Comparing different methods for the estimation of interbank intraday yield curves

Published date01 July 2020
AuthorAnastasios Demertzidis,Vahidin Jeleskovic
Date01 July 2020
Comparing different methods for the estimation of
interbank intraday yield curves
Vahidin Jeleskovic | Anastasios Demertzidis
Department of Economics, Quantitative
Methods in Economics, University of
Kassel, Kassel, Germany
Dr. Vahidin Jeleskovic, Department of
Economics, Quantitative Methods in
Economics, University of Kassel, Nora-
Platiel-Str. 4, D-34109 Kassel, Germany.
In this study, we compare three different models, namely, the NelsonSiegel
model (NSM), the Svensson model (SVM), and the DieboldLi model (DLM), for
the estimation of an intraday yield curve on the Italian interbank credit market e-
MID.Usingasample,whichspansfromOctober 2005 until March 2010, the first
important finding is that all three models arehighlysuitablefortheestimationof
an intraday yield curve providing superior empirical results when compared with
similar works on e-MID. The second important finding is that, based on different
in-sample statistics, the SVM dominates the other two models before, during, and
after the financial crisis from 2007. Moreover, the NSM seems to dominate the
DLM although these differences in goodness-of-fit between these two models may
not be statistically significant. Our findings are of high practical importance from
different perspectives regarding interbank credit markets, including the better
understanding of trading processes, the optimization of banks' trading strategies,
and monetary policy implications. Finally, our findings can be seen as the starting
point for further analysesinthisresearcharea.
DieboldLi model, e-MID, interbank credit market, intraday yield curve, NelsonSiegel model,
Svensson model
C12; C13; E43; G01
Interbank credit markets p lay a major role for the distri-
bution of liquidity among b anks. On these markets,
banks with a liquidity surplu s and banks with liquidity
needs can efficiently trade and thus optimize their
liquidity positions. Disto rtions on these markets re sult
often in liquidity crunches of b anks, which then have an
effect on the credit supply to households and firms
(Affinito, 2012).
Is there an implicit intraday interest on interbank
credits? This question has been assessed recently in differ-
ent papers, due to the fact that changes in the interest rate
during the day affect the refinancing costs of banks to a
high extend. Jurgilas and Žikeš(2014) and Merrouche and
Schanz (2010) in the United Kingdom and Furfine (2001
and 2002) in the United States asses this question. By
using linear models, they found out that there is a down-
ward trend in the intraday interest rate, meaning that the
interest rates in the analyzed interbank credit markets are
Received: 21 October 2019 Revised: 29 November 2019 Accepted: 4 December 2019
DOI: 10.1002/jcaf.22438
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided
the original work is properly cited.
© 2020 The Authors. Journal of Corporate Accounting & Finance published by Wiley Periodicals, Inc.
J Corp Acct Fin. 2020;31:5775. 57
higher in the morning and lower in the afternoon. In all
these studies, authors stress that these results are in line
with the theoretical argumentation given by themselves.
Abbassi, Fecht, and Tischer (2017) base their analysis on
secured funding data and use a linear model as well. They
find out that after the start of the financial crisis, theintra-
day term structure of interest rates may not be only mono-
tone falling during a day.
Regarding the e-MID market (Mercato Interbancario
dei Depositi), the only electronically organized interbank
credit in the Euro area and in the United States, different
studies focus on the estimation of an intraday term struc-
ture in different periods. Angelini (2000) was the first one to
analyze the intraday behavior of interest rates on the e-MID
market. Using a linear model for the intraday interest rates
and based on hourly means of the intraday interest rates in
the period from July 1993 to December 1996, he finds only
very weak evidence for an existing downward intraday term
This low evidence is shown in the estimated
term structure where the difference of the interest rate in
the morning and in the afternoon differs only to a very
small degree. Based on his premise, the main force of the
intraday interest rates are variations in the market liquidity.
