Discussion Paper No. 253
Japanese Interest Rate Swap Pricing

Junji Shimada , Toyoharu Takahashi ,Tatsuyoshi Miyakoshi , and Yoshihiko Tsukuda
February, 2010TOHOKU ECONOMICS RESEARCH GROUPGRADUATE SCHOOL OF ECONOMICS AND
MANAGEMENT TOHOKU UNIVERSITY

KAWAUCHI, AOBA-KU, SENDAI,

980-8576 JAPAN

Discussion Paper Series No. 253

Japanese Interest Rate Swap Pricing*’**byJunji Shimada a, Toyoharu Takahashi b ,Tatsuyoshi Miyakoshi c, and Yoshihiko Tsukuda dFebruary, 2010

Keywords: swap spread, Japanese swap pricing, time-varying coefficient
JEL Classification Number: G12; G14; C10aSchool of Management, Aoyama Gakuin University, Osaka University
Faculty of Commerce, Chuo UniversitycOsaka School of International Public PolicydGraduate School of Economics, Tohoku University* The second and third authors’ research were respectively supported by Grant-in-Aid for
Scientific Research (19530287) from Japan Society for the Promotion of Science) and Grant-in-Aid
20530271 from the Ministry of Education, Culture, Sport, Science and Technology ofJapan.
** An earlier version of this paper was presented at the All China Economics (ACE)bInternational Conference, Hong Kong in December, 2009. The authors are greatful for theparticipants. Many constructive comments from J. A. Batten are particularly helpful for
improving the paper.

Correspondence: Yoshihiko Tsukuda , Kawauchi, Aoba-ku, Sendai, 980-8576 JAPAN
Tel: +81-22-795-6302; fax: +81-22-795-6327
E-mail: tsukuda@econ.tohoku.ac.jp1Abstract:

This paper investigates the two questions on the pricing of interest rate swap in theJapanese market by applying a time varying coefficient regression model: (i) Do the risk
factors which determine the spread in the US market also hold in the Japanese market? (ii)
How does the degree of sensitivity of the swap spread to the risks vary over time (inparticular, focusing on the impact of the "Asian financial crisis" and the "global financial
crisis")?
Both default risk of counter party and liquidity risk price the swap spread in theJapanese interest rate swap market. But, influences to swap pricing of these two risks are
somewhat different. Roughly speaking, liquidity risk plays more important role in shorter
maturities and default risk is more important for longer maturities. The above two kind ofrisks play different roles during the financial crises of the "Asian financial crisis" in 1997
to1998 and the "global financial" crisis from 2007. The liquidity risk was a key factor in theformer crisis, but not in the latter crisis for longer maturities. Default risk of LIBOR does
not clearly display any determinants in the Japanese markets.

21. Introduction
The swap buyer makes a fixed interest payment in exchange for a variable cash flow
based upon a floating London Interbank Offered Rate (LIBOR). The interest rate that
determines the fixed payment is called the swap rate. The interest rate swap spread definedby the swap rate minus the par yield (i.e., a coupon rate when the price equals the facevalue) on a Treasury bond of the same maturity. In practice, the swap spread is the main
pricing variable of an interest rate swap. For example, a market participant might accept amarket maker’s bid quote of, say, a swap spread of 40 basis points for a 5-year swap against
3-month LIBOR. If the current yield on a 5-year Treasury note is 5.00%, then, by accepting
this quote, the participant has agreed to pay LIBOR and receive a fixed rate of 5.40%(Brown, Harlow, and Smith, 1994, p. 76, footnote 2). Such an actual institutional pricing ofswap rate (adding some risks to the par yield on a Treasury bond of the same maturity)
implies the pricing based on the par yield on a Treasury bond and also induces theco-integration (long-run equilibrium) in statistical sense between the swap rate and the paryield on a Treasury bond: see Morris, Neal, and Rolph (1998). On the other hand, the actual
institutional pricing of swap rate is supported in a theoretical sense. Cooper and Mello(1991) modeled an interest rate swap as the equivalent of an exchange of risky floating-ratebonds for risky fixed-rate bonds. As easily induced by these, when both bonds aredefault-free like Treasure bonds and bills, the swap rate should be the same as the par yield
on a Treasury bond. The standard interest rate swap rate adds the risk premium to the paryield on a Treasury bond, supporting the institutional pricing methods.
Based on the institutional and theoretical pricing, what kinds of risk premium areadded to the interest rate swap? 1 Or what is determinant of the interest rate swap spread?
Grinblatt (1995) attributes the swap spread to the liquidity difference between Treasurebonds and Eurodollar borrowings. Longstaff and Schwartz (1995), Duffie and Huang(1996) and Lekkos and Milas (2001), Blanco, Brennan and Marsh (2005), In, Brown andFang (2003), and Afonso and Strauch (2007) model swap spreads as a risk premium tocompensate swap counterparties for various risks. Their results were supported by theempirical tests. However, Lekkos and Milas (2001) have noted that the impact fromchanges in the term structure on swap spreads is not uniform across swap maturities. Hungand Chen (2007) find that liquidity premium is the only contributor to the 2-year swap
spread variance in monetary tightening cycles, and the impact of default risk varies acrossboth monetary cycles and swap maturities. They have analyzed whether the relative
importance of these determinants and consequently the swap spreads generating process
vary between the different monetary policy regimes in the USA.
However, the monetary policy and market conditions in Japan are very different fromthose of the USA. Hence, the following questions naturally arise: (i) Do the risk factors
which determine the spread in the US market also hold in the Japanese market? (ii) How
A natural question arises as to how the swapping firms obtain benefit or surplus fromswaps to compensate the swap counterparties: Lang et al (1998). Titman (1992) and Li andMao (2003) investigate the investor’s behaviors on the interest rate swap. These are indifferent research stream for interest rate swap from our research.
13

