Intervention by Central Banks in the Money Markets
John Thompson
CIBEF (www.cibef.com)
Liverpool Business School
Liverpool John Moores University
John Foster Building
Mount Pleasant
Liverpool
Email Address: [email protected]
October 2003
Abstract
Evidence provided by Kasman [1992] suggests quite wide differences between the
volatility of the overnight interest rate in six industrial countries over the period 1988
to 1991. Since that date the institutional environment has changed with i) the creation
of the Eurosystem in 2000 and ii) changes in the operating procedures of the Bank of
England. This paper examines the volatility of the overnight interest rates over the
period 31/12/99 to 17/9/03 in four major economies to see if the pattern of volatility
has changed in recent years. Volatility is measured in three ways, namely absolute
deviations from a moving average, moving standard deviation and GARCH.
Volatility of the overnight rate remains highest in the UK and there is little evidence
that volatility in this market does affect the 3-month market.
1
Introduction
Kasman [1992] reviewed the monetary operating procedures of central banks over the
period 1988 to 1991 in six major industrial countries, namely Canada, Germany,
Japan, Switzerland, UK and the US. One of the points of interest was consideration
of the differences between the volatility of overnight interest rates in the countries.
For the sake of convenience the relevant section of the table in Kasman is reproduced
in a slightly rearranged form below in Table 1a. The table indicated a low rate of
variability for Japan, followed by a quite close grouping of countries (US, Germany,
Canada) and two other countries (UK & Switzerland) with relative high degree of
volatility. Kasman also found little evidence of any transmission of volatility from
the overnight rate to the 3-month rate. Again for the sake of comparison his results
are shown in table 1b where the estimating equation is: same as equation
Yt = α + βXt + εt
(1)
Where Y is the 3-month and X the overnight measure of volatilty, which in
this case is the absolute deviation from the moving average.
Since the time of the study, major changes have taken place in the operating
procedures of the Bank of England, which, together with the creation of the
Eurosystem, raises the interesting question as to whether the incidence of volatility
has changed since that time in particular for the UK, Switzerland and the Eurosystem
(as compared with Germany). The United States and Japan are retained for the
purposes of comparison.
The structure of the paper is as follows. The various institutional arrangements will
be summarised in section 2 and the data summarised in section 3. The empirical work
will be reviewed in section 4 and the conclusions presented in section 5. At this stage
however it is important to realise that the paper does not attempt to explain the
operating procedures in the manner of say Hartman, Manner and Manzaneres [2001]
for the Eurosystem or Hamilton [1996] for the US. The object is rather to examine
the impact of these procedures on the overnight interest rate.
2
2
The Institutional Environment
2.1
The European Central Bank (ECB)
This section draws heavily on Buckle and Thompson [2005, forthcoming] The first
point to note is that in an aggregated balance sheet the sum of autonomous liquid
liabilities is larger than the corresponding figure for assets so that the banking system
incurs a liquidity deficit against the Eurosystem. Consequently there is a continual
need for liquidity by the banking system. This is satisfied through the use of the
monetary policy instruments thus providing the pivot for the determination of the
short-term rate of interest, which is, in itself, the centre piece of the operation of
monetary policy. The current account holdings include the minimum reserves
imposed on credit institutions within the system. Currently the minimum reserve ratio
is set at 2% of specified short-term liabilities of the institutions and this requirement
has to be met on average over a one-month maintenance period. The fact that the
reserve basis is calculated on an average rather than on a daily basis removes some of
the pressure from banks in their day-to-day operations. Reserve surpluses on some
days can be offset by deficits on others and conversely. The institutions receive
interest on these compulsory balances at a rate equal to the average rate of the weekly
tenders over the maintenance period. Excess reserves receive no such interest.
The most important policy instrument is Main Refinancing Operations (MRO).
MROs have provided roughly 75% of the liquidity needs of the institutions since the
system started. MROs are implemented through weekly tenders and have a maturity
of fourteen days. A further 25% of liquidity needs have been provided through the
Long-Term Refinancing Operations (LTRO). LTRO operations are operated once a
month and have a maturity of three months. The level of these balances is set in
advance by the ECB so that they play no active role in the management of liquidity.
