The Volatility and Correlation between the Exchange Rate of British
Pound and Euro: Based on the Comparison before and after Brexit
Yuke Mei
a
School of finance, Dongbei university of finance and economics, Dalian, 116012, China
Keywords: Exchange Rate, Brexit, GARCH Model, VAR Model.
Abstract: After becoming the first country in history to leave the EU, the UK went through a transition period of 11
months, which ended on December 31, 2020. At this point, the process of the UK's exit from the EU comes
to an end, and it is also the starting point of the future relationship between the UK and the EU. This paper
focuses on the changes generated in the sterling exchange rate and the euro exchange rate before and after the
UK's formal exit from the EU, so as to detect the changes in the volatility and correlation between the sterling
exchange rate market and the euro exchange rate market. By selecting exchange rate data from the RESSET
database, this paper uses the GARCH family model as well as the VAR model to compare the degree of
volatility and correlation between the British and European exchange rate markets before and after Brexit,
and analyze the changes in the return on the pound exchange rate and the return on the euro exchange rate
before and after Brexit, as well as the correlation between the exchange rate fluctuations of the two exchange
rate markets. Through theoretical and empirical analysis, the main findings and conclusions of this paper are
that after the formal exit from the EU, the volatility of both the pound exchange rate and the euro exchange
rate are strengthening, and the effectiveness of the exchange rate market is reduced. After the empirical study,
the price volatility spillover effect of the sterling exchange rate market is obvious and it takes longer to recover
from the shock of the UK's exit from the EU; while the euro market is subject to shorter shocks relative to the
sterling market, and the correlation between the sterling exchange rate and the euro exchange rate also
decreases with the UK's formal exit from the EU.
1 INTRODUCTION
There are many scholars who have conducted studies
on exchange rate markets and Brexit. In the process
of research on international exchange rate markets,
Kim (Kim 2006) conducted an empirical analysis by
selecting daily return data between the euro and
major foreign currencies (Kim, et al, 2006), and the
experimental results showed that the correlation
between the euro and the US dollar increased and t
1
he
correlation with the yen and the Australian dollar
volatility decreased. Later some scholars continued to
expand the research object, Bunda (Bunda 2009)
studied 11 years of exchange rate market index data
of 18 emerging markets and analyzed by GARCH
family model (Bunda, et al, 2009), and the results
showed that emerging markets are similar to
developed countries, there is a linkage between
exchange rate returns. After the financial crisis in
a
https://orcid.org/0000-0002-3357-8090
2008 and the European debt crisis in 2010, the study
of the impact of major contingencies on the volatility
between markets has gradually been included in the
vision of scholars. Among the more common studies
on yields, Kollias (Kollias 2011) uses yield pricing
models, among others, to observe whether major
events cause significant positive or negative
fluctuations in market prices (Kollias et al, 2011), and
Essaddam (Essaddam 2014) uses a GARCH model to
portray the impact of major shocks on yield volatility
(Essaddam, et al, 2014). In terms of targeting
exchange rate movements, Christiansen
(Christiansen 2010) provides an in-depth analysis of
the volatility and time-variability between the euro
and other currencies, and the study finds time-varying
characteristics between the euro exchange rate and
the exchange rates of other national currencies
(Christiansen 2012). In studying the interaction
between the sterling exchange rate and the euro
exchange rate, Favero et al. (2012) developed a non-
204
Mei, Y.
The Volatility and Correlation between the Exchange Rate of British Pound and Euro: Based on the Comparison before and after Brexit.
DOI: 10.5220/0011171000003440
In Proceedings of the International Conference on Big Data Economy and Digital Management (BDEDM 2022), pages 204-210
ISBN: 978-989-758-593-7
Copyright
c
2022 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
linear GVAR model and the results of the study
showed that the market spread between the euro and
sterling exchange rates are interdependent variables
(Favero 2012). By comparing the volatility between
the exchange rate of the British pound and the
exchange rates of the UK's major trading partners
before and after Brexit, Qiong Zhao (2019) shows
that the UK's exit from the EU leads to weaker
linkages between the UK market and the European
exchange rate market (Zhao, et al, 2019). Wang Lu
(2020) investigates the entire process of abnormal
exchange rate fluctuations during the referendum
period using a time series outlier diagnostic algorithm
and finds that all major exchange rates are
significantly affected (Wang, et al, 2019).