does the degree of sensitivity of the swap spread to the risks vary over the different market
conditions? The growth of interest rate derivatives from 1990 to 2006 in the Japanesemarket stands conspicuous. Interest rate options increased greatly to 44 trillion USD, whileinterest rate swaps soared over one trillion to 230 trillion USD2. Although, Japanese yeninterest rate swap now plays a pivotal role in the global market, we have only scarceresearch on the Japanese market so far. Therefore, this research will be important to shed alight on the swap pricing.
The purpose of this paper is to provide the Japanese swap pricing model and toinvestigate empirically whether the three risk factors of default risk of LIBOR, liquidity risk
and default risk of counterparty determine the swap spread. Further, we measure how theswap spread pricing the risks varies over the sample periods from 1996 to 2009 (inparticular, focusing on the impact of the "Asian financial crisis" and the "global financial
crisis"). We apply the time varying coefficient regression model with an EGARCH errorterm.
The empirical study in this paper reveals the following facts. Both default risk ofcounter party and liquidity risk price the swap spread in the Japanese interest rate swap
market. However, these two risks played different role during the two financial crises of the
Asian crisis in 1997 to1998 and the global financial crisis originated by the “subprime loan
problem” in 2007. The liquidity risk was a key factor in the Asian financial crisis, but not in
the global financial crisis for relatively long term maturities. Default risk of LIBOR does
not display any clear determinants in the Japanese markets.
The paper is organized as follows: Section 2 sketches the Japanese interest rate swap
markets. Section 3 explains the Japanese swap pricing model and statistical methods.
Section 4 describes data and preliminary analysis. Section 5 discusses the results of
empirical study on the pricing model for the Japanese market and Section 6 concludes thepaper.

2. Japanese Interest Rate Swap Markets
The market for interest rate derivatives, in general, and for swaps, in particular, hasgrown exponentially in the last decade. Recent estimates indicate that in the notional
outstanding volume of transactions of privately negotiated (over-the-counter) derivatives atthe end of December 2007, the total notional amount of interest rate swaps outstanding
amounted to $310trillion from that of $29 trillion at the end of 19973.
Among the major players, Japanese yen interest rate swap plays a pivotal role in the
global interest rate derivatives market. It amounts to an average of 17% of the total
outstanding interest rate derivatives worldwide. Given the importance of the yen ininternational trade and finance, it is not surprising that yen interest rate swaps form a
See Bank for International Settlements (2007, pp.7, Table1).
At that period, all counterparties (net) notional amounts outstanding are Euro 119, US
dollar 96, Japanese yen, 49, and Pound sterling 23 (in millions of US dollars). And interest
rate swap market shares by currency are Euro 40%, USD 34%, Yen 17% and Poundsterling 8%. Source: BIS(2009) OTC derivatives market activity in the second half of 20082
3

4

substantial proportion of this volume, next to those denominated in US dollars. The
expansion in the Japanese yen interest rate swap speaks for the importance of understanding
the yen swap pricing mechanism.
Interest rate swaps are sometimes quoted at a margin or spread above thegovernment bond nearest in maturity to the final date of the swap. This is because thegovernment bonds are often used as a partial hedge for mismatched swap portfolios orbooks. But in JPY swaps, we have the different quotation system. Interest rate swaps inJapan are not quoted by spread, but are quoted by absolute level. This is partly because of
the historical background of JPY interest rate swaps.
In mid 1980's, interest rate swap in Japan has launched. Many Japanese banks
started to run Swap desks, to hedge their swap position. In 1986, a US bank started market
make of the interest rate swaps in the Japanese market. At that time, JGB was thought to be"kinky" market. Transactions are concentrated on "benchmark issue"(shihyo meigara),
arbitrages were insufficient. For these reasons, the Japanese interest rate swap rates, not the
JGB rate, plays as a reference rate for mid to long term transaction, quotation was not based
spreads over JGB yields.
The situation began to change in late 1990's. The financial deregulation accelerates,
and the Ministry of Finance came to issue JGB of many varieties in maturity. Trades
dispersed, and the arbitrage became active and the role of the “benchmark issue” was overby the end of March 1999.

3.

Swap Pricing Model and Statistical Methodology

3.1 An Interest Rate Swap Pricing Model
An interest rate swap is a contractual agreement for one party to pay a fixed rateinterest every period in exchange for receiving a stream of cash flows based upon a floating
rate interest every period (say, LIBOR), where both rates are measured in annual bases.
First, we consider n swap settlements between long-run government bond par
yield and its short-run par yield on dates 1 to n. We assume there is no default risk for thegovernment bonds. Let us define the variables. L0 denotes a coupon rate on the long-run
government bond (fixed rate), SHORTi is a rate of 1-year government bond at time i(floating rate), S0 denote a swap rate at time 0 (fixed rate), ri is a floating interest rate ofdefault free pure discount bond of i-year maturity (i.e. 1/(1 + ri)i is discount factor for timei). Then, no arbitrage condition leads to the equationn1∑ (1 + r )

n

S =∑
i 0

1

=i 1 =i 1 (1 + ri )ii

E 0 (SHORTi−1 )(1)where E0() is the expectation operator based on the information up to time 0. We supposethat the investors hedge the SHORTi by using the following forward rate:5

(1 + ri )i
E0 (=
SHORTi )−1.
i −1(1 + ri −1 )(2)Then, the swap rate S0 is determined as:∑ 1 / (1 + r )=S∑ 1 / (1 + r )
n

0

i −1

i =1
n

i

i =1

i −1
i

− 1.

