Study on return and volatility spillover effects among stock, CDS, and foreign exchange markets in Korea

The key objective of this study is to investigate the return and volatility spillover effects among stock market, credit default swap (CDS) market and foreign exchange market for three countries: Korea, the US and Japan. Using the trivariate VAR BEKK GARCH (1,1) model, the study finds that there are significant return and volatility spillover effects between the Korean CDS market and the Korean stock market. In addition, the return spillover effects from foreign exchange markets and the US stock market to the Korean stock market, and the volatility spillover effect from the Japanese stock market to the Korean stock market are both significant.


Introduction
A number of studies have examined the effect of macroeconomic variables on financial asset returns. Since the work of Ross (1976), various macroeconomic variables such as GDP, inflation, and the trade balance as well as financial market variables such as interest rates and exchange rates have been tested to identify the influential factors for the expected return of a financial asset. However, few studies have been conducted about the relationships between macroeconomic volatility and asset market volatility. Schwert (1989) states that volatility in macroeconomic fundamentals and financial market factors are helpful in predicting stock return volatility, and vice versa.
The key objective of this study is to investigate the return and volatility spillover effects between domestic and international financial and asset markets focused on the Korean economy. In particular, the presence of return and volatility spillover effects from country risk and advanced economy asset markets to Korean asset markets is the primary interest in this study.
Before approaching the main subject, it is necessary to specify the concept of country risk. The Credit Default Swap (CDS) spread underlying government bonds is used as a measure of country risk in this paper. 1 The CDS premium generally rises when credit risk of the underlying asset increases. Hence, the CDS premium is interpreted as a measure of credit rating of the authorities or the institutions which issue the underlying asset. For this reason, the CDS premium which is on the basis of bond in foreign money issued by the each country's government is used well as an indicator which reflects the country's credit rating.
There have been considerable studies which show when external or internal economic and financial shocks affect the country's economy, the CDS market reacts sensitively and shows the current state through its index, called the CDS spread (see Remolona et al. 2008;Baum and Wan 2010;Longstaff et al. 2011). However, compared with the substantial amount of empirical and theoretical studies on the foreign CDS market since 2000, most studies related to credit risk in Korea have focused on the credit premium in 1 A CDS is a swap contract between two parties, a protection buyer, and a protection seller. A protection buyer who wants to transfer the credit risk pays a premium (spread) to the protection seller in exchange for a payment if a credit event occurs with a reference entity. As a bond holder buys a CDS to hedge the default risk, the characteristics of a CDS are similar to that of credit insurance. Another characteristic of a CDS is that it is a financial good which can be bought and sold by investors. the bond market because of immature market conditions and deficiency of data for the Korean CDS market. Recently, several pioneering works for the Korean CDS spread are in progress. Nam and Byun (2006) conduct empirical analysis to find deterministic elements of the Korean CDS spread. They find that variations of the Korean CDS spread is affected by the variations of past value of CDS spread itself, domestic macroeconomic fundamentals, and financial variables such as yields on government bonds, stock prices, and the won/dollar exchange rate. They also find that the CDS market is more efficient in reflecting the change of credit status in the underlying asset to the change of credit risk spread than is the bond market. Considering the determinants of the CDS premium underlying Korean government bonds, Kim (2009) finds that typically well-known determinants of the CDS premium such as the shortterm foreign debt ratio, exchange rate, and stock prices are ascertained to be statistically significant in the Korean CDS market. That is, he finds that the CDS premium decreases when stock prices increase and the exchange rate decreases.
Early studies on the relationship between CDS spread and other macroeconomic or financial market variables usually focus on the link between the levels of the series without considering the link between the returns or volatilities of the series. However, examining the relationship between returns or volatilities of the series reflects the current trend of studies on the analysis for the relationship between financial markets. In a study on the relationship between CDS spread change and stock return, Norden and Weber (2009) analyse the relationship among CDS, bond and stock markets empirically.
They find that stock returns affect CDS and bond spread changes, and the CDS market is significantly more sensitive to the stock market than the bond market is. Recent study of Meng et al. (2009) examines the volatility transmission among CDS, equity, and bond markets, and they find that volatility in any of the three markets is commonly transmitted to the other two markets using a multivariate GARCH model. This paper follows the stream of earlier studies about the relation between CDS market and other financial markets. However, the difference of the paper is to investigate the return and volatility spillover effects among stock market, CDS market and foreign exchange market for Korea, the US and Japan using a trivariate VAR GARCH model. The answers to these questions can be briefly summarized that there are significant return and volatility spillover effects between the Korean CDS market and the Korean stock market. In addition, the return spillover effects from foreign exchange markets and the US stock market to the Korean stock market, and the volatility spillover effect from the Japanese stock market to the Korean stock market are both significant.
The rest of the paper is organized as follows. Section 2 presents descriptive statistics and results of the tests on data. Section 3 lays out the econometric methodology. The main results are presented in section 4, and section 5 concludes the paper.