As noted above the main policy instrument is the MRO. Since June 2000, the weekly
tender for MROs has been conducted at variable rates of interest but the ECB
publishes a minimum rate for a tender below which no bids will be accepted. Bids at
the highest rate are accepted first and bids with successively lower rates being
accepted in turn until the total liquidity to be allotted has been exhausted. At these
variable-rate auction, the minimum bid rate indicates the monetary policy stance1.
Tenders can be received from eligible counterparties of which there were roughly
3600 in May 1999. Not all of these counterparties take part in tenders but between
January and May 2003, the average number of participants per tender varied between
124 and 350. The main instrument used in MRO operations is the REPO
2.2
The Bank of Japan (BoJ)2
Monetary Policy Meetings (MPM) are held once or twice a month and after each
meeting a guideline is announced. Currently monetary policy is implemented by
1
The ECB has retained the option of using fixed rate tenders, in which case the interest rate is directly
set at the auction.
2
This section draws on the full description of the Bank of Japan’s intervention in the money markets
contained in Miyanoa [2000].
3
interest rate targeting with the uncollateralised overnight call rate being the target for
the implementation of monetary policy.
Reserve ratios for banks and other financial institutions vary according to the size and
type of deposit with required reserves being calculated so that their cumulative total
over the month (16th first month to 15th second month) equals the required amount.
No interest is paid on the reserves. There is no requirement to meet the reserve
requirements on a particular day as long as they meet the requirement over the month.
Consequently the BoJ stresses that the degree of intervention in the money markets
should not be taken as any indication at all of the stance of its monetary policy.
The Bank determines the size of provision of funds with reference to the gap between
the expected divergence of the overnight call rate and its target level based on the
forecast of the market’s shortage or surplus of liquidity. A traditional yield auction is
held with bids being accepted in order of yield until sales/purchases meet the target.
Regular3 auctions are held throughout the day depending on whether the auction is for
same day or later day settlement. The maturity of the transaction is specified for each
auction but is typically six months or less.
Intervention in the market takes place via the outright purchase of securities as well as
REPO operations. Recently the latter method (i.e. REPO purchases of Treasury and
Financing Bills) has become the most heavily utilised method. For longer term
transactions, JGBs are used.
2.3 The Bank of Switzerland (SNB)
Monetary policy operated by the SNB is directed towards maintaining price stability
defined as averaging 2% per annum. Until the end of the 1990s, the development of
monetary aggregates was regarded as the main indicator of future inflation rates.
Since the beginning of 2000, the SNB takes into consideration a “broad range of real
and monetary indicators” (SNB [2003]).
The method of operation has changed since the publication of the Kasman paper.
During the 1980s and early 1990s foreign exchange swaps were the main method of
intervention in the money markets. Since 2000 the only instrument used has been
repo transactions with the vast majority creating liquidity (99%). The maturity of
such transactions is as follows:
Percentage of total Repo Transactions
Less than 1 week
1 week
2 weeks
Other
28
52
15
5
The target rate is the LIBOR 3-month rate which is normally higher than the repo rate
for two reasons: i) the repo rate is secure a secured loan whereas the 3-month LIBOR
3
Provision is made for additional operations n the light of unexpected market developments.
4
refers to unsecured lending and therefore contains a risk premium and ii) as can be see
above most repo intervention is for periods shorter than 3 months.
For more detailed information see SNB [2003].