(3)

Equation (3) implies that

1
1
S
A
+
A0
∑ i =1 (1 + r )i 0 0 (1 + r )n A0 =
i
n
n

(4)

where A0 is the face value of government bond. It means that the swap rate S0 is equal toyield to maturity of the n-year government bond (L0) , i.e. S0 = L0.
3.2 Pricing for Swap between the n-year Government Bond and LIBOR
Second, we consider the swap between the n-year government bond and LIBOR.
We define the swap spread as SP = S - L: the difference between swap rate for privatebonds exchange and the long-run government bond yield. The long-run government bondyield is a swap rate for short-run for government bonds on the same maturity. Lekkos andMilas (2001), Blanco, Brennan and Marsh (2005), Huang and Chen(2006), In, Brown andFang (2003), Huang and Chen (2007)and Afonso and Strauch (2007) consider thefollowing. Comparing (i) the risks between the short-run private and government bondyields, (ii) the risk between the short-run government bond yield and the long run
government bond yield (i.e., the swap rate of government bonds), and (iii) the risk between
the long run government bond yield and the swap rate of private bonds, the swap spread SP
must be expressed by a function of some risk components, such as

SP = f (TR, LR, DR ) ,(5)

where TR (default risk of LIBOR) , LR ( liquidity risk ) and DR (default risk of counterparty against the government bonds). Assuming linearity for simplicity, we have

SPt = TRt + LRt + DRt(6)

We use Eq.(6) as a base model of theoretical analysis. We have to construct the empirical6

model for Eq.(6). All of risk variables are proxies made by the other financial variables.
Then, Eq.(6) can be rewritten as follows:

SPt =c0 + β1PTRt + β 2 PLRt + β 3 PDRt

(7)

where PTR, PLR, and PDR are proxies for TR, LR and DR respectively. This generalmodel nests the previously proposed hypotheses; the LIBOR risk hypothesis ( β1 > 0 ), theLiquidity risk hypothesis ( β 2 > 0 ), and Default risk hypothesis ( β 3 > 0 ). These hypotheses
were supported by many previous literatures (Longstaff and Schwartz (1995); Duffie andHuang (1996); Lekkos and Milas (2001); In, Brown and Fang (2003); Afonso and Strauch(2007); Huang and Chen (2007), Grinblatt (1995) and Huang and Chen (2007)). These risks
make the swap price increase. On the other hand, Morris, Neal, and Rolph (1998) found thecointegration between the swap rate and the par yield of Treasure bonds, the LIBOR risk
and Default risk.
In this paper, we take the 1st difference of Eq. (6) and employ two types of empiricalmodels. The first is the ordinary constant coefficient model as∆SPt = c 0 + c1∆SPt −1 + β1∆PTR t + β 2 ∆PLR t + β 3 ∆PDR t + ε t(8)ε t I t -1 ~ N(0, σ t2 )where ∆ denotes a lag operator and the coefficients β i ( i = 1, 2, 3) are constant over time.
In the volatility of error term, we assume EGARCH model as

ln σ t2 = φ0 + φ1 ln σ t2−1 + φ2 ( ε t -1 σ t -1 + φ3 ε t -1 σ t -1 ) .

(9)

However, the response of investors to the risk factors may possibly differ over timedepending on the state of economy. For instance, the investors may be more sensitive to thedefault risk of counterparty during periods of weak economy than periods of strong
economy. Then the coefficient β 3 is larger during the former periods than the latter. We
investigate this hypothesis by using a time varying coefficient model:∆SPt = c 0 + c1∆SPt −1 + β1,t ∆PTR t + β 2,t ∆PLR t + β 3,t ∆PDR t + ε t . (10)The coefficients vary over time and follow the random walk process7β i,t =β i,t −1 + ηt ,
ηt ~ N ( 0, σ i2 ) ,i =1, 2, 3.
(11)

where the initial values of β1,0 , β 2,0 and β 3,0 are given fixed, and they are regarded asparameters to be estimated. The volatility of error term is also assumed to be followed by
the EGARCH process in Eq. (9). The equations (9), (10) and (11) constitute a state space
representation of a time series with an unobservable state variable 4. We can simulate theprocess of {βi,t }t =1 ( i = 1, 2,3) by Kalman filter algorithm.
T

