling them when premiums are high.
5
Most CLNs are sold in units of 2 billion yen and are highly customized to suit each investor’s preferences.
6
As a typical example, the coupon payment to investors in CLNs categorized as first-to-default (FTD) is terminatedand only part of the principal of the CLNs is paid back to investors when one of the firms referenced by the CLN
contract defaults. The rise of CLNs in the Japanese credit market is largely driven by the issuance of such FTD-type
CLNs.
-4-

curve would shift up when, for example, the demand for protection increases due to a larger need forrisk hedging (i.e., t=1).7 We conjecture that the sharp rise in CDS spreads during the recent financial
crisis actually emerged due to such shifts in both protection selling and buying.
There have been many investors in Japan who require products with higher risks andhigher returns than offered by traditional investment assets (e.g., Japanese government bond). Overthe last decade, securities firms have been providing various securitized products such as mortgage
backed securities (MBS) and CLNs to investors with a high risk-return appetite. This rising demand
for securitized products has led securities firms to sell protection in CDS markets to procure theunderlying assets for securitized products. One of our main conjectures is that such demand pressurein the securitized products markets, which works as supply pressure in the CDS market, plays acentral role in the determination of premiums in the CDS market.

3. Related Literature
The pricing implications of imbalances in supply and demand have received considerable
attention in theoretical studies on CDS markets (e.g., Bollen and Whaley 2004; Brunnermeier andPedersen 2009; Garleanu et al. 2009). However, when it comes to empirical studies on CDS pricing,
despite their substantial number (e.g., Huang et al. 2003; Longstaff et al. 2005; Ericsson et al. 2009;
Scheicher 2008), there are hardly any that explicitly that take into account the notion of supply anddemand. A notable exception is the study by Tang and Yan (2011), which employs the difference
between the number of bids and offers as a proxy for imbalances in supply and demand. They showthat such imbalances have a statistically significant and sizable impact on CDS spreads. Similar to
the approach taken in this paper, they attempt to take into account the simultaneous determination of
CDS prices and transaction volumes by using two-stage least squares estimation. The present study
takes the analysis a step further and explicitly examines shifts in the protection seller and buyer
curve and the impact of such shifts on CDS spreads – something that is not discussed in Tang andYan’s (2011) study.
While the impact of supply and demand imbalances in CDS markets has remained largely
unexplored, this is not the case for other financial markets. Starting from the pioneering study by
Kraus and Stoll (1972), numerous studies, such as Chordia et al. (2002), Chordia and Subramanyam(2004), Coval and Stafford (2007), Sarkar and Schwartz (2009), and Hendershott and Menkveld(2012) have examined and confirmed the impact of supply and demand and on stock prices.
Similarly, Greenwood and Vayanos (2010) and Krishnamurthy and Vissing-Jorgenson (2012) haveexamined the role of supply and demand in the determination of government bond prices, while Ellul
et al. (2011) did the same for corporate bond prices. Against this background, the role of supply and7

We will provide more details on the mechanisms further below.
-5-demand in the determination of CDS prices remains an important gap in the literature, which thepresent study seeks to fill.

4. Data and Empirical Framework
4.1. Data and Hypotheses
This section provides a description of the data we use for our empirical analysis and setsout our hypotheses. We begin by describing our data. As our variable representing CDS premiums,
we use the Markit iTraxx Japan (iTraxx_P) index. This is an index of the CDS premium in theJapanese credit market and consists of a basket of five-year CDSs for 50 investment-grade Japanesefirms with the highest market liquidity.8 This index, which is updated daily, is computed from the
spreads reported by licensed market makers.
In contrast with the ready availability of such price data, data on the quantity of CDS
transactions is difficult to obtain due to the lack of a centralized clearing system. Therefore, we
instead use data on the issuance of CLNs (CLN_ISSUE_Q) from January 2002 to March 2011, which
we collected from information released by Rating and Investment Information Inc. (R&I).
Specifically, the data on CLN issuance that we use for our empirical analysis consist of roughly 400
issuances worth almost 1.1 trillion yen. We exclude two large issuances, that by Bank of Tokyo
Mitsubishi UFJ in 2006 and that by Mizuho Corporate Bank in 2009, as outliers.9 We construct
weekly frequency data and compute the moving average of CLN_ISSUE_Q, since the impact of
CLN issuance on the CDS market is presumably not limited to the exact date of issuance but also
extends to adjacent periods. This could be the case when, for example, the timing of the CDS
transactions associated with the origination of CLNs are spread around the date of CLN issuance.
Note that there are still a large number of zeros for CLN_ISSUE_Q in our dataset after taking themoving average. For consistency with the quantity data, we therefore transform the daily iTraxx
Japan data into weekly data by taking the average for each week.
As detailed in the next subsection, we model price determination in the CDS market as anequilibrium between protection selling and buying. Specifically, we consider traditional investors in
the Japanese credit market such as Japanese domestic banks and various institutional investors as
outright protection sellers. To measure their risk-taking capacity, we use the level of the Nikkei 225
Stock Index (NKY_AVG). In order to take the average investment return on alternatives toinvestments in CLNs into account, we use the five-year yield on Japanese government bonds(JGB_5Y). Another variable we include is the average change in credit ratings of existing CLNs. To