Descriptions of data and statistical characteristics
Weekly data for Korean, US and Japanese stock returns, Korean CDS spread change, and Korean-US and Korean-Japanese exchange rate changes are used to compose financial and asset market variables for the MGARCH model. KOSPI, S&P 500, and NIKKEI 225 are used for Korean, US and Japanese stock market indices, respectively, which are obtained from the Korea Centre for International Finance (KCIF). The CDS spread underlying the five-year maturity Korean government bond is used, because the five-year is not only the most common liquid maturity in the swap market but it is also widely announced to the public. The Korean CDS spread data are obtained from the KCIF. The data source of the two exchange rates is the Bank of Korea. The data period starts from the first week of January 2002 and ends at the fourth week of February 2010.
All weekly data are composed on the basis of Friday's observation. When there is no observation on Friday due to reasons such as public holiday, observation of the day before (Thursday) is used as a replacement.   Figure 1 shows negative process compared to the time path of CDS spread. This implies that the Korean stock market booms during economically stable periods of low country risk. Figure 1 displays the gradual increase in the Korean stock market index to more than double when the CDS spread was low during the stable period from 2004 to 2007. However, the Korean stock market index dropped immediately when the CDS spread soared in 2008. Hence, it is expected that there might be a negative relationship between Korean stock price and country risk.
Another interesting issue of this paper is the identification of the contagion from the advanced asset market to the Korean asset market. Figure 2 shows the time series of stock market indices for the US and Japan. The stock market is employed in this paper as a representative asset market for three countries: Korea, the US and Japan. The US stock price is adopted as a global stock price, and the Japanese stock price is adopted as a regional stock price. The time paths of two indices look very similar to that of the Korean stock market index in Figure 1. From these figures, it is also expected that the Korean stock market has a close relationship with the US and Japanese stock market.

Figure 2 here
Along with the CDS spread, fluctuations in the exchange rate also reflect variation of domestic country risk since the exchange rate generally shows a sensitive response to the credit status of the country. In addition, the foreign exchange market plays a role inestablishing the first contact from the variation in international financial markets through the exchange rate, and it spreads the effect to the domestic economy. The time series of the Korea won/US dollar exchange rate and Korea won/Japanese yen exchange rate are illustrated in Figure 3.
When using the first difference variables, some information regarding a possible linear combination between the levels of the variables may be lost. However, relationships between financial markets are analysed using the first difference of the log of returns and changes instead of using the original level series of financial data in this paper. I concentrate on returns because financial time series usually do not satisfy the basic assumption of the stationary process required to avoid spurious inferences based on regression analysis.

Autocorrelation test
The Ljung-Box Q-statistics are used to test for independence of higher relationships as manifested in volatility clustering by the MGARCH model (Huang and Yang 2000). The Ljung-Box Q-statistics and their p values by 20 lags and leads are reported in Table 1.
According to the Ljung-Box Q-statistics and p-values in Table 1

Characteristics of financial time series
Although volatility is not directly observable, it has some characteristics that become known empirically and are commonly seen in financial market returns (changes) as cases of stylized fact. 2 First, financial market returns exhibit volatility clustering, which means that large volatilities tend to be followed by large volatilities and small volatilities tend to be followed by small volatilities. Second, volatility varies within some fixed range over time. Third, the empirical distribution of financial market returns shows characteristics of non-normal distribution such as leptokurtic, skew, and fat tail.
Before modelling and estimating the spillover effects, investigation regarding the presence of these stylized facts in three asset market returns and three financial market changes is performed.
In Figure 4, the left column displays the time plots of returns and changes in each financial market ( t y ), and the right column illustrates the squared series from the followed by large returns (changes). Moreover, the fact that volatility varies within some fixed range over time is also observed.