4. Data and Preliminary Analysis
We use daily data ranging from March 29, 1996 to September 15, 2009 which arecollected from the Bloomberg and the Nikkei Financial Quest. The number of observation
is 3187. As far as we are aware, this dataset constitutes the highest frequency as well as thelongest sampling period for virtually all studies on swap spreads in Japan. We define thevariables in the following:
S = Swap rate, L = Government-bond yield, S – L = Swap spread
The swap rates and the Government-bond yields of 2-, 3-, 5-, 7-, and 10-year maturity
are used and the swap spreads are difference between the rates with same maturity.
PTR = the proxy of LIBOR risk
Following to Huang and Chen (2007), we use the conditional volatility of
6-month-LIBOR as LIBOR risk5.
PLR = the proxy of Liquidity risk
Grinblatt (1995) uses the spread between LIBOR and Government-bond yield tomeasure a proxy for liquidity risk. In a similar way, we adopt the spread between the 1-year
LIBOR and the 1-year Government bond yield. For instance, during periods of weakeconomy, the Government bond are considered more liquid than the LIBOR, and swaps
thus command a larger liquidity premium.
PDR =the proxy of Default risk of counterparty
A number of proxies for the default risk have been mentioned in the literature. Sorensen
and Bollier (1994) evaluates the price of swap counterparty default. According to theirmodel, the price of default equals the volatility of the short rate. Given that swap default
spreads are unobservable, many studies including Minton (1997) and Duffie and Singleton(1997) use the corporate quality spread (Baa-Aaa), while Huang and Chen (2007) used theThis type of models was used for investigating the dynamic efficiency of the stock
markets in the emerging economies by Rockinger and Urga (2000), and Rockinger andUrga (2001).
5 For calculating volatility, we used the rate of change in the 6-month-LIBOR process inpercentage point exposition and applied the AR(1)-EGARCH model.
48spread between the corporate bond and the government bond for the same maturity. In asimilar line to their argument, we use "Nikkei public and corporate bond index(Nikkei kousyasai index)" as corporate bond6. This index has three kinds ofmaturity, "short (under 3- year)", "middle (over 3- year but under 7- year)","long (over 7- year)". We define PDR2y = CB (short) - JGB2y, PDR3y =CB(middle) - JGB3y, PDR5y = CB(middle) - JGB5y, PDR7y = CB(middle) JGB7y and PDR10y = CB(middle) - JGB10y.
We plot all the variables used by this paper in Figures 1(1) through 1(4). From
Figure1(3), we can see that there is very low interest rate period from 2001 to 2006. This
period is called the "zero-interest-rate period". The "Bank of Japan Monetary Policy
Meetings: Announcement of Decisions" specifies the "zero-interest-rate period" and the"quantitative easing period". The quantitative easing policy was operated from 3/19/1999 to
3/9/2006. Based on this consideration, we split the whole sample period into the three
sub-periods: the pre-zero-interest-rate period (29/3/1996 to 3/16/2001), thezero-interest-rate period (3/19/2001 to 3/9/2006), and the post-zero-interest-rate period(3/10/2006 to present time). This partition is generally consistent with the feature of
movements of 1 year JGB yields in Figure 1(3).
From Figure1(4), we observe the following two facts for swap spreads: (i) Swap
spreads are at the low levels during the "zero interest rate period", even those for longer
maturity are negative at some times in this period, while they are at the higher levels during
both the pre-zero interest rate period (i.e., the periods of financial turmoil in Japan) and thepost- period. (ii) The spreads for 7-year and 10-year maturity steeply decline during theperiod of the "global financial crisis" originated by the subprime loan problem, while thespreads for shorter maturity are relatively stable.
Figure 1(5) indicates the proxy variables of risks. We find that (i) The LIBOR risk
(volatility of 6-month LIBOR) are very small during the zero-interest-rate period. (ii) The
liquidity risk drastically increases after the end of zero-interest-rate period. (iii) The default
risks fluctuate more widely over time than the other two risk factors do, and a hump exists
in the period of the "Asian financial crisis" and also in the "global financial crisis". The
graphical observation on the swap spreads and the risk factors suggests that swap spreads
might be related to these risk factors, supporting the Eq.(8).
Table 1 shows summary statistics for all the variables in level used in this paper. The
sample averages of the swap rates and the JGB increase along with maturity. However, theaverage of the swap spreads decrease with maturity. The ADF tests for the level data
indicate that all variables follow unit root process, except for SP2y (2-year Swap Spread)and PTR (volatility). This fact justifies for analyzing the 1st difference of the processes.
Table 2 shows summary statistics for the1st difference of swap spreads and the proxy of
risk. The Ljung-Box test for the first difference process of swap spreads is significant,indicating that the spreads are serially dependent. And the Ljung-Box test for the squared
process of spreads is also significant, showing heteroscedastic volatility. These findings
support applying the empirical model of (8) and (9).
The data of Nikkei kousyasai index from 8/6/2002 to 9/24/2002 are missing. The
number of missing data is 33. We omitted these periods from our analysis.

69[ INSERT Figures 1(1) to 1(5) ][ INSERT Tables 1 and 2 ]As a preliminary analysis, we examined the Granger causality from PTR (volatility),
PLR (Liquidity), and PDR (default) to Swap spread, even though our main interest iscontemporaneous relationships between the swap spread and the risk factors. We apply the
VAR(p) model with the four variables in difference formyt =( ∆SPt , ∆PTR t , ∆PLR t , ∆PDR t )' ;yt = A0 + A1 yt −1 + ... + Ap yt − p + ut ,(12)

where the length of lags is determined by the SIC (Swartz information criterion). Table3
summarizes the results of the Granger causality tests. Roughly speaking, PLR (Liquidity)
does Granger cause Swap spread, but PDR (default) does not cause. However, the testing
results of PTR (volatility) are not conclusive. These findings are basically consistent withthe results of Huang and Chen (2007).
[ INSERT Table 3 ]5. Empirical Results(i) Non time-varying coefficient model
Tables 4(1) to (4) report the estimated results in Eq. (8) and (9) for each of 2- through10- year maturity. The model is estimated by using the full samples and each of threesub-samples. We can see from the full sample s case of Table 4(1) that (i) the coefficientsfor PDR are significant for all maturities. (ii) The coefficients for PLR are significant for
shorter maturities (2-year and 3-year) and insignificant for longer maturities (5-year, 7-year
and 10-year). (iii) The coefficients for PTR are not significant for any maturities. These
three facts are common to all three sub-sample periods with a few exceptions. Hence, we
can safely conclude that (i) Liquidity risk plays relatively important role in swap pricing forthe shorter maturities. (ii) As maturities become longer, the default risk plays relatively
important role, while influence of liquidity risk become smaller. These estimated result canbe intuitively acceptable, and also partially support the recent empirical studies from the US
markets which find some risk factors as determinants on swap interest rates in the papers(Lekkos and Milas:2001; In, Brown and Fang:2003; Afonso and Strauch:2007; Huang and
Chen:2007).
Looking closely at the values of estimated coefficients, we can see that they varyfrom period to period. This suggests that the coefficients of risk factors may vary over time.