2.4
The Bank of England (BoE)
Fundamental changes have taken place in the operating procedures of the BoE since
1997. Prior to 1997, open market operations were mainly conducted via the purchase
or sale of sterling Treasury Bills and eligible bank bills again mainly via the Discount
Houses. In 1996 the gilt repo market was reformed allowing more operators to
participate and this became the method of intervention and the Discount Houses
disappeared. A further major change took place in April 2000, when the
responsibility for managing the exchequers cash position was transferred to the
newly-created Debt Management Office (DMO). The DMO’s market objective is to
offset the cash imbalances on every business day so as to avoid any disturbance in the
supply of central bank money and, therefore, and pressure on interest rates. In pursuit
of this strategy, the DMO has traded on a daily basis with a number of counterparties
in a wide range of assets. It should be emphasised that in these operations the DMO
is a price taker in that it does not seek to influence interest rates. In the autumn of
1997, The BoE was granted operational independence in that it sets the level of its
official rate of interest (currently the two-week repo rate) so as to meet the
government’s target rate of inflation. The level of this rate is set at its monthly
meeting by the Monetary Policy Committee comprised of 5 BoE members and 4
outside members.
The power to influence rates comes from the fact that the market is continuously short
of funds. In recent years the stock of bank notes has been growing by around £2
billion a year thus draining liquidity from the banking system. This effect is
reinforced through by the fact that, on average around £2 to £2.5 billion of refinancing
matures each day (BEQB, Summer 2002, page 155). Consequently, the daily
shortages are quite large so that the BoE intervenes in the money markets on a daily
basis mainly through repos.
The daily operations of the BoE can be summarised briefly as follows:
1. An initial forecast is made of the daily liquidity shortage. This is amended
throughout the day.
2. Two regular rounds exist for intervention (9:45 am and 2:30 pm)
3. At 3.30 bids can be made for overnight funds at a rate 100 basis points above
the Bank’s official repo rate. This, in effect, sets a ceiling for the overnight
interest rate. In addition settlement banks can bid for funds at a rate of 150
basis points above the official repo rate.
4. An overnight deposit rate exists with a rate of 100 basis points below the
official repo rate. This, in practice, sets a floor for the overnight rate.
5. In this process, it should be noted that banks required to hold 0.15 per cent of
their eligible sterling liabilities as non-operational reserves at the BoE. This is
not a reserve requirement in the strict sense as they are non-interest bearing
are, in reality, a tax on banks to finance the operations of the BoE.
5
This operational procedure is reviewed in the Bank of England Quarterly Bulletin
March 2002 and the slight amendments were outlined in consultation document
released on 11/7/03 and confirmed in a notice dated 27/8/003.
2.5
The US Federal Reserve (USFR)
The USFR currently targets the federal funds rate of interest rather than a specific
quantity of reserves. In fact in 1995 it commenced to state explicitly its target level
for the federal funds rate.
Each morning an estimate of demand for reserves is provided for the current and
future two 2-week reserve maintenance periods. Based on this information the
strategy for intervention in the markets is drawn up to ensure that the quantity of
reserves is consistent with the targeted federal funds rate. Generally intervention is
carried once a day.
Two types of operations are employed; i.e. outright and temporary operations.
Outright operations are used to offset long-term imbalances between the demand and
supply of reserves. Nowadays, outright operations (mainly purchases because of the
reserve drain through the public’s demand for cash) are conducted by way of treasury
bills and treasury coupons. In 1997 the average maturity of marketable treasury
securities held by USFR was 42 months. As the name suggests, temporary operations
are used to offset large daily imbalances. The main method intervention is by way of
repo agreements conducted in treasury securities. Intervention is the money markets
is supported by discount window borrowings (Edwards [1997].
The depository institutions are required to hold reserves specified as a percentage of
deposit liabilities (currently 10% for transaction deposits and zero for non-transaction
deposits). No interest is paid on reserve holdings. This ratio is calculated as an
average over a 2-week computational period to be held over a 2-week maintenance
period. The differentiation between transaction and non-transaction balances permits
movement between these to ease reserve pressures. Such movements are limited in
number to six per month for each customer so that the sixth such transaction transfers
the remaining funds in the customer’s account to a transaction balance.
For a more detailed account of the USFR’s monetary policy operations see Edwards
[1997].