Baglioni and Monticini (2008), apply also a linear
model using hourly means to estimate the intraday term
structure in the sample from January 2003 until December
2004. They find weak statistical evidence for a downward
trend in the intraday structure, which is also reflected in a
relatively small difference between interest rate in the
morning and in the afternoon. They state that the main
drive behind these movements is the higher credit risk, in
terms of the counterparty risk, in the morning rather than
in the afternoon.
Using two data samples from 11th of July to 10th of
September 2007, Baglioni and Monticini (2010) redo their
analysis from the year 2008. In this second analysis, they
find evidence for a downward trend in the intraday term
structure, which becomes steeper after the outbreak of
the financial crisis in 2007. In addition, here they state
that these facts can be observed due to higher credit risk
in the morning than in the afternoon.
Baglioni and Monticini (2013) also estimate an intraday
term structure on the e-MID market, using three different
extended linear models, based on the difference of the aver-
age of the interest rates between 09:00 a.m. and 01:00 p.m.,
called the morning rate, and the average of interest rate
between 02:00 p.m. and 06:00 p.m. called the afternoon
rate. By using a sample ranging from January 2007 to April
2009, they again find evidence for a downward trend in the
term structure of interests. Based on their models, this
downward trend becomes even steeper after the outbreak
of the financial crisis in August 2007 and the steepest after
the collapse of Lehman Brothers in September 2008. They
also argue that the intraday interest differs from the morn-
ing to the afternoon due to higher counterparty credit risk
as well as due to market liquidity constraints. Furthermore,
they state that the interest rates may be influenced by
incoming news in this particular period.
Furthermore, Demertzidis and Jeleskovic (2016) intro-
duced the concept of the spot intraday yield curves (SIYCs)
and differ from the previous studies in two major points,
namely, the use of tick-by-tick interest rate data and the
use of a nonlinear model. For the time period from October
2005 to March 2013, they showed that the SIYC can be
which is used by many researchers and central banks
(Diebold & Rudebusch, 2013), namely by the NelsonSiegel
model (NSM). The authors achieve an R
of up to .424 on
average, which is remarkably high since they us e tick-by-
tick data. The authors conclude that one should move from
the assumption of linear models for the estimation of SIYC
toward explicit modeling of the nonlinear dynamics. The
second very interesting empirical result is that the
goodness-of-fit become significantly higher after the out-
break of the financial crisis. Thus, one should expect higher
nonlinear systematic dynamics of yield curves during tur-
moil on interbank credit markets. The authors attribute
this fact to the more intensive process of incoming news
within a day during the financial crisis.
The NSM has been modified and extended by many
researchers. Among others, Bliss (1996) with his three-
factor model interpretation, Björk and Christensen
(1999), with their five-factor NSM, Christensen, Diebold,
and Rudebusch (2009) and Christensen, Diebold, and
Rudebusch (2011) with their arbitrage free interpretation
of the NSM and Chen and Niu (2014) with their adaptive
dynamic NSM, modified and/or extended the model.
One important model modification which improves
the original NSM significantly from the theoretical as well
as from a practical point of view is proposed by Svensson
(1994) (Svensson model [SVM]). The major highlight of
the SVM is modeling a second hump in the yield curve.
This model is used for the estimation of the yield curve by
many central banks, including the ones of Germany, Nor-
way, Spain, Sweden, and Switzerland (BIS, 2005).
According to De Pooter (2007), this model should be used
when estimations of a larger variety of yield curves or
more complex dynamics of the yield curves is necessary.
Hence, this model should be used in times of higher vola-
tility, for example, in times of a financial crisis.
The SVM is also used by many researchers for the
estimation of the yield curve for different markets.
Among others, Schich (1997) for the German bond mar-
ket, Clare and Lekkos (2000) for the bond yield curves in
the United States, Germany, and the United Kingdom,
and Gürkaynak, Sack, and Wright (2007) for the U.S.

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