10[ INSERT Table 4 ](ii)Time-varying coefficient model
In this subsection, we investigate how the sensitivity of the investors in the Japaneseinterest rate swap market to the risk factors changes over the time from 1996 through 2009.
Table.5 shows the estimated results for the time varying model of Eq. (9), (10) and (11).
The coefficients of β1,0 , β 2,0 and β 3,0 are the estimates of initial values of β1,t , β 2,t and β3,trespectively, and σ(βi). are the estimates of σi . In the time varying coefficient model, theestimates of β1,t , β 2,t and β3,t move along with time.
[ INSERT Table 5 ]Figure 2 illustrates the estimated series of time varying coefficients for PLR and PDR7.
The coefficients of β 2,t and β 3,t represent the magnitude of response to the risk factors of
PLR and PDR respectively.
[ INSERT Figure 2]

First, we look at the coefficients of β 3,t for the default risk of the counterparty(PDR). For relatively longer maturity series, the values of β 3,t are high at the beginningstage of time, and have a declining trend toward 2007. This result is consistent with ourconstant coefficient analysis and can be interpreted as follows. The Japanese financial
institutions had been suffered from the accumulated bad loans during the 1990s and the"Asian financial crisis". Therefore, the participants in the Japanese interest swap market
were highly sensitive to the default risk of the counterparty in these periods especially for
longer maturities. Then, the problem of bad loans was changed for the better in 2000s. The
investors were becoming less sensitive to the default risk. But, the "global financial crisis"
hit the countries over the world in 2007, and the Japanese swap spread seems to havebecome sensitive to the default risk again. This tendency is not clear for 2 year maturities,
but as the maturity become longer, the down slope tendency is becoming apparent.
However, the series of β 3,t for 10-year maturity looks flat in the period of the "global

7

We omitted graphs for the coefficients of PTR ( β1,t ) because the coefficient stays fixed

constant at the level of initial value for each year of maturity. This is clearly seen from thefact σ ( β1 ) = 0 in Table 5.

11

financial crisis". This may be concerned with steep drop of swap spread in the same period
although we cannot identify the reason behind this observation. These empirical results arecoincident with our constant coefficient analysis.
Second, we move to the coefficients of β 2,t for the liquidity risk (PLR). We canobserve from Figure 2 that (i) for all maturities, β 2,t does not have any obvious time trends,
but fluctuates wildly in comparison with β 3,t . (ii) For all maturities, β 2,t has a big humparound 1997, which may be a reflection of rising risk caused by the "Asian financial crisis".
The liquidity risk played a dominant role in this period. (iii) For 2-year and 3-year
maturities, β 2,t definitely increased in the period of the global financial crisis after 2007,
while for longer maturities it did not increase in this period. The short term interest rate
swap market in Japan was quite a sensitive to the liquidity risk caused by the global
financial crisis. These results are coincident with our analysis by using the constantcoefficient model.
Finally, we compare the values of β 2,t and those of β 3,t . The Japanese economy has
experienced the two financial crises of the "Asian financial crisis" in 1997 to1998 and the"global financial crisis" originated by the subprime loan problem in 2007. By careful visual
examination of Figure 2, we find that (i) the graph of β 2,t is basically above that of β 3,t for
2-year and 3-year maturities, the two graphs are roughly even for 5-year maturity, and theorder of magnitudes of the two graphs is reversed for the 7-year and 10-year maturities. (ii)
During the "Asian financial crisis", β 2,t is almost always above β 3,t for all maturities

although the difference is getting small along with length to maturity. The liquidity risk
dominated the default risk in this period. (iii) During the "global financial crisis",

β 3,t dominates β 2,t for 5- year, 7-year and 10-year maturities, but β 2,t dominates β 3,t for
2-year maturity.

The default risk and the liquidity risk played different role in the two financial crises
for determining the swap spread in the Japanese interest rate swap market. For shorter
maturities, in particular, 2- year, the liquidity risk is a key factor both in the period of the"Asian financial crisis" and the "global financial crisis". However, for 5-year and 7-year
maturities, the liquidity risk played dominant role in the former crisis, while the default risk
played more important role in the latter crisis.
6.

Concluding Remarks
In this paper we investigated the two questions: (i) Do the risk factors which
determine the spread in the US market also play the same role in the Japanese market? (ii)
How does the degree of sensitivity of the swap spread to the risks vary over the sample
periods from 1996 to 2007 (in particular, focusing on the impact of the recent "global
12

financial crisis").
We examined the three risk factors of default risk of LIBOR, default risk of counterparty and liquidity risk. The findings of our study are as follows. First, both default risk ofcounter party and liquidity risk price the swap spread in the Japanese interest rate swap
market. But, influences to swap pricing of these two risks are somewhat different. Roughly
speaking, liquidity risk plays dominant role in the shorter maturities while default risk ismore important for the longer maturities. In particular, the two risks played different role
during the two financial crises of the "Asian financial crisis" in 1997 to1998 and the "global
financial" crisis from 2007. The liquidity risk was a key factor in the Asian financial crisis,but not in the global financial crisis for longer maturities. Second, default risk of LIBOR
does not clearly display a determinant in the Japanese markets. The estimated results
support the previous empirical work from the US markets.