8

The reasons that we focus on the Markit iTraxx Japan index rather than the CDS premium for each of the 50 firms
are twofold. First, it is difficult to map the information on CLN issuance for each CLN issue to the referenced
individual firms. Second, the Markit iTraxx Japan index is traded in the market as an individual investment tool.
9
These two synthetic CDOs were issued for risk hedging against the banks’ loan portfolios.
-6-

precisely measure the impact of rating changes, we multiply the issuance amount of each CLN by
the concurrent change in the rating of the CLN, the latter of which takes one (minus one) when the
CLN is downgraded (upgraded) by one notch.10 We conjecture that a larger value of this variable(RATING_CHANGE) is associated with a higher credit risk of the CLN portfolio, which leads
protection sellers to require a higher premium and to be more cautious about any additional
investment. Protection sellers’ investment attitude may also be related to the availability of loan
investments. Suppose banks face a very low level of loan demand and need to find alternative
investment opportunities. In this case, such investors may be willing to sell protection at a relatively
low premium. To take this conjecture into account, we use the aggregate-level loan-to-deposit ratioof commercial banks (LOAN_DEPOSIT) reported by the Bank of Japan as another exogenous shifterof the protection seller curve. The hypothesis we test for these variables is as follows:

Hypothesis 1: The upward-sloping protection seller curve shifts upward (i.e., protection sellers arewilling to sell less protection at the same premium as before) when NKY_AVR decreases (investors’
risk-taking capacity decreases), JGB_5Y increases (the returns on other investments increase),
RATING_CHANGE increases (the risk of holding CLNs increases), and/or LOAN_DEPOSIT
increases (business opportunities in commercial banks’ main business improve).
We assume that speculative investors such as hedge funds and investment banks are thebuyers of outright protection. As factors shifting the protection buyer curve, we use the difference
between three-month dollar Libor (London inter-bank offered rate) and the three-month yield of U.S.
treasury bills (LIBOR_TREASUR3M), which we regard as a measure of the marginal funding cost offinancial institutions and which can be seen as a measure of risk in financial markets. We conjecturethat higher risk in the future as measured by a higher LIBOR_TREASUR3M leads speculative
investors to buy protection, which results in an upward shift of the protection buyer curve.
We also measure the change in the potential losses or gains from CLN purchased at time s
as of the current period t (MARK_TO_MKT). For simplicity, we assume that the maturity of all
CLNs is 5 years, which means that all of the existing CLNs have been issued during the five years
preceding t.11 Since a CLN issued at time s matures five years after s, semi-annual coupon
payments are made at time sk/2k

1,2, ⋯ ,10 . We denote the number of coupon payments

on a CLN issued at time s during the period t to s

5 by X s, t . Thus, MARK_TO_MKT isexpressed as the product of (i) the principal of the CLN issued at s (A ), (ii) the price change
between the issuance date s and t P

P , and (iii) X s, t .12 Since the existing CLNs at time10

An upgrade by one notch means, for example, a change from A to A+.
We focus on the potential losses and gains on CLNs with a maturity of 5 years, since these are the most actively
traded CLNs in the CDS market.
12
For simplicity, we further assume that 1year consists of 52 weeks.
11-7-were issued during the period from

5 to , we aggregate this measure over these periods to13

construct MARK_TO_MKT.

