Contagion in futures FOREX markets for the post-Global Financial Crisis: A multivariate FIGARCH-cDCC approach

This paper seeks to investigate the time-varying conditional correlations to the futures FOREX market returns. We employ a dynamic conditional correlation (DCC) Generalized ARCH (GARCH) model to find potential contagion effects among the markets. The under investigation period is 2014-2019. We focus on four major futures FOREX markets namely JPY/USD, KRW/USD, EUR/USD and INR/USD. The empirical results show an increase in conditional correlation or contagion for all the pairs of future FOREX markets. Based on the dynamic conditional correlations, KRW/USD seems to be the safest futures FOREX market. The results are of interest to policymakers who provide regulations for the futures FOREX markets.


Introduction
The purpose of this paper is to investigate the potential contagion effects among four major futures FOREX markets by taking into account the volatility transmission between the markets. We consider the JPY/USD, KRW/USD, EUR/USD and INR/USD futures FOREX markets from 2014 to 2019. We quantify contagion using the dynamic conditional correlation (DCC) Generalized ARCH (GARCH) model.
The motivation for examining contagion is as follows. First, to the best of our knowledge, there is no other empirical research investigating the conditional second moments of the distribution of among futures FOREX markets (Figure 1) (spillover effects) (Allen & Gale, 2000;Caramazza, Rizzi & Salgado, 2004;Kaminsky, Carmen & Vegh, 2002). Spillovers refer to the impact that events in one market can have on another market. Second, the existence of contagion between the above markets is of great importance, since the under investigation period is the aftermath of the global financial crisis of 2008. Fourth, contagion results reveal common explanatory factors, revealing an underlying financial mechanism.
Furthermore, three interesting aspects emerged from this paper. Firstly, based on the descriptive statistics, JPY/USD demonstrates the largest fluctuations compared to the rest markets, indicating that JPY/USD is the most immune futures FOREX market. Secondly, the results of the cDCC-FIGARCH(1,d,1) model show the existence of volatility spillovers. Thirdly, dynamic conditional correlations show evidence of contagion for all the pairs of markets.

Literature Review
The main body of the current literature investigates the linkages between derivative markets with financial markets (Belke & Gokus 2011;Fonseca & Gottschalk;2012;Tokat 2013). Belke and Gokus (2011) examine the volatility transmission among the daily equity prices, CDS premiums and bond yields returns for four large US banks for the period 2006-2009. By employing a BEKK-GARCH model, they capture spillover effects. Fonseca and Gottschalk (2012) examine the volatility spillovers among CDS premium and equity returns for Australia, Japan, Korea and Hong Kong at firm and index level. They use weekly data during the period 2007-2010 and they show empirical evidence of spillover effects. Tokat (2013) empirically3 investigates the spillover effects between daily 5-year maturity sovereign CDS values for Brazil and Turkey denominated in USD, iTraxx XO index and CDX index during the period from 2005 to 2011. He employs a full BEKK-GARCH model and he proves empirically the existence of spillovers.
Additionally, there are several studies investigating linkages between oil crude oil future contracts with macroeconomic figures, financial markets and commodities. (Haigh & Holt, 2002;Guo & Kliesen, 2005;Malik & Hammoudeh, 2007;Driesprong, Jacobsen, & Maat, 2008). Haigh & Holt (2002) develop a theoretical model for a representative energy trader that simultaneously employs crude oil, heating oil, and natural gas futures to hedge future price uncertainty. They use weekly spot and future price data during the period from 7th December 1984 until 26th September 1997 for crude oil, unleaded gasoline and 2 heating oil sourced from Bridge/CRB. They find that the multivariate GARCH methodology, which takes into account volatility spillovers between markets, reduces significantly the uncertainty. Guo and Kliesen (2005) examine whether crude oil futures prices have a negative and significant effect on future gross domestic product (GDP) growth. They use daily values of crude oil futures traded on the New York Mercantile Exchange (NYMEX) during the period 1984-2004 by employing granger causality tests. The results confirm their hypothesis of a negative effect from crude oil futures prices to future gross domestic returns when incorporating oil price changes in their model.