13

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rate debt, Journal of Finance 50, 789-920.
Minton, B. (1997), An empirical examination of basic valuation models for plain vanilla
US interest rate swaps, Journal of Financial Economics, 44, 251 −277.
Morris,C., R, Neal, and D.Rolph (1998), Credit Spreads and Interest Rates : A
Cointegration Approach, Federal Reserve Bank of Kansas City ResearchWorking Paper, RWP 98-08.
Rockinger, M., and G.. Urga (2000), The Evolution of Stock Markets in Transition
Economies, Journal of Comparative Economics, 28, 456-472.
Rockinger, M., and G. Urga, (2001), A Time-Varying Parameter Model to Test for
Predictability and Integration in the Stock Markets of Transition Economies,
Journal of Business and Economic Statistics, 19, 1, 73-84.
Sorensen, E. H., & Bollier, T. F. (1994), Pricing swap default risk. Financial Analysts
Journal, 50, 23−33.
Titman, S., (1992), Interest rate swaps and corporate financing choices. Journal of Finance
47, 1503–1516.

14

Table.1 Summary Statistics for Level of the Variables
Swap rate(St)Mean
Std Dev.
Skew
Kurt
ρ(1)
ADF

SR2y
0.591
0.392
0.566
2.655
0.998
-2.199

SR3y
0.765
0.453
0.713
3.413
0.998
-2.379

SR5y
1.120
0.543
0.820
3.959
0.997
-2.465

SR7y
1.439
0.586
0.854
4.058
0.997
-2.592

SR10y
1.798
0.585
0.807
3.993
0.997
-2.585

JGB rate(Lt)
Mean
Std Dev.
Skew
Kurt
ρ(1)
ADF-test

JGB2y
0.283
0.262
0.533
1.989
0.997
-2.371

JGB3y
0.431
0.337
0.638
2.659
0.997
-2.664

JGB5y
0.604
0.380
0.670
3.058
0.996
-2.741

JGB7y
0.982
0.487
0.970
4.256
0.995
-3.074

JGB10y
1.310
0.544
1.161
4.714
0.995
-3.043

Swap Spread(SPt=St-Lt)
Mean
Std Dev.
Skew
Kurt
ρ(1)
ADF-test

SP2y
0.161
0.088
0.814
2.848
0.985
-3.720**

SP3y
0.161
0.101
0.808
3.292
0.988
-3.197

SP5y
0.137
0.080
0.053
2.705
0.985
-3.285

SP7y
0.129
0.102
0.317
2.862
0.989
-2.820

SP10y
0.111
0.135
-0.1222.258
0.990-3.018Proxy of Risk
Mean
Std Dev.
Skew
Kurt
ρ(1)
ADF-test

PDR2y
0.743
0.484
0.466
2.279
0.999
-1.098

PDR3y
0.870
0.378
0.420
1.955
0.996
-1.787

PDR5y
0.491
0.321
0.613
2.699
0.997
-1.372

PDR7y
0.669
0.199
0.928
3.570
0.992
-1.952

PDR10y
0.291
0.206
1.590
5.748
0.994
-1.651

Proxy of Risk
PTR
PLR
Mean
1.366
0.194
Std Dev.
3.281
0.173
Skew
6.099
1.570
Kurt
54.025
4.384
ρ(1)
0.949
0.995
ADF-test-10.651*-2.204Note : ρ(1) denotes 1st order auto-correlation. ADF-test denotes t-value of ADF test. The 10% ,5% and 1% critical values are -3.961, -3.411 and -3.127 respectively. "**" and "*" denotestatistically significant at 1% and 5% level respectively.

15

Table.2 Summary Statistics for the 1st Difference
Swap Spread(SPt=St-Lt)
Mean
Std Dev.
Skew
Kurt
ρ(1)
Q(12)
ρ(1)-2
Q(12)-2

SP2y
0.000
0.021
-0.61514.820-0.203274.9410.280
997.218

SP3y
0.000
0.022
-0.63217.213-0.213241.4370.351
1176.063

SP5y
0.000
0.022
-0.45314.737-0.253298.1910.327
999.632

SP7y
0.000
0.024
-0.146
11.538-0.267306.7220.273
1069.909

SP10y
0.000
0.025
-1.00535.820-0.221228.8560.285
413.349

Proxy of Risk
Mean
Std Dev.
Skew
Kurt
ρ(1)
Q(12)
ρ(1)-2
Q(12)-2

PDR2y
0.000
0.031
-4.898111.196-0.225178.477
0.023
2.076

PDR3y
0.000
0.037
-0.2217.477-0.348418.1940.253
393.131

PDR5y
0.000
0.042
0.058
6.765
-0.406554.5240.340
624.921

PDR7y
0.000
0.050
0.046
4.195
-0.431606.7450.352
1074.844

PDR10y
0.000
0.047
0.031
4.668
-0.421596.1660.354
1058.706

Proxy of Risk
PTR
PLR
Mean
-0.0020.000
Std Dev.
0.869
0.021
Skew
12.871
0.066
Kurt
269.650
11.071ρ(1)0.214-0.217Q(12)289.951207.942ρ(1)-20.133
0.303
Q(12)-2
95.423931.929
Note : ρ(1) denotes 1st order auto-correlations of 1st difference process and ρ(1)-2 denotes
those of squared process. Q(12)-1 denotes the Ljung-Box Statistics of 1st difference process
and Q(12)-2 denotes those of squared process. The 5% critical values are all 21.03.

