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With the openness and marketization of China’s financial market accelerating, the linkage between various financial markets is increasingly significant. By utilizing VAR model and asymmetric GARCH (1,1)-BEKK model, this paper analyzes the price spillover effect and the volatility spillover effect among stocks returns, exchange rate of returns and money rate. The results show that 1) between currency market and stock market there is only unidirectional mean spillover effect from currency market to stock market; 2) however, there exists asymmetrical bidirectional mean spillover effect both between stock market and money market and currency market and money market, which exhibits time-varying variance and volatility persistence; 3) there exists bidirectional volatility spillover effect between currency market and money market, however there is only unidirectional volatility spillover effect from stock market to money market, which is demonstrated from money market to currency market.

With the continuous development of the global economy, the economic globalization and financial liberalization deepened, the capital flows and information dissemination between financial markets gradually enhanced. Both international financial market and sub-market are showing an increasingly significant linkage effect. When a market’s price fluctuates under some shocks, other market asset prices may also be affected. Meanwhile, market participants will usually predict the trends of other market’s price according to one market’s price, resulting in expectation changes self-realization, which is so-called the market spillover effect (Hamao et al., 1990). Spillover effects include mean spillover effects and volatility spillover effects. The mean spillover effect usually refers to that yield of one market has influence on other markets, which can be positive or negative. For example, the decline in interest rates may lead to the rising in the stock market, which means the relationship between interest rate is negative. However, volatility spillover effects mean that the fluctuations of one market return (changes in variance of yield) have impact on other markets. And this effect can be large or small but no positive and negative differences. From the perspective of economic vision, volatility spillovers can be seen as the risk transfer between different markets.

Stock market, exchange market and money market are an important part of financial market. They can not only realize the optimization of resource distribution but also and diversify market risk. What’s more, they are also the main place for government to implement monetary policy and macroeconomic regulation. In an open economic environment, stock price (asset price), exchange rates and interest rates are several important policy instruments for government to maintain national economic security and financial stability. By timely interventing interest rates, exchange rates and asset prices, the government can effectively mitigate the effects of external shocks on macroeconomic so that the entire financial system can run well. In the process of market-oriented reform of interest rate and exchange rate formation mechanism, Chinese stock market was subject to fluctuate greatly. Therefore, to make clear that the relationship and mechanism of the financial sub-market, we have attracted the academic, practical and financial authorities. Currently, deeply studying the synergistic effect between the financial markets in China not only helps to understand the interacted relationship between the financial market, but also has a certain reference significance for preventing the financial risk and the financial market reform and other aspects of policy formulation.

As to the stock market and the spillover effect between the foreign exchange market, foreign scholars have a more in-depth study. The performance of the linkage between the stock market and the foreign exchange market in different countries is variation. Morales (2008) [

Upon the relationship between the money market and the foreign exchange market, the theoretical circles have developed a relatively consistent and mature theory. Hoffmann (2007) [

In recent years, with the continuous progress of China’s financial market reform, stock market, foreign exchange market and the linkage between the money market is gradually strengthening, the domestic academic draw more attention to this phenomenon. Xiao et al. (2011) [

According to above literature, we conclude that domestic and foreign scholars use various empirical methods to study the stock market and exchange market, exchange market and money market and the linkage between money market and stock market in different countries, confirming that there is mean spillover effect or volatility spillover effect in various countries. But these studies focus mostly on two markets including stock market and exchange market, money market and exchange market, or stock market and bond market and so on. They can’t comprehensively examine the dynamic relationship between financial markets. This paper is to integrate stock price, RMB exchange rate and interest rate into a system, and use the data to analyze the dynamic relationship between the three markets, which can help institutional investors and financial regulators fully understand the relationship. In addition, based on the existing research, this paper comprehensively analyzes the Chinese stock market, the foreign exchange market and the money market, which makes the conclusion more robust and reliable. As the stock index, exchange rate and money market interest rates are changing every day, this paper intends to use the ternary VAR-GARCH-BEKK model to analyze the daily data of three variables and further confirm whether there is a single or bi-directional effect.