As MARK_TO_MKT becomes negative, the potential losses for CLN holders becomelarger (i.e., if the CLNs issued at time

have a very low coupon rate, investors incur large losses attime ). We conjecture that the protection buyer curve shifts up as this value falls. This would be thecase when securities firms, which are assumed to square their positions, buy more protection because
their sell-position against outright protection buyers is incurring losses. Such losses require securities
firms to provide additional collateral to the outright protection buyers in order to fulfill the CDS
contract (i.e., the counter-party risk increases for the original outright buyer). However, the securities
firms are not allowed to use the principal of the CLNs they received when the CLNs were issued.
Rather, the securities firms are required to hold the principal as collateral in case an actual credit
event occurs and the firm referenced by the CLNs defaults. In order to obtain funds they can use asadditional collateral, securities firms can buy protection (i.e., short cover) and obtain the collateralfrom the new protection seller in the transaction. In addition, the securities firms may want toprocure the protection in advance to prepare for the selling request from original outright protection
buyers. In any case, the existence of such “new” protection buyers generates an upward shift of theprotection buyer curve. The hypothesis relating to the protection buyer curve can thus be stated asfollows:

Hypothesis 2: The downward-sloping protection buyer curve shifts upward (i.e., protection buyers
are willing to buy more protection for the same protection fee) when LIBOR_TREASUR3M
increases (protection buyers have a stronger speculative motive for buying protection) and/or
MARK_TO_MKT decreases (protection buyers have a stronger short-cover motive).
A full list of the variables we use in our estimation, their definitions, and summary
statistics is provided in Table 1. Further, Table 2 presents the correlation coefficients between thevarious variables. Our observations cover the period from August 2004 to April 2011, spanning a
total of 348 weeks.

4.2. Empirical Framework
Our goal in this paper is to estimate the supply and demand functions of protection with
non-truncated price data (P: iTraxx_P) and truncated quantity data (Q∗ : CLN_ISSUE_Q). For thispurpose, we consider a two-equations model consisting of equations 1

1 and 1

2 , where

the first equation represents the seller function and the second represents the buyer function. As we

13

Given the large variation of P P , we apply a monotonic transformation to P P by using the product of(i) the sign of P P and (ii) the square root of the absolute value of P P , instead of simply using P P .
-8-detailed above, Q∗ is truncated at zero. Q∗ takes a positive value when CLNs are issued in theweek, and zero otherwise. Specifically, the model looks as follows:
P

γ Q∗

X β

u

1

1

Q∗

γ P

X β

u

1

2

if Q

Q∗

0,

Q∗

0

Here, X represents the exogenous shift variables for the protection seller curve (i.e.,
NKY_AVR, JGB_5Y, RATING_CHANGE, and LOAN_DEPOSIT), while X

represents theexogenous shifters for the protection buyer curve (i.e., LIBOR_TREASUR3M and MARK_TO_MKT).
This system is identical to the model proposed by Nelson and Olson (1978) and refined by Amemiya(1979). Note that if we did not need to take into account the limited dependent variable Q∗ , wecould simply run the usual two-stage least squares estimation for the simultaneous equation system.
However, in order to deal with the fact that CLN issuance often takes a zero value, we need to use
the model above.
As explained in detail by Nelson and Olson (1978) and Amemiya (1979), the predictedvalues of the endogenous variables are estimated using OLS or MLE in the first-stage regression.
The parameters Π , Π

in the reduced-form equations 2

1 and 2

2 , which represent thecoefficients associated with all the exogenous variables X, are estimated from this first-stage
regression as follows:14
P

XΠ

v

2

1

Q∗

XΠ

v

2

2

if Q

Q∗

0,

Q∗

0

where
Variance

Covariance matrix of v , v

As in Amemiya (1979), the results of the first-stage regression Π , Π , where Π andΠ

are respectively the OLS and Tobit MLE estimates, are used to estimate the structuralparameters γ , γ , β , β . Note that uthat 12

1 and 1

2 into 1v

γ v and u

2 are identified from 2

1 and 2v

γ v need to be satisfied so

2 . Substituting the results from1 yields the following expression, which provides us with α through standard

OLS estimation:

14

A similar issue is discussed in the paper by Keshk (2003), which explains the Stata command for simultaneous
equation probit models.
-9-

P

γ XΠ

γ v

X β

u

γ XΠ

X β

v

X Π ,Jγβw ≡ XHα

w

γ X Π

Π ,

γ X Π

Π
3

Where
XJ

X , w

v

H

Π ,J , αγβα as follows:

Here, we can compute α

α

γ
β

α

γ
β

H′X′XH

H′X′w

This allows us to further compute the variance-covariance matrix of α :V ασ

H′X′XH2γ σγ

H′X′XHH X XV Π X XH H X XH

Given the relationship between Πand w , we can use the following formula proposed by

Amemiya (1979) with regard to V w

to compute V α , which we need to correctly evaluate α :