Figure 4 here
To examine another characteristic of non-normal distribution, Table 2 provides a summary of the descriptive statistics of each asset market return and financial market change. According to the Jarque-Bera statistic in  inappropriate. When modelling with non-constant variance (heteroskedasticity), there is a way to model the changing variance due to the characteristics of leptokurtic and fat tail in data. ARCH-and GARCH-related models are useful to capture the nonlinear data.

Methodology
It has become clear that globalization of financial markets requires advanced econometric models capturing the correlation between the financial markets in the aspect of return and volatility. The multivariate GARCH (MGARCH) model has been commonly used to estimate the relationships between the volatilities of several financial markets since the studies by Bollerslev et al. (1988) and Engle and Kroner (1995). 3 In this paper, the trivariate GARCH model is constructed to provide an insight into the nature of interaction among domestic and foreign financial markets. There is a reason that the trivariate GARCH model is employed; MGARCH models have a well-known weak point that the number of parameters to estimate increases very rapidly as the number of variables increases. Thus, a trivariate GARCH model is suitable to analyse the return and volatility spillover effects among the Korean CDS market, Korean stock market, and one other financial market.
The autoregressive stochastic process of financial market returns (changes) is given in the following conditional mean Equation (2).
where t i y , is the return (change) of financial market i between time t-1 and t, i µ is a long-term drift coefficient of financial market i, ij γ indicates the coefficients for lagged own market returns (changes) and other financial market returns (changes), and  (2) is considered is that it is convenient to analyse the return spillover effects and dynamic relationships using the impulse response function between financial market returns and changes.
Since BEKK model ensures a positive semi-definite conditional variance and covariance matrix, which is a requirement needed to guarantee non-negative estimated variances, BEKK model from Engle and Kroner (1995) is used. The BEKK parameterization is written as follows: 4 where ij ω are elements of a 3 × 3 lower triangular matrix with six parameters of constants C. A is a 3 × 3 square matrix of parameters and shows how conditional variances are correlated with past squared errors. The elements ( ij α ) of matrix A measure the degree of innovation from financial market i to another financial market j.
B is also a 3 × 3 square matrix of parameters, and its elements ( ij β ) indicate the persistence in conditional volatility between financial market i and market j. The following log-likelihood function is maximized for the trivariate GARCH model with the assumption that errors are normally distributed: where θ is the vector of parameters to be estimated, N is the number of financial markets in the system being estimated, and T is the number of observations. Since the log-likelihood function in this case is non-linear, the Marquardt algorithm is used as an iterative algorithm to estimate the parameters.

Empirical results
To examine the return and volatility spillover effects between change in Korean CDS spread and the Korean stock return, these return and change are commonly included in all four cases. In addition, the won/dollar exchange rate change, won/yen exchange rate change, US stock return, and Japanese stock return are used one after another for the third financial market return or change in each case to investigate another spillover effect from the third financial market return or change to the Korean stock return and Korean CDS spread change.
Estimation for return and volatility spillover effects is conducted using a trivariate GARCH model, and analysis for dynamic interactions between returns and changes are performed using impulse response functions obtained from the unrestricted VAR (1) framework of conditional mean Equation (2). The structure of the four cases is organized as follows:  For better understanding, simple figures for the results of return and volatility spillover effects for Case I and Case II are presented in Figure 5. Some empirical research provides evidence of return spillover effects between the stock market and the foreign exchange market (see Roll 1992;Dumas and Solnik 1995;Choi et al. 1998;Phylaktis and Ravazzolo 2005). They find the presence of bidirectional return spillover effects between the foreign exchange market and the stock market. In contrast to these results, during the data period for Korea, there is a unidirectional return spillover effect from foreign exchange markets to the Korean stock market.