2.6
Final Comments
In the late 1960s there was a quite widespread debate on whether central banks should
control the interest rate or the quantity of high-powered money (i.e. banks’ balances at
the central bank plus cash in circulation). Perhaps the debate is best summed up by
Poole [1970] who, using a basic IS/LM model, advocated the use of an interest-rate
6
policy if the monetary side of the economy is more unstable than the real side and
conversely a quantity-of-money policy if the real side is more unstable than the
monetary side. The debate, as far as the practice of the central banks surveyed above
is concerned, has been resolved in favour of interest rate targeting. In fact the role of
money aggregates in the decisions on interest rate changes seem to be diminished.
For example the SNB [2003] states:
“until the end of the 1990s the development of monetary aggregates was
of prime importance. Today the national bank bases its decisions on a
broad range of real and monetary aggregates.”
and Edwards [1997] states:
“By late 1982, it had become clear that financial innovation had weakened
the historical link between M1 and the economic objectives of monetary
policy and the FOMC began to make more decisions about money market
conditions using a wider array of economic and financial variables to
judge the need for an adjustment in short-term interest rates.”
3
Data
The data series were derived from DataStream and cover the period 31/12/99 to
17/9/03 (969 observations in total). Daily data is used.
The overnight call rate series are:
Eurosystem:
Japan
Switzerland
UK
US
European Overnight Index Average (offered rate) EONIA
Overnight Call Rate (middle rate)
Swiss interbank next day (bid rate)
Interbank (middle rate)
Federal Funds Rate (middle rate).
The total number of observations is 969 but in the case of the centred moving average
and moving standard deviation series discussed below, the number of observations is
reduced to 941.
The 3-month rates are defined as follows:
Eurosystem:
Japan
Switzerland
UK
US
4
Euribor 3-month (offered rate)
Uncollateralised 3-month Rate (middle rate)
Swiss Interbank 3-month rate (bid rate)
3-month Interbank (middle rate)
US Treasury Bill 3-month rate (middle rate).
Empirics
7
Volatility of the interest rates is measured in this study in three ways; i) the absolute
deviation from a centred moving average of length 29 days4, ii) a moving standard
deviation also of 29 days and iii) an ARCH model calculated over the whole period
and the ARCH regression variance series saved. These measures were calculated for
both the overnight and 3-month rates.
Determination of the absolute deviation and moving standard deviations require no
further explanation. As regards the ARCH models a wide number of such models
exist – see see Bollerslev, Chou and Kroner, 1992) but in the empirical literature the
most commonly selected model is the GARCH(1,1) model. For the interest series for
the Eurosystem, Japan and the UK the GARCH (1,1) model was successful but less so
for the US data. In this latter case and EGARCH (1,1) model proved to be successful.
The GARCH (1,1) estimated model took the following general form:
Mean equation:
Variance Equation:
Yt = α + βYt-1 + εt
σ2t = α + γε²t-1 + δσ2t-1 + εt
(2a)
(2b)
Whilst for the EGARCH model, the mean equation is the same but the variance
equation’s general form is:
Variance Equation:
logσ2t = α+γlogσ2t-1+Φ|(εt-1/σt-1)|+Ώ((εt-1/σt-1) (2c)
Equation 2(a) is of course, a simple autoregressive equation. This can be justified by
the order of integration of the various series. In each case were i) unable to reject the
hypothesis that the levels variable were not stationary but ii) accept the hypothesis
that the difference variables were stationary implying that the level variables were
I(1)5,6.
In all cases of estimation, the coefficient β in the mean equation was significantly
different from zero at the 5% level – in fact in many instances the level of significance
was considerably higher. For the GARCH estimates, the ARCH and the GARCH
terms were also highly significant. In the case of US interest rates where EGARCH
was used, the EGARCH term was highly significant. The one defect of the estimates
concerns the residuals, which for none of the equations was it possible to accept the
hypothesis that they were normally distributed at any reasonable level of
significance7.
Summary results are shown in table 2 whilst figures 1 to 3 show the behaviour of the
measures over time. Whilst the statistics cannot be compared between the various
methods they can be compared for the same method between the various countries.