V w

V v

XV w X

γ E Π

Π

2γ σ

XX

σ

Xv

X Π ,Jγβw ≡ XGαΠγ XV Π X

γ X XV Π X X

From the same manipulation of 2Q∗γ E v ′X Π

1 and 1

2 , we can derive an expression similar to 3 :

w

4

where
XJ

X ,w

G

Π ,J , α

v

γ X Π

Π ,

γ
β

As demonstrated by Amemiya (1979), θ ≡ α , σargmax L Π , α , σlinearizing the normal equation 4 , assuming that v , vfollow the normal distribution N 0, v ,is estimated byand constructing the likelihood function for the Tobit estimation. We obtain the following result:- 10 -

θ

θ ≡

α
σ

α
σ

X′X

X′v

E

∂ logL∂θ ∂θ ′

∂logL
∂θ

E

∂ logL∙ Π∂θ ∂H ′

Π

where
Π

Π

means both sides of the equation have the same asymptotic distribution.
Given that the following relationship holds, we can compute V α :
Π
σ

G 0 α
0′ 1 σ

V α

GV Π

G

γ σ

2γ σ

GV Π

G

GV Π

X′X

V Π

G GV Π

G

In this context, it is worth noting that the instrumental variable Tobit model proposed bySmith and Blundell (1986) and Newey (1987), which considers the following limited information
simultaneous equations system with one structural equation (i.e., one endogenous variable) in
5

1 and

P

γ Q∗

X β

X Π

X Π

∗

Q

5

2 , produces the same estimators, but the standard errors are different:
u
v

5

1

5

2

In the next section, we present the estimated coefficients of the simultaneous equation systemconstructed above, for which statistical inference is made by using the variance-covariance matrix
computed as above. We also show the results for the model represented by

5

1 and

5

2

for comparison.

5. Estimation Results
5.1. Baseline Estimation Results
The baseline results of our empirical analysis are presented in Table 3. The columns on theleft show the results for the first-stage regression, while those on the right show those for thesecond-stage regression. The first-stage estimation regressing CLN_ISSUE_Q on all the exogenous
variables is provided in the upper part on the left-hand side. The results of this estimation are used toestimate the seller curve in the second stage, which is shown in the upper part on the right. Similarly,- 11 -

the first-stage estimation regressing iTraxx_P on all the exogenous variables is presented in thelower part on the left-hand side and the results are used to estimate the buyer curve in the second
stage. The results are shown in the lower part on the right-hand side. For the second-stage regression,both standard errors based on the variance-covariance matrix computed as in Amemiya (1979) andnon-corrected standard errors used for the model represented by 5

1 and

5

2 are shown.

The non-corrected standard errors underestimate the true standard errors because they do not reflect
the errors from the first-stage estimation.
Let us take a look at the results. First, the upper and lower parts on the right-hand side
show that the protection seller curve has a significant positive slope (1.5175), while the protection
buyer curve has a significant negative slope (-1/0.5482), which is consistent with our conjecture.15
Second, the protection seller curve shifts down (i.e., protection sellers are willing to sell more
protection at the same premium as before) when general economic conditions improve (i.e.,
NKY_AVG is higher). Third, as the yield on Japanese government bonds decreases (i.e., JGB_5Y
falls), protection sellers attempt to sell more protection. The latter result implies that Japanese
government bonds are an alternative investment asset to CLNs. Fourth, such a downward shift of theprotection seller curve can be also observed when opportunities for loan investments by banks
decrease (LOAN_DEPOST falls). When banks find it difficult to invest the deposits they take into
traditional loan assets, they tend to use the funds to buy, for example, CLNs, as discussed above.
Fifth, protection sellers also tend to sell more protection when the risk of CLN portfolios is lower(i.e., RATING_CHANGE is lower).
The lower part of the second-stage estimation represents the estimated protection buyer
curve. The negative-sloping buyer curve shifts upward when the speculative motive becomesstronger (i.e., LIBOR_TREASUR3M increases) and/or the short-cover motive becomes moresignificant (i.e., MARK_TO_MKT decreases).
Figure 4 depicts the protection seller and buyer curves for five sub-periods using theestimated coefficients from Table 3 and the values for the exogenous variables for the fivesub-periods. As can be seeing in panels (a) and (b) of Figure 4, the two curves intersect at relatively
low levels of iTraxx_P – below 100 basis points – during the early part of our observation period.
The intersection shifts up somewhat in the run-up to the collapse of Lehman Brothers in September
2008 (Figure 4(c)) and then jumps to 300 basis points and more in the wake of the collapse of
Lehman Brothers (Figure 4 (d)). Interestingly, the price dynamics prior to the collapse of Lehman
Brothers are mainly driven by a shift in the protection seller curve. On the other hand, shifts in boththe protection seller and buyer curves led to the sharp rise in iTraxx_P after the Lehman collapse,
which confirms our conjecture that both sides contributed to the sharp rise in CDS premiums.