However, most of the current literature focuses on
a comprehensive analysis of the exchange rates of
several major world currencies, lacking a separate
study between the euro and the pound, two types of
European currencies, so there is still some room for
research in the analysis of the impact of the UK's exit
from the EU. This paper, on the basis of the earlier
scholars' research, analyzes the impact of the UK's
exit from the EU on the European monetary system,
separately analyzes the changes in volatility and
correlation between the exchange rates of the British
pound and the euro, and explores the impact of the
volatility caused by the UK's exit from the EU on the
exchange rates of the British pound and the euro from
the price spillover effect and the volatility spillover
effect.
In the research process, this paper decided to
adopt an empirical research method. By using the
data of the British pound exchange rate and the euro
exchange rate before and after the formal exit of the
UK from the European Union, this paper builds a
VAR model and a GARCH model to analyze the log
returns of the exchange rate and investigate the price
spillover effect and the volatility spillover effect on
the British pound exchange rate and the euro
exchange rate, respectively.
2 CHARACTERISTICS OF
EXCHANGE RATE MARKET
VOLATILITY
2.1 Pound Sterling Exchange Rate
Market
The pound exchange rate fell continuously after the
UK began preparations for a formal exit from the EU.
Over the following three long years of Brexit
negotiations, the pound exchange rate moved
differently with each Brexit proposal. By January
2020, the UK was in the critical phase of its imminent
formal exit from the EU and caught up in a sudden
new crown epidemic. The dual pressures have had a
significant impact on the sterling exchange rate
market and indeed European currency markets.
However, in late 2020, new economic stimulus
policies were introduced in the Eurozone and the UK,
combined with the successful development and
application of several new crown vaccines, which
mitigated the impact of the new crown epidemic and
allowed the UK to avoid a disorderly exit from the
EU to the greatest extent possible. In turn, at the end
of 2020, after the UK and Europe in reaching a trade
agreement, the pound against the dollar trend has
entered the upward channel. And given that the pound
is severely undervalued against the dollar, with Brexit
officially in place, the pound will have far more
upside against the dollar than the euro against the
dollar in 2021.
2.2 Euro Exchange Rate Market
A look at the changes in the euro's movement over the
last six years reveals a strong correlation between
changes in the euro exchange rate and EU policy.
Between mid and late 2014, the European Central
Bank lowered its benchmark interest rate twice in line
with the Fed's movements and the euro depreciated
by 10% relative to the dollar. The European Central
Bank announced another impending quantitative
easing in January 2015, and the euro continued to
dive against the dollar between the policy
announcement and its implementation, with the shock
in the euro exchange rate exacerbated by the events
of the 2016 Brexit referendum in the period
thereafter.
Given the large impact of the epidemic on the
eurozone economy, the ECB continued to implement
a more accommodative monetary policy, with interest
rates and asset returns remaining largely low. The
euro exchange rate saw an appreciative move in April
2020 as we entered 2020, i.e. after the formal signing
of the Brexit agreement between the UK and the EU.
3 CORRELATION ANALYSIS OF
THE BRITISH POUND AND
THE EURO
3.1 Price Spillover Effects
Price spillovers i.e. due to the existence of liquidity
and transmission of funds and information and
consumer information in the market itself, yields are
affected not only by their own prior period yields but
also by the current and prior period yields of other
The Volatility and Correlation between the Exchange Rate of British Pound and Euro: Based on the Comparison before and after Brexit
205
assets. For example, the spread between the yield on
10-year gilts and the yields on other countries' bonds
or US Treasury bills over the same period, 3-month
European sterling deposits, i.e. sterling deposits
placed with non-UK banks, and UK equities all have
varying degrees of influence on the sterling exchange
rate. Where the yield on the Euro exchange rate can
also have a crossover effect on the Pound exchange
rate. As the UK was also a member of the EU, there
is a clear correlation between the fluctuations in
exchange rate yields between the sterling exchange
rate market and the euro exchange rate market.
3.2 Volatility Spillover Effects
Volatility spillover effects mainly measure the
transmission of volatile information among exchange
rate markets, and the causes of volatility in an
exchange rate market may include not only its own
volatility but also the volatility of other markets. For
the euro and the pound, before Brexit, the pound as
one of the European currencies, due to monetary
policy, economic and trade relations, capital flows
and other factors show a strong synergy with the euro.