The pattern of behaviour was the same for all measures of volatility. The overnight
4
The length of 29 days was selected to represent approximately 1 calendar month but one which was
centred. Kasman chose a centred 30-day moving average and we wished to make our study as
comparable as possible with Kasdman’s.
5
The only exceptions were in the case of the UK overnight and the Japanese 3-month interest rates
where the ADF test indicated stationarity of the levels variable but the Phillips/Perron test indicated
non-stationarity.
6
For the sake of brevity the detailed results of these tests are not included in the paper but are available
from the author on request. This applies to other empirical work throughout the paper.
7
Given the large sample size, the rejection of the hypothesis that the residuals are normally distributed
should not cause any undue inconvenience.
8
volatility was the lowest for Japan, which is perhaps not surprising given the fact that
policy is directed towards this rate. Volatility was similar for all three measures for
the US and Eurosystem, with a slightly higher degree of volatility for Switzerland.
The UK stood out with a significantly higher level of volatilty being recorded. These
results accord with those reported by Kasman [1992] with the main difference being
that our results showed a lower level of volatility in the Switzerland rate than that
reported by Kasman. This no doubt reflects the changes in the operation of monetary
policy by the Swiss National Bank discussed in section 2.3.
Probably the overnight rate is of lesser importance in the financial environment than
the longer-term rates. We take the 3month rate as an indicator of financial conditions
in the longer term whilst noting that it is still a relatively short-term rate. For this
reason we report in table 3 the same measures of volatility for three-month rates in the
same markets. Similarly figures 4-6 show the pattern of volatility over time. The
contrast with the results reported in Table 2 is quite noteworthy. For all countries the
volatility measures are similar. In general the volatility for the 3-month rate as
evidenced by the measures adopted in our study are lower than those shown for the
overnight rate in table 2. Two differences are apparent: i) Japan now records the
highest (if only slightly) measure and ii) the measures for UK now conform to the
measures reported for the other countries.
This seems to suggest that the volatility in the overnight rate does not influence to any
great extent the volatility of the 3-month rate. We now propose to test this hypothesis
by i) regressing the 3-month volatility measures (i.e. the mean absolute deviation and
the moving standard deviation) on the corresponding overnight measures ii) including
the overnight-GARCH volatility as a determinant of the 3-month GARCH volatility
and iii) using the Granger [1969] causality test. In the case of the first test of all
necessary to ascertain that both the overnight and 3-month measures of volatility are
in fact stationary. A summary of significance of the relevant augmented DickeyFuller and the Phillips/Perron statistics are shown in Table 4 and it can easily be seen
that the hypothesis that the variables are I(1) is substantially rejected in all cases. As
we are accepting the alternative hypothesis that the relevant variables are stationary,
we can now proceed on to the estimation by OLS of the same equation used by
Kasman [1992] for both measures of volatility, i.e.:
Yt = α + βXt + εt
(1)
Where Y is the 3-month and X the overnight measure of volatilty.
We also added lagged measures of Y until the hypothesis that the error terms were
autocorrelated was rejected at the 5% level.
The estimation results are shown in Table 5. The estimated equations are not entirely
satisfactory in three respects:
1. In three equations (Switzerland both measures and US Absolute deviation)
autocorrelated error terms remained after introducing 10 lagged values of the
dependent variable.
2. In all cases heteroscedasticity remained a problem so that error terms quoted
are so that the quoted ‘t’ values are based on White heteroskedasticityconsistent standard errors.
9
3. The error terms are never normally distributed. Again, given the large sample
size, this is not a serious problem.
For the absolute deviations, the coefficient β in equation 2 above is not significantly
different from zero in only two out of the five estimated equations but for two of the
other three equations autocorrelation remains a problem. The position for the moving
standard deviations is almost reversed, we are able to reject the hypothesis that β = 0
in all the equations but note that, in the case of Switzerland, the estimated equation is
still polluted with autocorrelated errors.