15

Note that, in this estimation, we set CLN_ISSUE_Q as the dependent variable and, in order to compare theseslopes, we need to take the inverse of the estimate.
- 12 -

5.2. Two Sources of Potential Bias
In this subsection, we examine the two potential biases originating from (i) ignoring
simultaneity and (ii) ignoring the limited dependent variable. First, the right-hand side of Table 4shows the estimated coefficients when we ignore the simultaneous equation system. In thisestimation, the price (quantity) is regressed on the quantity (price) and all other exogenous variables
simply using the OLS (Tobit) specification instead of employing two-stage estimation. The
estimation based on the incorrectly specified iTraxx_P model (i.e., the upper part on the right-handside) yields, for example, an insignificant coefficient on LOAN_DEPOSIT. The impact of the twovariables NKY_AVG and JGB5Y, which was found to be significant in the baseline estimation, also
becomes insignificant in this estimation. These results mean that it is necessary to consider bothdemand and supply to examine the determinants of CDS premiums.
Second, to investigate the role of another source of bias, namely that resulting fromignoring the limited dependent variable, we implement linear instrumental variable estimations for
iTraxx_P and CLN_ISSUE_Q, the results of which are shown in Table 5. Given that the purpose ofthis exercise is to examine the bias associated with ignoring that CLN_ISSUE_Q is truncated, theestimation is implemented using regular two-stage least square estimation instead of the model in
1

1 and 1

2 . The results indicate that the signs of the coefficients are consistent with thoseof the baseline estimation. To investigate whether the economic impact of each of the exogenous
variables is similar in the two estimations, we compute the change in the predicted value of iTraxx_P
when each variable increases by one standard deviation. The results are shown in Table 6.16 The
column labeled “Baseline” shows the results for the baseline estimation, while that labeled “Ignoring
LDV” shows those when ignoring that CLN_ISSUE_Q is truncated. The impacts of the shift
variables for the protection seller curve (i.e., NKY_AVG, JGB5Y, RATING_CHANGE, and
LOAN_DEPOST) are almost twice as high in the case of the incorrectly specified model. Thisimplies that we would overestimate the impact of these variables if we do not correctly take into
account the truncation of CLN_ISSUE_Q.
As another comparison between the correctly and incorrectly specified models, the center
column in Table 6 also shows the computed magnitude of each covariate in the estimation of the“single” equation, which ignores the simultaneity. The fact that the loan-to-deposit ratio is not
significant in the incorrectly specified single equation model suggests that the quantitative impact ofa change in the loan-to-deposit ratio would be measured incorrectly if we do not take thesimultaneous equation system into account. Figures 5 and 6 compare the observed price and quantity
dynamics with the model prediction. The figures show that our model predicts the price and quantity
dynamics reasonably well.
16

The results in Table 6 are obtained by solving the simultaneous equation system.
- 13 -

6. Conclusion
This paper examined the determinants of CDS premiums by employing a simultaneous
equation system consisting of the demand for and supply of protection. The results suggest that CDS
premiums rise when the protection supply curve shifts upward, which may occur when investors’
risk-taking capacity decreases, the returns on alternative investment assets increases, average credit
ratings of existing CLNs in the market deteriorate, and/or business opportunities in commercial
banks’ main business improve; CDS premiums also rise when the protection demand curve shifts
upward, which may occur when the speculative motive and/or the short-cover motive become
stronger. The analysis also showed, however, that the quantitative impact of these factors would bemisestimated unless the simultaneous determination of supply and demand as well as the limited
dependent variable are taken into account. These results mean that, to understand fluctuations in
CDS premiums, it is necessary to explicitly consider demand and supply factors just as in the case of
prices of other financial assets, as well as the truncated data on transaction quantities.
The research presented in this study could be expanded in a number of directions. One
such direction would be to extend our analysis to the determinants of single name CDS spreads
through a panel estimation framework. In order to measure the outright demand for protection withregard to exposure to individual firms, however, we need to collect more comprehensive transaction
data. Second, a further, potentially interesting extension would be to apply the model in this paper toexplicitly analyze the determinants of the spreads of corporate bonds. Third, an important remaining
issue would be to analyze transactions among market makers, which in this paper are assumed toplay a neutral role. We believe all of these extensions would provide further insights to gain a better
understanding of pricing in the CDS market.