And the end of the referendum, the euro exchange
rate of the pound exchange rate trend occurred in a
clear sign of divergence. The reason for this is that
the ongoing Brexit negotiations at the time had a
significant impact on the pound exchange rate market
and the euro exchange rate market.
4 EMPIRICAL ANALYSIS
4.1 Data Selection
In this paper, the pound to dollar exchange rate and
the euro to dollar exchange rate are selected as
variables for two different time periods and the
exchange rates are indirectly marked up. The first
time period before the formal exit from the EU, i.e. 1
January 2014 to 31 January 2020, and the second time
period after the formal exit from the EU, i.e. 31
January 2020 to 31 March 2021, respectively. The
daily returns on the sterling exchange rate and the
daily returns on the euro exchange rate for the
corresponding periods are then continued to be
selected and processed, following which the
corresponding four variables are obtained as shown
in Table 1. All data were obtained from the RESSET
database.
Table 1: Variables.
Variables Variable Meaning
RGBPB
GBP exchange rate yields from 1 January
2014 - 31 January 2020 (before official
Brexit)
RGBPA
GBP exchange rate yields from 31 January
2020 - 31 March 2021 (after official Brexit)
RERUB
Euro exchange rate yields from 1 January
2014 - 31 January 2020 (prior to official
Brexit)
RERUA
Euro exchange rate yields from 31 January
2020 - 31 March 2021 (after official Brexit)
4.2 Data Processing
After selecting the daily closing prices of the
exchange rates in both phases, this paper uses
logarithmic first order difference to obtain the daily
returns. 𝑅
is the daily return on day t, the 𝑃
and𝑃

are the exchange rate daily closing prices on
day t and (t-1), respectively.
𝑅
=𝑙𝑛𝑃
−𝑙𝑛𝑃

(1)
4.3 Correlation Test of Variables
4.3.1 Unit Root Test
In this paper, the ADF unit root test is selected in the
form of a test that includes a trend term and an
intercept term.
Table 2: ADF unit root test.
Variables ADF value 1% threshold
probability
(
math.
)
conclude
RERUB -41.01785 -3.434265 0.0000 smoothly
RERUA -14.35927 -3.99374 0.0000 smoothly
RGBPB -39.73734 -3.434265 0.0000 smoothly
RGBPA -13.52014 -3.99374 0.0000 smoothly
Based on the results in Table 2, it can be seen that
the results of the unit root test are smooth.
BDEDM 2022 - The International Conference on Big Data Economy and Digital Management
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4.3.2 ARCH Effect Test
Before proceeding with the GARCH model
modeling, the presence of autoregressive conditional
heteroskedasticity in the error term needs to be tested,
and in this paper, the ARCH-LM method is chosen to
test for ARCH effects.
Table 3: ARCH effect test.
Variables F-statistic P-value
RERUB 39.86798 0.0000
RERUA 7.701291 0.0059
RGBPB 49.21345 0.0000
RGBPA 12.88510 0.0004
It can be seen from Table 3 that the p-values of
the F-statistics are all less than 0.05, indicating that
there is a significant ARCH effect in the series of
GBP exchange rate and EUR exchange rate returns
before and after Brexit, so the GARCH model can be
used to study the volatility spillover effect between
the two exchange rate markets.
4.3.3 Determination of the Lag Order
Before building a VAR model for the data before and
after the Brexit, the lag order in the VAR model needs
to be judged. By setting different lag lengths, the most
appropriate lag order is selected under each criterion
such as AIC, SC and LR.
Table 4: Lagged order test.