As far as the absolute deviations (see table 1) are concerned the results do not reflect
those obtained by Kasman where there was little or no evidence of any transmission
of volatility from the overnight to the 3-month market. The various values of the DW
statistic quoted in his table suggest that higher order autocorrelation may be a problem
with his results. We now turn to the ARCH estimates.
The mean equations took the same form as noted above in equation (1) but the
relevant overnight variance became an additional regressor in the variance equation,
which took the following general form:
σ23mt = α + γε²t-1 + δσ2t-1 + σ2ont + εt
(3)
where the subscripts on and 3m refer to overnight and 3 month time periods.
The estimation results are shown in table 6. As in the case of the OLS estimations the
error terms were never normally distributed but, again, this does not seem to be a
serious problem. We also utilised the ARCH-LM test to check for any remaining
ARCH effects. In all cases except that of Japan we were unable to reject the null
hypothesis at the 5% level that the error terms were free of ARCH effects. Turning
now to the actual results it can be seen that in three cases the coefficient on the lagged
variance was significantly different from zero at the 5% level but that in the case of
the Eurosystem and Switzerland, the size of the coefficient was quite small so that it
does not seem to be important. In the case of Japan the estimated β coefficient is
dubious because of the continued coexistence of ARCH effects.
Finally we carried out Granger Causality tests (see Granger [1969]). Since we
assumed 4 lags would be sufficient for the test, this involves estimating bivariate
regressions of the following form:
Yt = α + β1Yt-1 + β2Yt-2 + β3Yt-3 + β4Yt-4 + γ1Xt-1 + γ2Xt-2 + γ3Xt-3 +
γ4Xt-4 + εt
(4)
Xt = α + δ1Yt-1 + δ2Yt-2 + δ3Yt-3 + δ4Yt-4 + λ1Xt-1 + λ2Xt-2 + λ3Xt-3 +
λ4Xt-4 + µt
(5)
The test then takes the form of testing whether the coefficients on the lagged terms are
significantly different from zero. If the lagged values on X (i.e. the γs) are
significantly different from zero in (4) and those on Y (δs) in (5) are not significantly
from zero, then causation is unidirectional from X to Y. The converse would also
apply. If the coefficients for both sets of lagged variables in equations (4) and (5) are
significantly different from zero then causation is bi-directional. Independence would
10
be assumed if the coefficients on the lagged values of the variable other than the
dependent variable were not significantly different from zero.
The estimation results are show in table 7. There is little indication of the overnight
rate ‘Granger’ causing the 3-month rate with the exception of the US. In this latter
case causation would appear to be bi-directional. In the case of the UK, the tests
suggest that the rates are independent.
Conclusions
We have re-examined the question of volatility in the money markets and central bank
intervention. Our methodology is based on i) absolute deviations from a centred
moving average, ii) moving standard deviation and the application of GARCH
estimation.
Our conclusions may be summarised as follows:
1. Volatility of the overnight interest rates has been reduced in the case of
Switzerland but remains higher in the UK than in the other countries.
2. In contrast 3-month interest rate volatility is similar for all the countries
concerned.
3. Despite using a variety of econometric techniques, there seems little evidence
of the transmission of interest-rate volatility from the overnight to the 3-month
interest rate markets.
4. Kasman [1992] concluded that the higher levels of volatility in the overnight
money markets in Switzerland and the UK pointed to the fact that these two
countries maintained low reserve requirements. This evidence is supported by
our study for the UK. One possible reason for the effect of low reserve
requirements is that banks have less flexibility in the management of their
reserve position with low reserve requirements and this leads to greater
fluctuations in the overnight rate.
References
Andersen, T.G., T.Bollerslev, F.X.Diebold and P.Labys [2003] ‘Modelling and
forecasting realized volatility’ Econometrica, 71, 579-625.
Bollerslev, T., R.Y.Chou and K.F.Kroner (1992) "ARCH modelling in finance: a
review of the theory and empirical evidence" Journal of Econometrics, 52, 5-59.