- 14 -

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- 16 -

Figure 1: CDS Market

Outright Protection Buyers(Receive Protection &Pay Premium)

Outright Protection Sellers(Provide Protection &Receive Premium)

CDS Market (MM: Market Maker)

MM

MM

MM

MM

MM

MM

- 17 -

Figure 2: CDS and CLN Markets
CLN Market

CDS Market

CLN Coupon Payment

Premium Payment= CDS Premium payment
Outright
Protection
Sellers

Securities
Firms

Outright
Protection
BuyersBuy CLN

Sell Protection= Sell protection(through CDS)

Figure 3: Protection Seller and Buyer Functions
P: CDS Premium

Buyer (t=1)
Seller (t=1)

Seller (t=0)
Buyer (t=0)

Q: CDS Transaction Volume
Seller sells protection & Buyer buys protection

Note: The figure shows the protection selling and buying curves at t=0 (e.g., prior to an event) and t=1 (after the
event).

- 18 -

Figure 4: Demand for and Supply of Protection in Five Subperiods(a) 2006/11-2007/4
500

400

iTraxx

300

200

100

0

-100
-100

0

100

200
CLN Issue Amount

300

400

500

400

500

(b) 2007/7-2007/12
500

400

iTraxx

300

200

100

0

-100
-100

0

100

200
CLN Issue Amount- 19 -

300

Figure 4 (continued): Demand for and Supply of Protection in Five Subperiods(c) 2008/2-2008/7
500

400

iTraxx

300

200

100

0

-100
-100

0

100

200
CLN Issue Amount

300

400

500

400

500

400

500

(d) 2008/10-2009/3
500

400

iTraxx

300

200

100

0

-100
-100

0

100

200
CLN Issue Amount300(e) 2010/3-2010/8
500

400

iTraxx

300

200

100

0

-100
-100

0

100

200
CLN Issue Amount

300

Note: Each figure plots the protection selling and buying curves based on the estimated results. The intersections of
the two curves are obtained by solving the simultaneous equation system.

- 20 -

Figure 5: Predicted Price
600

500

Basis Points

400

300
P
Predicted P
200

100

0
2004/08/06

2005/08/06

2006/08/06

2007/08/06

2008/08/06

2009/08/06

2010/08/06-100

Note: P stands for the actually observed iTraxx Japan, while Predicted P is the model prediction. Each point isobtained by solving the estimated simultaneous equation system.

Figure 6: Predicted Quantity
250

200

Basis Points

150

Q

100

Predicted Q

5002004/08/06

2005/08/06

2006/08/06

2007/08/06

2008/08/06

2009/08/06

2010/08/06-50

Note: Q stands for the actually observed CLN issuance volume, while Predicted Q is the model prediction. Each point
is obtained by solving the estimated simultaneous equation system.
- 21 -

Table 1: Summary Statistics

Variable

Definition

Unit

Obs.

Mean

Std. Dev.

Min.

Max.

iTraxx_P

Markit iTraxx Japan

bp

348

93.37

97.13

16.26

552.94

CLN_ISSUE_Q

Issued CLN amount

100 million
yen

348

22.72

35.63

0.00

214.00

NKY_AVG

Monthly average of Nikkei 225
Stock Index

yen

348

12629

3012

7257

18191

JGB_5Y

Yield of 5-year Japanese
government bonds

bp

348

84

33

23

154

RATING_CHANGE

Issued amount of each CLN times
the concurrent change in its ratings(1 if downgraded and -1 if
upgraded)

-

348

2113

2756

-23

6993

LOAN_DEPOSIT

Loan to deposit ratio

%

348

75.68

1.74

70.43

78.29

MARK_TO_MKT

Potential gains (positive number)and losses (negative number) from
CLNs investment-348-17.5726.85-117.55

6.14

LIBOR_TREASUR3M

3-month Libor minus yield on 3month US treasuries

bp

348

58.95

60.03

9.99

410.93

Note: The table shows the summary statistics for the variables used in the estimation. Our observation period isfrom August 2004 to April 2011, providing 348 weekly observations for each of the variables.

- 22 -

Table 2: Correlation Coefficients(Obs.=348)
(1)

(1)

(2)

(3)

(4)

(5)

(6)

(7)

iTraxx_P

1.00(2) CLN_ISSUE_Q

-0.14

1.00

(3) NKY_AVG

-0.68

0.38

1.00

(4) JGB_5Y

-0.25

0.46

0.80

1.00

(5) RATING_CHANGE

0.58

-0.38

-0.73

-0.63

1.00

(6) LOAN_DEPOSIT

-0.07

0.15

0.36

0.52

-0.68

1.00

(7) MARK_TO_MKT

-0.94

0.01

0.57

0.10

-0.38

-0.11

-0.54

(8) LIBOR_TREASUR3M

0.37

0.43

-0.04

0.30

-0.13

0.24

1.00

(8)

1.00

Note: The table shows the correlation coefficients for the variables used for the estimation. Our observation period isfrom August 2004 to April 2011, providing 348 weekly observations for each of the variables.