The Model
We use the univariate FIGARCH(p,d,q) model to quantify the standardized residuals (first subsection). Then, we use the estimated standardized residuals to produce the multivariate conditional variance matrix by employing a cDCC model (second subsection). Last subsection presents the log-likelihood theoretical framework.

Univariate FIGARCH(p,d,q) Model
By using a constant (μ), the empirical set-up of the mean equation for the daily future market returns ( ) is represented by the following equation: is the standardized residuals such that: = �ℎ , where ~(0, ) and ~(0,1) where ℎ is defined as the univariate conditional variance matrix and is the standardized errors. Furthermore, is the multivariate conditional variance matrix.
It follows the definition of the univariate FIGARCH(p,d,q) model (Baillie, Bollerslev & Mikkelsen, 1996) to generate the conditional variance matrix (ℎ ): where ω is mean of the logarithmic conditional variance, and a(L) are autoregressive polynomials of order p and q so that: Furthermore, the selected lag order is equal to 1, as many other researchers have mentioned as sufficient to estimate the univariate conditional variance matrix, i.e. Bolleslev, Chou and Kroner, (1992), among others.

Multivariate cDCC Model
To model the dynamics of the conditional variance of the standardized residuals ( ), we employ the cDCC model of Aielli (2009). In this model, the variance covariance matrix( ) (N x N matrix) evolves according to: �, N is the number of markets (i = 1,…,N). In this model the correlation matrix ( ) is given by the transformation: In addition, we define = � 11, For the cDCC model, the estimation of the matrix � and the parameters α and β are intertwined, since � is estimated sequentially by the correlation matrix of the u t * . To obtain u t * we need however a first step estimator of the diagonal elements of Q t . Thanks to the fact that the diagonal elements of Q t do not depend on � (because ���� = 1 for i = 1,…,N), Aielli (2009) proposed to obtain these values 11, ,.., , as follows: for i = 1,…,N. In short, given α and β, we can compute 11, ,.., , and thus u t * , then we can estimate � as the empirical covariance of u t * .

Log-likelihood Estimation
In order to estimate the model, we use Full Information Maximum Likelihood (FIML) methods with student's t-distributed errors: where Γ(.) is the Gamma function, k is the number of equations, and ν is the degrees of freedom.

Data Characteristics
We where is the price of future market on day t and −1 is the price of future market on day t-1.
Appendix A shows the summary statistics for future FOREX market returns. JPY/USD shows larger fluctuations compared to the rest markets, considering the highest maximum (0,015012) the lowest minimum return (-0,011822) values and the std. deviation (0,0023655). In addition, all future FOREX market returns are positively skewed, except the case of INR/USD. Moreover, all market returns present excess kurtosis (fat tails). Jarque-Bera statistic results suggest the rejection of the null hypothesis of normality for all markets. ADF unitroot test results imply that the market returns are appropriate for further testing. The ARCH tests imply the presence of heteroskedasticity for all markets. The GPH test results show that JPY/USD future market has long memory (0 < d < 0,5) and the rest future markets (KRW/USD, EUR/USD, INR/USD) are anti-persistent processes (-0,5 < d < 0).
In Appendix B, the actual series of future markets and their respective logarithmic returns are graphed for INR/USD (Graph A), JPY/USD (Graph B), KRW/USD (Graph C) and EUR/USD (Graph D). The most striking characteristics of the graphs are: (1) all actual series follow a downward trend, and (2) all market returns are highly volatile.