Buckle, M.J. and Thompson, J.L. (forthcoming) ‘The UK financial system: theory and
practice’ 4th edition, Manchester University Press, Manchester. UK.
Edwards, C.L. [1997], ‘Open market operations in the 1990s’, Federal Reserve
Bulletin, Nov, 859-874
Hamilton, J.D. [1996], ‘The daily market for federal funds’, Journal of Political
Economy, 104, 26-55.
Hartman, P., Manna, M. and Manzaneres, M. [2001], ‘The microstructure of the Euro
money market’, Journal of International Money and Finance, 20, 895-948.
Kasman, B. [1992] ‘A comparison of monetary policy operating procedures
11
in six industrial countries’, Federal Reserve Bank of New York, 17, no. 3,
5–24.
Miyanoya, A. [2000] ‘A guide to Japan’s market operations’ mimeo, Financial
Markets Division, Bank of Japan.
Poole, W. [1970], ‘Optimal choice of monetary policy instruments in a simple
stochastic macro model’, Quarterly Journal of Economics, 84.
Swiss National Bank [2003], ‘The monetary policy concept (as at January 2003)’
http://snb.ch/e/geldpolitik/content_konzept.html
12
Table 1 Overnight Interest Rate Volatility 1988 to 1991
(a)
Mean Absolute Deviation of Daily Observations in Basis Points
Japan
US
Germany
Canada
UK
Switzerland
8.2
14.4
15.2
18.3
30.9
35.5
Source:
Kasman [1992] Table A1.
(b)
Transmission from Overnight to 3-Month Rates
Country
Germany
Constant
0.05
(1.46)
Japan
0.04
(0.90)
Switzerland -0.13
(0.79)
UK
0.14
(7.14)
US
0.12
(4.79)
Β
0.25
(1.28)
0.22
(0.41)
0.70
(2.07)
-0.01
(0.14)
-0.16
(0.95)
R̄ 2
DW
-0.02 1.92
-0.01 2.34
0.23
2.32
-0.01 1.67
-0.01 2.23
Source Kasman [1992] Table A2
13
Table 2 Overnight Interest Rate Volatility 31/12/99 to 17/9/03
(Basis points)
Method
Eurosystem Japan Swiss UK
Absolute Deviation
8.8
14.8
Moving Standard Deviation*
Garch*a
15.2
*
a
0.6
1.1
11.3
46.7
18.1
1.8
15.6
54.8
53
US
9.8
15.2
13.5
Average over the period
Represented by the standard deviation rather than the variance
14
Table 3 3-Month Interest Rate Volatility 31/12/99 to 17/9/03
(Basis points)
Method
Eurosystem
Japan
Swiss
U
K
US
Absolute Deviation
Moving Standard Deviation*
Garch*a
3.0
6.2
2.6
5.3
7.5
3.8
3.3
4.9
6.8
3.5
5.6
3.6
9.2
4.5
*
a
7.2
Average over the period
Represented by the standard deviation rather than the variance
15
Table 4 Summary of Unit Root Tests
(a) Absolute Deviation
Country
Overnight
3 Month
ADF
Phillips/Perron ADF
Phillips/Perron
Eurosystem
Japan
Switzerland
UK
US
a
a
a
a
a
(4)
(3)
(8)
(2)
(11)
a
a
a
a
b
a
a
a
a
a
(1)
(4)
(10)
(1)
(3)
a
a
a
a
a
(b) Moving Standard Deviation
Country
Overnight
3 Month
ADF
Phillips/Perron ADF
Phillips/Perron
Eurosystem
Japan
Switzerland
UK
US
a
a
a
a
a
(2)
(4)
(3)
(1)
(1)
a
a
b
a
b
a
b
a
a
a
(1)
(8)
(2)
(2)
(4)
a
b
a
a
b
The figures in brackets in the ADF columns represent the number of lags in the ADF
equation
Rejection of the hypothesis that the variable is I(1) is indicate by a at the 1% level and
b at the 5% level
16
Table 5 Transmission of Overnight Volatilty to the 3-Month Rates