Figure 5 here
In the meantime, although there are significant unidirectional volatility spillover effects from two foreign exchange markets to the Korean CDS market, there is no significant volatility spillover effect from two foreign exchange markets to the Korean stock market. Some empirical research provides different results of volatility spillover effects between the stock market and the foreign exchange market. Francis et al. (2002) and Wu (2005) find significant bidirectional volatility spillovers between the stock market and the foreign exchange market. Beer and Hebein (2008) find significant volatility spillovers from the foreign exchange market to the stock market for several countries. To the contrary, Kanas (2000) and Kim (2001) find the presence of unidirectional volatility spillover from the stock market to the foreign exchange market.
Although there are no volatility spillover effects between the Korean-US foreign exchange market and the Korean stock market, the significant unidirectional volatility spillover effect from the Korean stock market to the Korean-Japanese foreign exchange market is in line with the results of Kanas (2000) and Kim (2001).
In terms of the relationship among the CDS, foreign exchange, and stock markets, Nam and Byun (2006) claim a significant effect from the variations of stock prices and the exchange rate to the variation of the Korean CDS spread. Baum and Wan (2010) indicate the significant effect from the second moment of the stock index to the CDS spread. The results of this study are consistent with those of foregoing studies that there is a significant return spillover effect from the foreign exchange market to the CDS market and from the CDS market to the stock market, and a significant volatility spillover effect from the stock market to the CDS market. immediately and returns to a steady-state level in one month to one standard deviation increasing shocks of the two exchange rate changes. Since increase in the exchange rate, which implies an increasing risk premium in foreign exchange market, is related to increasing country risk, the result of the increasing Korean CDS spread change is reasonable. This result is consistent with that of Kim (2009). To the contrary, the Korean stock return shows negative response immediately and recovers to the pre-shock level within one month to increasing shocks of the two exchange rate changes. This result is the same as previous research that draws the conclusion of a negative relationship between foreign exchange rate change and the Korean stock return (Chung 2002). The flow approach of Dornbusch and Fischer (1980) affirms that currency movements affect international competitiveness and the balance of trade position. As a result, the real output of the country is changed, and then this changed economic activity affects current and future cash flows of companies and stock prices. From this perspective, a depreciation in the Korean currency leads to increasing Korean exports, and consequently this will cause an increase in Korean stock prices due to increased output. In contrast, when the Korea currency is depreciated, prices rise because of increased import prices, and this will cause domestic interest rates to rise. The stock prices will fall because of higher interest rates. In addition, because of expected foreignexchange loss stemming from the sudden rise in exchange rate, investment of foreign capital in the Korean asset market will not increase.  Frankel 1983). In addition, if the Korean stock price rises, this will lead to the growth of wealth, which will increase the demand for money. The excess demand for money will cause interest rates in Korea to rise, and in this situation, more foreign capital will be attracted and increase the foreign demand for the Korean currency (see Gavin 1989). As a result, the Korean currency will appreciate. Thus, the overall effect on the exchange rate will depend on the relative strength of the various competing effects (Phylaktis and Ravazzolo 2005). For the Korean economy during the data period, increase in the Korean stock return shock has a positive influence on exchange rate changes.

US and Japanese stock markets, the Korean CDS market, and the Korean stock market
The empirical results for Case III and Case IV, which include two large countries' stock returns, the Korean CDS spread change and the Korean stock return are reported in Table 4.  (2001), who shows that the regional influences are the cause of volatility in the markets, whereas international volatility has no impact on small stock markets. Beirne et al. (2010) conclude that return and volatility spillover effects exist from global or regional stock markets to local emerging markets. Studies by Karolyi (1995), Chou et al., (1999), Worthington and Higgs (2004), Harris and Pisedtasalasai (2006), and Sun and Zhang (2009) are also in line with this result. They show that there are return and volatility spillover effects from the advanced stock market to the smaller stock market. Although a study by Bala and Premaratne (2003) shows that the volatility spillover effect from the smaller stock market to the dominant stock market is plausible, most of the other earlier research concludes that spillover effects are significant only from the dominant market to the smaller market. Because the Korean stock market is relatively small, it is plausible that the influence from the Korean stock market and the Korean CDS market to global stock market such as that of the US and a regional stock market such as that of Japan is insignificant, although some statistics indicate significance.
Hence, only results are reported without further explanation.
To observe the time varying impulse responses of return and change series to positive financial market return and change shocks in the unrestricted VAR(1) model reported in Equation (2), the results with one standard error bands are presented in Figure 9 for Case III and in Figure 10 for Case IV. Figures 9 and 10

Conclusion
This study examines the return and volatility spillover effects among several domestic and foreign financial markets in Korea for the period from the first week of January