lag LogL LR FPE AIC SC HQ
Post-Brexit
0 1943.619 NA 6.96e-10 -15.40967 -15.38166
*
-15.39840
*
1 1948.894 10.42550 6.89e-10 -15.41980 -15.33576 -15.38598
2 1952.144 6.371118 6.93e-10 -15.41384 -15.27379 -15.35749
3 1957.452 10.31930 6.86e-10 -15.42422 -15.22814 -15.34532
4 1962.027 8.825035 6.83e-10 -15.42879 -15.17669 -15.32735
5 1966.552 8.653397 6.80e-10 -15.43295 -15.12482 -15.30897
6 1973.847 13.83804 6.63e-10 -15.45910 -15.09496 -15.31258
7 1982.848 16.93121
*
6.37e-10
*
-15.49880* -15.07863 -15.32973
8 1984.608 3.282021 6.48e-10 -15.48102 -15.00482 -15.28941
Pre-Brexit
0 12348.55 NA
*
5.82e-10
*
-15.58907
*
-15.58230
*
-15.58656
*
1 12351.33 5.557788 5.83e-10 -15.58754 -15.56721 -15.57999
2 12353.64 4.609836 5.84e-10 -15.58541 -15.55152 -15.57282
3 12355.71 4.122175 5.85e-10 -15.58297 -15.53553 -15.56535
4 12356.27 1.106581 5.88e-10 -15.57862 -15.51763 -15.55596
As can be seen from the Table 4, the lag order in
the post-Brexit phase should be 7 according to the
optimal criterion, while in the pre-Brexit phase, the
optimal lag order is 0 according to different criteria,
and a lag order of 0 means that the variables do not
meet the modeling conditions of the VAR model, so
this paper finally decides to adopt a general linear
model to conduct a simple regression analysis of the
two variables in the pre-Brexit phase.
4.3.4 Stability Test
The stability of the model is tested again after
determining the lag order, and the AR root test results
show that the characteristic roots fall within the unit
circle, so the VAR model constructed in this paper is
stable.
4.4 Modeling and Effects Analysis
4.4.1 VAR Model Results
VAR modeling is performed only for GBP exchange
rate returns and EUR exchange rate returns after
formal exit from the EU.
Table 5: VAR modeling results.
V
ariables RERUA (-1) ERERUA (-2) RERUA (-3) RERUA (-4) RERUA (-5) RERUA (-6) RERUA (-7)
RERUA 0.031627* 0.075935* -0.168947** -0.017687* 0.085813** -0.072016* 0.093485**
RGBPA 0.008421 0.218075* -0.328837 0.130962 0.158315* -0.058723* -0.199245*
variable RGBPA (-1) RGBPA (-2) RGBPA (-3) RGBPA (-4) RGBPA (-5) RGBPA (-6) RGBPA (-7)
RERUA 0.091273** 0.041363** 0.073354** -0.053260** 0.008907** -0.130022* -0.040966**
RGBPA 0.168805* 0.257843* 0.257843* -0.145745* 0.101457* -0.109013* -0.058465*
The Volatility and Correlation between the Exchange Rate of British Pound and Euro: Based on the Comparison before and after Brexit
207
The output of the VAR model in Table 5 shows
that the pound exchange rate is still influenced by its
own pre-Brexit exchange rate as well as the euro
exchange rate after the UK formally leaves the EU,
but the coefficients are less significant. Based on the
data from a simple general linear regression of the
UK's pre-Brexit exchange rate in this paper, the
regression coefficient between the pre-Brexit return
on the pound exchange rate (RGBPB) and the return
on the euro exchange rate (RERUB) is 0.651240,
which has a p-value of 0.0000, a significant result.
This implies that the degree of explanation of the
Euro exchange rate return on the Pound exchange rate
return is high, indicating that the two exchange rate
returns are highly correlated and the Euro exchange
rate has a significant impact on the Pound exchange
rate before the UK leaves the EU. However, it can
also be seen that after the UK has carried out a formal
exit from the EU, the overall level of significance of
the coefficient between the pound exchange rate and
the euro exchange rate is significantly lower,
indicating that the post-Brexit pound exchange rate
market and the euro exchange rate market does still
have a spillover effect, but the volatility of the return
spillover effect is not very obvious, the degree of
mutual influence between the two has been reduced.
Figure 1: Impulse response function graph
As can be seen from the impulse response
function results graph in Figure 1, after the UK's
formal exit from the EU, the euro exchange rate
returns and the pound exchange rate returns are
subject to their own factors when the shock, in the
first two periods are fast declining trend, indicating
that the shock is strong at the beginning, the market
produces significant volatility, the subsequent change
amplitude slowed down, but the shock response time
is longer. For the two markets between the impact of
each other's yields when the shock, in the euro
exchange rate by the positive shock of the change in
the exchange rate of the pound first showed an
upward trend, and then gradually smooth, later there
is a small decline, the overall volatility of the shock
by the pound is not large. And when the pound by the
euro shock in the early appear rapid downward trend,
the response is stronger than the euro, and the overall
view of the euro exchange rate on the impact of the
pound exchange rate is negative, the response time of
the pound market compared with the euro market is
also longer.