(OLS Estimation)
(a) Absolute Deviation
Country
Coefficient (β) No of lags t value** R̄ ²
Eurosystem 0.011
Japan
0.023
Switzerland 0.048
UK
-0.001
US
0.0690
2
2.445
0.802
5
0.323
0.613
10*
4.693
0.642
2
0.449
0.362
10*
4.524
0.656
(b) Moving Standard Deviations
Country
Coefficient (β) No of lags t value** R̄ ²
Eurosystem
Japan
Switzerland
UK
US
0.001
-0.016
0.002
0.002
0.003
2
8
10*
3
2
1.025
0.997
0.900
0.991
1.932
0.994
1.721
0.995
0.533
0.997
* Note that serial correlation of the error term is not eliminated after 10 lags
** t value based on White heteroskedasticity-consistent standard errors
17
Table 6 Transmission of Overnight Volatilty to the 3-Month Rates
(GARCH Estimation)
Country
Coefficient (β) Z Value
Eurosystem
Japan
Switzerland
UK
USA
0.00035
9.60
-0.46576
2.07
0.00280
4.84
0.00014
0.38
0.02087
0.58
18
Table 7 Granger Causation Tests
Country Measure
Direction of Test
Europe Standard Deviation Overnight to 3 month
3 month to Overnight
Absolute Deviation Overnight to 3 month
3 month to Overnight
Accept
X
9
X
9
Japan
Standard Deviation Overnight to 3 month
3 month to Overnight
Absolute Deviation Overnight to 3 month
3 month to Overnight
X
9
X
X
Swiss
Standard Deviation Overnight to 3 month
3 month to Overnight
Absolute Deviation Overnight to 3 month
3 month to Overnight
X
9
9
X
UK
Standard Deviation Overnight to 3 month
3 month to Overnight
Absolute Deviation Overnight to 3 month
3 month to Overnight
X
X
X
X
US
Standard Deviation Overnight to 3 month
3 month to Overnight
Absolute Deviation Overnight to 3 month
3 month to Overnight
9
9
9
9
9 indicates non-rejection of the hypothesis at the 5% level that the first variable does
not Granger cause the second variable
X indicates rejection at the 5% level of the hypothesis that the first variable does not
Granger cause the second variable
19
Figure 1: Overnight Volatility - Absolute Deviation
300
250
Basis Points
200
Eonia
US
150
Japan
Uk
Swiss
100
50
0
20/01/2000
20/07/2000
20/01/2001
20/07/2001
20/01/2002
20
20/07/2002
20/01/2003
20/07/2003
Figure 2: Overnight Volatility - Moving Standard Deviation
140
120
100
UK
80
Eonia
US
Japan
60
Swiss
40
20
0
20/01/2000
20/07/2000
20/01/2001
20/07/2001
20/01/2002
21
20/07/2002
20/01/2003
20/07/2003
Figure 3: Overnight Volatility - Garch
200
180
160
140
Basis Points
120
Eonia
UK
100
US
Japan
Swiss
80
60
40
20
0
31/12/1999
29/12/2000
28/12/2001
22
27/12/2002
Figure 4: 3-Month Volatility - Absolute Deviation
80
70
60
Basis Points
50
Euribor
Japan
UK
40
US
Swiss
30
20
10
0
20/01/2000
20/07/2000
20/01/2001
20/07/2001
20/01/2002
23
20/07/2002
20/01/2003
20/07/2003
Figure 5: 3-Month Volatility - Moving Standard Deviation
60
50
40
Euribor
Japan
30
UK
US
Swiss
20
10
0
20/01/2000
20/07/2000
20/01/2001
20/07/2001
20/01/2002
24
20/07/2002
20/01/2003
20/07/2003
Figure 6: 3-Month Volatility GARCH
45
40
35
30
Basis Points
Eurobor
Japan
25
Swiss
UK
20
US
US
15
10
5
0
31/12/1999
29/12/2000
28/12/2001
25
27/12/2002