Comparing different methods for the estimation of interbank intraday yield curves

• Published date: 01 July 2020
• DOI: http://doi.org/10.1002/jcaf.22438
• Author: Anastasios Demertzidis,Vahidin Jeleskovic
• Date: 01 July 2020

BLIND PEER REVIEW

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

Correspondence

Dr. Vahidin Jeleskovic, Department of

Economics, Quantitative Methods in

Economics, University of Kassel, Nora-

Platiel-Str. 4, D-34109 Kassel, Germany.

Email: Jeleskovic@uni-kassel.de

Abstract

In this study, we compare three different models, namely, the Nelson–Siegel

model (NSM), the Svensson model (SVM), and the Diebold–Li 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.

KEYWORDS

Diebold–Li model, e-MID, interbank credit market, intraday yield curve, Nelson–Siegel model,

Svensson model

JEL CLASSIFICATION

C12; C13; E43; G01

1|INTRODUCTION

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;31:57–75. wileyonlinelibrary.com/journal/jcaf 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

structure.

1

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

modeledandestimatedbyastandardnonlinearmodel

which is used by many researchers and central banks

(Diebold & Rudebusch, 2013), namely by the Nelson–Siegel

model (NSM). The authors achieve an R

2

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.

2

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.

58 JELESKOVIC AND DEMERTZIDIS