16

Table.3 Testing Results of Granger Causality fromthe Risk Factors to the Swap Spread
Years tomaturity
Lag-length(p)
Risk factors
PTR
PLR
PDR

2Y

3Y

5Y

7Y

10Y

2

3

3

3

5

6.741*(0.010)6.829**(0.009)1.362(0.243)0.434(0.510)8.314**(0.004)0.726(0.394)2.646(0.071)1.934(0.145)5.971**(0.003)3.375*(0.034)
3.789*(0.023)0.067(0.935)0.861(0.354)8.878**(0.003)0.351(0.554)Note : The entries are values of test statistics which is asymptotically distributed as
chi-square with p degrees of freedom. The null is that the Granger causality does not exist.
P-values are in parenthesis. "**" and "*" denote statistically significant at 1% and 5% level
respectively.

17

Table.4 Estimation Results of EGARCH Model(1) Full Sample period (3/29/1996 - 15/9/2009 : Obs. = 3187)
Yearstomaturity
2
3
5
7
10

Const

SL(t-1)

PTR

PLR

PDR

EGARCH

c0

c1

β1

β2

β3

φ1

φ2

φ3

φ4

0.000
(0.000)0.000(0.000)0.000(0.000)0.000(0.000)0.000(0.000)-0.127(0.019)-0.118(0.021)-0.179(0.022)-0.191(0.026)-0.139(0.026)0.000(0.001)0.000(0.000)-0.001(0.001)0.000(0.001)0.000(0.000)0.288**(0.022)0.139**(0.015)0.018(0.014)0.034*(0.017)-0.002(0.017)0.043*(0.018)0.054**(0.006)
0.055**(0.006)
0.061**(0.004)0.053**(0.006)-0.122(0.017)-0.214(0.026)-0.244(0.048)-0.222(0.038)-0.217(0.050)0.997(0.002)0.127(0.018)0.043(0.022)0.993(0.002)0.991(0.005)0.994(0.003)0.991(0.004)0.207(0.024)0.228(0.027)0.239(0.029)0.200(0.032)0.057(0.025)0.054(0.033)0.039(0.036)0.025(0.033)(2) Pre zero interest rate period (3/29/1996 - 16/3/2001: Obs. = 1191)
Years
tomaturity
2
3
5
7
10

Const

SL(t-1)

PTR

PLR

PDR

c0

c1

β1

β2

β3

φ1

φ2

φ3

φ4

0.001
(0.001)0.001(0.001)0.000(0.001)0.000(0.001)0.000(0.001)-0.174(0.027)-0.238(0.032)-0.241(0.037)-0.262(0.035)-0.212(0.041)-0.001(0.001)0.000(0.001)-0.001(0.001)0.000(0.001)0.000(0.001)0.269**(0.027)0.143**(0.021)0.030(0.019)0.077*(0.030)0.051(0.027)0.230**(0.028)0.130**(0.019)0.143**(0.021)0.145**(0.018)0.144**(0.024)-0.338(0.085)-0.474(0.106)-0.473(0.088)-0.331(0.104)-0.429(0.117)0.978(0.009)0.969(0.012)0.970(0.010)0.976(0.012)0.964(0.014)0.228(0.040)0.320(0.046)0.344(0.041)
0.222(0.046)0.249(0.054)0.121(0.048)0.097(0.047)0.042(0.063)0.027(0.081)
0.041(0.083)18

EGARCH(3) Zero interest rate period (19/3/2001 - 9/3/2006: Obs. = 1154)
Year
2
3
5
7
10

Const

SL(t-1)

PTR

PLR

c0

c1

β1

β2

0.000
(0.000)0.000(0.000)0.000(0.000)0.000(0.000)0.000(0.000)-0.101(0.034)-0.046(0.037)-0.100(0.033)-0.184(0.050)-0.168(0.037)0.012(0.009)0.018(0.011)0.021(0.011)0.013(0.019)0.034**(0.011)

PDR
**

0.158
(0.050)0.153*(0.068)-0.022(0.054)-0.037(0.070)0.102(0.102)

EGARCH

β3

φ1

φ2

φ3

φ4

0.037
(0.024)0.050**(0.009)0.057**(0.010)0.053**(0.005)
0.061**(0.010)-0.156(0.067)-0.215(0.070)-1.795(0.492)-0.612(0.146)-0.845(0.358)0.992(0.006)0.989(0.005)0.850(0.050)0.965(0.013)0.928(0.036)

0.096(0.030)0.147(0.041)0.445(0.070)0.373(0.058)0.260(0.063)0.034(0.025)0.025(0.039)0.103(0.054)0.017(0.066)0.020(0.053)(4) Post zero interest rate period (10/3/2006 - 15/9/2009 : Obs. = 842)
Year
2

Const

SL(t-1)

PTR

PLR

c0

c1

β1

β2

PDR
β3
**

EGARCH
φ1

φ2

φ3

φ4

0.000
-0.025
0.001
0.205
0.008
-0.124
0.994
0.097
0.012
(0.000)(0.037)(0.001)(0.031)(0.014)(0.059)(0.006)(0.027)(0.032)
**
*
3
0.001
0.008
0.000
0.091
0.027
-0.135
0.994
0.104
0.061
(0.000)(0.045)(0.001)(0.025)(0.012)(0.064)(0.005)(0.036)(0.050)5
0.000-0.011-0.001-0.0010.025**-0.277
0.985
0.183
0.064
(0.000)(0.038)(0.001)(0.021)(0.007)(0.080)(0.006)(0.057)(0.055)
*
**
7
0.000
-0.041-0.0010.005
0.058-0.378
0.977
0.232
0.091
(0.000)(0.040)(0.001)(0.018)(0.007)(0.090)(0.007)(0.056)(0.040)
10
0.000
0.047
0.000
-0.051*0.017-0.4420.972
0.269-0.038(0.000)(0.048)(0.001)(0.026)(0.009)(0.128)(0.011)(0.061)(0.052)
Note : "**" and "*" on the columns of SP(t-1), PLR and PDR denote statistically significant at 1% and 5% level
respectively. Standard errors are in parenthesis.