- 23 -

Table 3: Baseline Results
Simultaneous equation
First Stage
Protection seller curve

Coef.

Std. Err.

Second Stage

Tobit

CLN_ISSUE_Q
JGB_5Y

Dep. Var. = iTraxx_P
CLN_ISSUE_Q

0.00290.00190.1852

NKY_AVG

0.1376

JGB_5Y***-0.00540.0015

LOAN_DEPOSIT-7.7658

1.8255 *** LOAN_DEPOSIT

MARK_TO_MKT-0.1872

0.1411

cons

0.3606 ***0.1678 ***-0.0251

0.0041***0.0019 ***0.4029**0.1872 ***0.02700.0046***

RATING_CHANGE

0.0021 ***25.34415.7413 ***2.6580 ***-1664.6280

456.4465 ***211.2360 ***0.0417 ***0.2626544.9784

1.51750.8902RATING_CHANGE

LIBOR_TREASUR3M

143.5038 *** cons

Obs.

348

Obs.

348

LR chi2

165.51

F

255.34

Prob. > chi2

0.0000Prob. > F

0.0000Pseudo R-squared

0.0575

Adj. R-squared

0.7856

Log Likelihood-1357.34

Root MSE

44.97

Protection buyer curve

OLS

Protection buyer curve

Dep. Var. = iTraxx_P
iTraxx_P-0.5482

0.0912 ***0.1154 ***-1.59280.3578 ***0.4457 ***0.25380.0458***0.0530 ***4.8671***5.8669 ***NKY_AVG-0.0003

JGB_5Y

0.05150.0860RATING_CHANGE

0.00790.0009 ***LOAN_DEPOSIT

0.16401.1384

MARK_TO_MKT-3.2859

0.0889 *** MARK_TO_MKT

cons

0.0012-0.1650
15.8964

Tobit
Dep. Var. = CLN_ISSUE_Q

iTraxx_P

LIBOR_TREASUR3M

NonCorrected
Std. Err.

Corrected
Std. Err.
OLS

Protection seller curve

Dep. Var. = CLN_ISSUE_Q
NKY_AVG

Coef.

0.026689.3725***

LIBOR_TREASUR3M
cons

24.2595

Obs.

348

Obs.

348

F

1138.03

LR chi2

124.480.0000Prob. > F

0.0000Prob. > chi2

Adj. R-squared

0.9516

Pseudo R-squared

0.0432

Root MSE

21.37

Log Likelihood-1377.85

Notes: ***, **, and * indicate statistical significance at the 1, 5, and 10% level, respectively. The dependent variable is either iTraxx or
CLN_ISSUE. The left-hand side shows the results of the first-stage reduced form regression. The right-hand side shows the second stage
regressions for the protection seller and buyer functions. The column "Corrected Std. Err." shows the standard error adjusted following themethodology employed by Nelson & Olson (1978) and refined by Amemiya (1979), while the column "Non-Corrected Std. Err." shows theunadjusted standard error.

- 24 -

Table 4: Ignoring Simultaneity
Simultaneous equation (from Table 3)
Corrected
Second Stage
Coef.
Std. Err.
OLS
Protection seller curve

Single equation
Coef.

OLS

Dep. Var. = iTraxx_P
CLN_ISSUE_Q

Dep. Var. = iTraxx_P

0.3606 *** CLN_ISSUE_Q

1.5175

Std. Err.

***-0.0461

0.0361

NKY_AVG

NKY_AVG-0.0251

0.0041-0.00020.0009

JGB_5Y

0.89020.4029 **JGB_5Y

0.06030.0701RATING_CHANGE

0.02700.0046 *** RATING_CHANGE

0.00770.0009 ***LOAN_DEPOSIT

cons

25.3441-1664.6280

5.7413456.4465******

LOAN_DEPOSIT-0.1603

1.0760

MARK_TO_MKT-3.29020.1763 ***LIBOR_TREASUR3M-0.1547

0.0389 ***cons

39.511983.7058

Obs.

348

Obs.