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4.4.2 GARCH Model
Table 6: Estimation results of the pre-Brexit GARCH model.
V
ariable RERUB RGBPB
Models GARCH GARCH
modulus P-value modulus P-value
α
0.035287 0.0000 0.036686 0.0000
β
0.963156 0.0000 0.955948 0.0000
Log likelihoo
d
6137.996 6327.289
AIC -7.727783 -7.966338
SC -7.707482 -7.946037
Table 7: Estimation results of Post-Brexit GARCH model.
V
ariable RERUBA RGBPA
Models GARCH GARCH
modulus P-value modulus P-value
α
0.112537 0.0481 0.154713 0.0079
β
0.801979 0.0000 0.738681 0.0000
Lo
g
likelihoo
d
1045.497 960.8205
AIC -7.973155 -7.344773
SC -7.904869 -7.262604
From the results in Table 6 and Table 7, it can be
seen that after the formal exit from the EU, the euro
and sterling market returns are still volatile, the sum
of the ARCH term and GARCH term coefficients for
euro exchange rate returns is 0.914516 and the sum
of the ARCH term and GARCH term coefficients for
sterling exchange rate returns is 0.893394, the sum of
the coefficients in the post-Brexit GARCH model for
both is less than 1. However, compared to the pre-
Brexit become smaller than before Brexit, indicating
that the conditional heteroskedasticity of the two
exchange rate markets is less persistent in response to
shocks after Brexit, the coefficients of the GARCH
terms of both markets have decreased, and the
coefficients of the ARCH terms have become larger,
indicating that the volatility of the respective
exchange rate markets has strengthened and market
effectiveness has decreased.
5 CONCLUSIONS
The market shock from the Brexit event has been
persistent. During the period from the Brexit
referendum in 2016 until the formal exit from the EU
in early 2020, the pound exchange rate and the euro
exchange rate have been subject to persistent shocks,
and the pound exchange rate yield has also suffered a
new round of strong shocks after the formal exit from
the EU, and the exchange rate is more volatile, while
the euro exchange rate is subject to smaller shocks
than the pound. At the same time, through the image
above response, the pound exchange rate market and
the euro exchange rate market are affected by each
other's prior yield shock and the effect is more
obvious, indicating that the price volatility spillover
effect in the two markets. This effect is with the
implementation of the post-Brexit trade agreements
gradually weakened, and will eventually gradually
level off.
There is significant aggregation of exchange rate
returns in the pound exchange rate market and the
euro exchange rate market. Both before and after the
UK's formal exit from the EU, there is a significant
ARCH effect in both exchange rate markets,
indicating that there is significant aggregation of
exchange rate returns in both markets. The ARCH
term coefficient increases after the formal exit of the
UK from the EU compared to the pre-Brexit period,
and the respective volatility of the GBP and EUR
markets strengthens, but the effectiveness of the
markets decreases. According to the current exchange
rate market, the movements of the sterling exchange
rate market and the euro exchange rate market are
also gradually diverging, and the correlation between
the two exchange rate markets has weakened.
The linkage between the pound exchange rate
market and the euro exchange rate market has
weakened. The results of the VAR model and the
results of the GARCH model test show that, due to
the re-establishment of the British-European political
and economic trade relations, the close linkage
between the sterling exchange rate market and the
The Volatility and Correlation between the Exchange Rate of British Pound and Euro: Based on the Comparison before and after Brexit
209
euro exchange rate market has weakened compared
with the period before the formal exit of the United
Kingdom from the European Union, and the sterling
exchange rate and the euro exchange rate have
produced more obvious differences in response to
each other's shocks, and the volatility spillover effect
between the markets has decreased. With the formal
exit of the United Kingdom from the European
Union, the mutual impact between the two markets
has also been reduced by the different measures taken
by the United Kingdom and the European Union with
regard to future developments.
ACKNOWLEDGMENTS
I would like to thank every teacher who helped me
during the writing process. From the selection of my
thesis to its completion, my teaching assistant
provided me with strong assistance in every step of
the process, maintained patience and guided me to
study and experiment independently. After this paper
was completed, the thesis teacher maintained a
professional and rigorous attitude in proposing
changes to the details of the thesis and assisted me in
completing the final draft. There are still many
shortcomings in my paper, but this writing experience
and my teacher's help will definitely benefit me in my
future studies.
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