19

Table.5 Estimation Results of Time Varying Parameter Model
Const

SL(t-1)

c

c1

β1,0

σ(β1)

β2,0

σ(β2)

β3,0

σ(β3)

φ1

φ2

φ3

φ4

2

0.000
(0.000)-0.061(0.018)-0.001(0.000)0.000(0.000)-0.050(0.517)0.036(0.011)

0.066(0.282)0.040(0.019)-0.021(0.029)0.998(0.003)0.110(0.015)0.305(0.163)3

0.000(0.000)-0.077(0.021)0.000(0.000)0.000(0.000)0.048(0.157)0.032(0.003)0.165(0.018)0.009(0.001)-0.056(0.016)0.993(0.002)

0.198(0.022)0.236(0.053)5

0.000(0.000)-0.109(0.136)-0.002(0.002)0.000(0.001)

0.282(0.173)0.015(0.045)0.263(0.092)0.009(0.001)-0.143(0.004)0.982(0.001)0.308(0.085)0.121(0.206)7

0.000(0.000)-0.112(0.007)0.000(0.000)0.000(0.000)0.330(0.170)0.049(0.008)0.254(0.034)0.004(0.001)-0.033(0.015)0.995(0.002)0.228(0.017)0.094(0.041)10

0.000(0.000)-0.092(0.000)0.000(0.000)0.000(0.000)0.126(0.180)0.055(0.001)

0.542(0.056)0.007(0.000)-0.147(0.004)0.981(0.000)0.275(0.016)0.097(0.038)

Year

PTR

PLR

PDR

EGARCH

Note : The coefficients of βi,0 denote initial values of βi,t. (i = 1, 2, 3), and σ(βi). denote the estimates of σi in equation (11).Standard
errors are in parenthesis.

20

Figure.1 (1) Swap Rate(St)
4
3.5
3
2.5
2

10yr
7yr
5yr
3yr
2yr

1.5
1
0.5
0
3/96

3/98

3/00

3/02

3/04

3/06

3/08

Figure.1 (2) JGB(Japanese Government Bond) rate (Lt)
4
3.5
3
2.5
10yr
7yr
5yr
3yr
2yr

2
1.5
1
0.5
0
3/96

3/98

3/00

3/02

3/04

3/06

3/08

Figure.1 (3) 1year JGB(Japanese Government Bond) rate
1.2
0.8
0.4
0
3/96

3/98

3/00

3/02

3/04

21

3/06

3/08

Figure.1 (4) Swap Spread ( SPt = St - Lt)
0.6

S-L：2YR

0.4
0.2
0
-0.2
3/96

3/98

3/00

0.6

3/02

3/04

3/06

3/08

3/04

3/06

3/08

3/04

3/06

3/08

3/04

3/06

3/08

3/04

3/06

3/08

S-L：3YR

0.4
0.2
0
-0.2
3/96

3/98

3/00

0.6

3/02

S-L：5YR

0.4
0.2
0
-0.2
3/96

3/98

3/00

0.6

3/02

S-L：7YR

0.4
0.2
0
-0.2
3/96

3/98

3/00

0.6

3/02

S-L：10YR

0.4
0.2
0
-0.2
3/96

3/98

3/00

3/02

22

Figure.1 (4) Proxy of Risk(a) PTR : LIBOR Risk ( = Volatility of LIBOR6M)
25
20
15
10
5
0
3/96

3/98

3/00

3/02

3/04

3/06

3/08

(b) PLR : Liquidity Risk( = LIBOR1Y - JGB1Y)
1
0.8
0.6
0.4
0.2
0
3/96

3/98

3/00

3/02

23

3/04

3/06

3/08

(c) PDR : Default Risk (CB - JGB)
2.5

PDR2y

2.0
1.5
1.0
0.5
0.0

3/96

3/98

3/00

2.0

3/02

3/04

3/06

3/08

3/04

3/06

3/08

3/04

3/06

3/08

3/04

3/06

3/08

3/04

3/06

3/08

PDR3y

1.5
1.0
0.5
0.0

3/96

3/98

3/00

1.5

3/02

PDR5y

1.0
0.5
0.0
3/96

3/98

3/00

1.5

3/02

PDR7y

1.0
0.5
0.0

3/96

3/98

3/00

1.5

3/02

PDR10y

1.0
0.5
0.0

3/96

3/98

3/00

3/02

24

Figure.2 Estimates of Time Varying Parameters
1.6

2YR

PLR

PDR

1.2
0.8
0.4
0
-0.4
03/96

03/98

03/00

1

03/02

03/04

03/06

PLR

3YR

03/08

PDR

0.6

0.2

-0.2
03/96

03/98

03/00

0.8

03/02

03/04

5YR

03/06

PLR

03/08

PDR

0.4

0

-0.4
03/96

03/98

03/00

1

03/02

03/04

7YR

03/06

PLR

03/08

PDR

0.5
0
-0.5
-1
03/96

03/98

03/00

03/02

25

03/04

03/06

03/08

1

10YR

PLR

PDR

0.5
0
-0.5
-1
03/96

03/98

03/00

03/02

26

03/04

03/06

03/08