348

F

255.34

F

582.13

Prob. > F

0.0000Prob. > F

0.0000Adj. R-squared

0.7856R-squared

0.9526

Root MSE

44.97

Root MSE

21.36

Protection buyer curve

Tobit

Tobit

Dep. Var. = CLN_ISSUE_Q

Dep. Var. = CLN_ISSUE_Q

iTraxx_P-0.5482

0.0912 *** iTraxx_P
NKY_AVG***

0.18640.1816-0.00510.0014 ***LOAN_DEPOSIT-7.7340

1.9530 ***MARK_TO_MKT-0.3015

0.36100.25650.0504 ***543.4174

154.0935 ***-1.59280.35780.25380.0458 *** LIBOR_TREASUR3M

24.2595

4.86710.0024

RATING_CHANGE
MARK_TO_MKT
cons

0.07540.0029

JGB_5Y

LIBOR_TREASUR3M***-0.0344

cons

Obs.

348

Obs.

348

LR chi2

124.48LR chi2

22.42

Prob. > chi2

0.0000Prob. > chi2

0.0000Pseudo R-squared

0.0432

Pseudo R-squared

0.0575

Log Likelihood-1377.85

Log Likelihood-1357.26

Notes: ***, **, and * indicate statistical significance at the 1, 5, and 10% level, respectively. The dependent variable is either
iTraxx or CLN_ISSUE. The left-hand side shows the second stage estimation results from Table 3. The right-hand sideshows the results obtained from the OLS and Tobit estimations which regress either iTraxx or CLN_ISSUE on all theexogenous variables and either CLN_ISSUE or iTraxx.

- 25 -

Table 5: Ignoring the Limited Dependent Variable
Simultaneous equationconsidering LDV (from Table 3)
Second Stage
Protection seller curve

Coef.

Simultaneous equation
without considering LDVCorrected
Std. Err.
OLS

Second Stage
Protection seller curve

Dep. Var. = iTraxx_P
CLN_ISSUE_Q
NKY_AVG-0.0251

Std. Err.
OLS

Dep. Var. = iTraxx_P

0.3606 *** CLN_ISSUE_Q

1.5175

Coef.

0.0041*****1.64070.3754 ***NKY_AVG-0.0256

0.0036 ***JGB_5Y

0.89020.4029

JGB_5Y

1.00140.3471 ***RATING_CHANGE

0.02700.0046 *** RATING_CHANGE

0.02660.0033 ***25.40844.4336 ***-1683.7840

350.7460 ***LOAN_DEPOSIT

cons

25.3441-1664.6280
Obs.

348

5.7413***

LOAN_DEPOSIT

456.4465 *** cons
Obs.

348

F

255.34

F

91.42

Prob. > F

0.0000Prob. > F

0.0000Adj. R-squared

0.7856R-squared

0.5420

Root MSE

44.97

Root MSE

66.21

Protection buyer curve

Tobit

Protection buyer curve

OLS

Dep. Var. = CLN_ISSUE_Q

Dep. Var. = CLN_ISSUE_Q

iTraxx_P-0.5482

0.0912 *** iTraxx_P-0.3971

0.0790 ***MARK_TO_MKT-1.59280.3578 *** MARK_TO_MKT-1.06730.3337 ***LIBOR_TREASUR3M

0.25380.0458 *** LIBOR_TREASUR3M

0.23170.0632 ***27.38635.3824 ***cons

24.2595

4.8671

***

cons

Obs.

348

Obs.

348

LR chi2

124.48

F

50.61

Prob. > chi2

0.0000Prob. > F

0.0000Pseudo R-squared

0.0432R-squared

0.2691

Log Likelihood-1377.85

Root MSE

30.59

Notes: ***, **, and * indicate statistical significance at the 1, 5, and 10% level, respectively. The dependent variable is either
iTraxx or CLN_ISSUE. The left-hand side shows the second stage estimation results from Table 3. The right-hand sideshows the results obtained from the two IV estimations without considering the limited dependent variable (i.e.,
CLN ISSUE Q) in the estimation.

- 26 -

Table 6: Comparison of Economic Impacts

Predicted change in iTraxx_P(bp)

Change in Exogenous Variable

Baseline
Δ1 std. dev. ↑ in

NKY_AVG

Singleequation

Ignoring
LDV

-24.6

0.0

-46.7

JGB_5Y

9.7

0.0

20.3

RATING_CHANGE

24.3

21.3

44.4

LOAN_DEPOSIT

14.4

0.0

26.8

MARK_TO_MKT

-21.2

-88.4

-15.5

7.5

-9.3

7.5

LIBOR_TREASUR3M

Note: The column "Baseline" shows the predicted change in iTraxx_P in the case that eachcovariate increases by one standard deviation. The results are based on the estimated parameters in
Table 3. The next two columns show the results of the same exercise based on the estimatedparameters in Tables 4 and 5, respectively. All changes in iTraxx_P are measured in terms of bp.

- 27 -