Empirical Results
We divide this section into three subsections. In the first subsection, we show the empirical results from the cDCC-AR(1)-FIGARCH(1,d,1) model. In the second subsection, we present the estimates of Spearman's rank correlation. Third subsection demonstrates the mean values of conditional variances and covariances. Fourth subsection states the dynamic conditional correlation coefficients. p-Value 0,0000 0,0000 0,0000 0,0007 Notes. Table 1 presents the results of univariate AR(1)-FIGARCH(1,d,1) model. ** and *** signify statistical significance at the 5% and 1% levels, respectively.   (1980) and McLeod and Li (1983). In Panel C we see the information criteria of AR(1)-FIGARCH(1,d,1)-cDCC model. The symmetric positive definite matrix Q t is generated using one lag of Q and of u * . P-values have been corrected by 2 degrees of freedom for Hosking 2 (50) and Li-McLeod 2 (50) statistics. ** and *** signify statistical significance at the 5% and 1% levels, respectively.

Simple Correlation Analysis
We use Sprearman's rank correlation to measure the financial contagion phenomenon by computing the mean correlations. Given the T observations, the T raw scores , (i ≠ j = 1,…,N markets and t = 1,…,T observations) are converted to ranks , .
Using the covariance of the rank variables ( � , �) and the standard deviations of the rank variables ( and ), we calculate the correlation coefficients ( , ) as follows: We show the empirical results above in table 3. Results reveal the highest rank correlation for the pairs of markets KRW/USD-INR/USD ( 2 , 4 ), JPY/USD-EUR/USD ( 1 , 3 ) and KRW/USD-EUR/USD ( 2 , 3 ). In addition, we observe that the Spearman's rank correlation between JPY/USD and KRW/USD( 1 , 2 ) is not statistically significant, indicating a lower level of integration between the two markets.

Mean Values of Conditional Variances and Covariances
Appendix C states the estimated mean values (ℎ ���� , with , = 1, … , ) of conditional variances and covariances. Weassume that the mean values reflect the own volatility and the cross-volatility spillover effects. We generate and store the conditional variances and covariances by employing the cDCC -FIGARCH model and then, we estimate the mean values.
In Appendix D, we present the conditional variances for INR/USD, JPY/USD, KRW/USD and EUR/USD. All markets demonstrate high levels of volatility. Interestingly, we observe time varying levels of fluctuations.

Dynamic Conditional Correlations Characteristics
Appendix E reports the descriptive statistics of the dynamic conditional correlations (DCCs) of the six pairs of markets generated by Equation 5. The highest mean value (0,83398) is observed between JPY/USD and EUR/USD. Moreover, the DCC between KRW/USD and EUR/USD experiences larger fluctuations considering the the second highest maximum value (4,9157e-006) and the highest std. deviation value (7,7824e-007). The Skewness, Excess Kyrtosis and the Jarque-Bera test statistics indicate that the DCCs for all the pairs of markets are not normally distributed. Based on Figure 3 below, we analyze the pairwise DCCs as follows.

Conclusions
This paper investigates the potential spillovers and contagion among the JPY/USD, KRW/USD, EUR/USD and INR/USD futures FOREX markets. Specifically, we quantify volatility transmission by employing a fourvariate cDCC-FIGARCH(1,d,1) model. The under investigation period is from 2014 until 2019. To the best of our knowledge, this is the first empirical study, investigating volatility spillover effects among major futures FOREX markets.
We find interesting results. Spearman's rank correlation results reveal the highest rank correlation for KRW/USD-INR/USD and JPY/USD-EUR/USD, revealing a level of integration for the above markets. The mean values of conditional variances and covariances show that KRW/USD demonstrates the highest own volatility, showing that KRW/USD is the most immune futures market. Results indicate strong evidence of volatility spillover effects. Based on DCCs, results state significant evidence of contagion effects for all the pairs of markets. DCCs have mostly negative values during the mid-2015 until mid-2016 for the pairs of markets JPY/USD-KRW/USD and JPY/USD-INR/USD, presenting no contagion effects.
A natural extension to this article would be to investigate the potential contagion mechanisms during the period 2007-2012 global financial crises. In particular, we focus on the revelation of possible contagion effects among JPY/USD, KRW/USD, EUR/USD and INR/USD futures markets.