In the present study, we adopt a three-variable GARCH-BEKK model developed by Engle and Kroner to investigate volatility spillover between three markets. The advantage of the BEKK specification is that it does not impose any restriction on the correlation structure between the variables.

Usually, the AIC and SC information criteria can be used to choose the optimal lag length of GARCH process (i.e., the values of p and q). However, in the study of T. Bollerslev, they found an interesting result. With small numbers of parameters, GARCH (1,1) process is sufficient to model the variance dynamics of financial time series. So similar to the previous researches, we select one lag for the mean and variance equations.

Generally, the mean equation of a three-variable GARCH (1,1) model can be defined by the following equations:

r s r , t = α s t + ∑ i = 1 n λ s r i r e r , t − i + ∑ i = 1 n δ s r i r i r , t − i + ∑ i = 1 n φ s r i r s r , t − i + ε s r , t (1)

r e r , t = α e r + ∑ i = 1 n λ e r i r e r , t − i + ∑ i = 1 n δ e r i r i r , t − i + ∑ i = 1 n φ e r i r s r , t − i + ε e r , t (2)

r i r , t = α i r + ∑ i = 1 n λ i r i r e r , t − i + ∑ i = 1 n δ i r i r i r , t − i + ∑ i = 1 n φ i r i r s r , t − i + ε i r , t (3)

In the above three formulas, n is the optimal lag order of the VAR model. ε s r , t , ε e r , t , ε i r , t are the residual term for the mean equation, respectively.

The variance equation of the volatility spillover effect is as follows:

H t = C ′ C + B ′ H t − 1 B + A ′ ε t − 1 ε ′ t − 1 A (4)

where:

H t = ( h 11 , t h 12 , t h 13 , t h 21 , t h 22 , t h 23 , t h 31 , t h 32 , t h 33 , t ) , B t = ( b 11 b 12 b 13 b 21 b 22 b 23 b 31 b 32 b 33 ) C = ( c 11 0 0 c 21 c 22 0 c 31 c 32 c 33 ) , A t = ( a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ) (5)

A, B are 3 × 3 order matrix, The elements in main diagonals of A represent the ARCH effect between the various markets; The elements in main diagonal of B represents the GARCH effect. a i j and b i j ( i ≠ j ) reflect the ARCH and GARCH effect of market i to market j. H t is the conditional covariance matrix.

The model is estimated by the maximum likelihood estimation method optimized by the BHHH algorithm to obtain the final estimate of the variance-cova- riance matrix with corresponding standard errors. The conditional log likelihood function l(θ) can be expressed as follows:

l ( θ ) = − T log ( 2 π ) − ( 1 / 2 ) ∑ t = 1 T ( ln | H t | ) + ε ′ t H t ε t (6)

where T is the number of observations and θ represents the vector of all unknown parameters.

The empirical data sets used in this study consist of daily CSI 300 index, 7-day interbank interest rate and the central parity of the US dollar against the yuan.

^{1}Wind is the market leader in China’s financial information services industry, similar to Bloomberg in USA.

All the data are collected from Wind Database^{1}, and encompass the period from

June 2005 to December 2016. After excluding the some data, we get 2666 sets of data. For the Shanghai and Shenzhen 300 Index and the exchange rate, respectively, calculate the market rate of return, the formula is as follows:

R t = ln ( P t / P t − 1 ) × 100 % (7)

For the purpose of exploring the trend of data distribution and finding extreme data, descriptive statistical analysis should be done before these data was used. Therefore, it is necessary to take this analysis method in this paper.

As seen in

Max | 8.93 | 1.84 | 12.25 |

Min | −9.69 | −0.56 | 0.92 |

Mean | 0.05 | −0.007 | 2.94 |

Std | 1.89 | 0.12 | 1.25 |

Skewness | −0.56 | 3.61 | 1.27 |

Kurtosis | 6.11 | 61.31 | 6.56 |

JB | 1212.68*** | 383,467.8*** | 2127.82*** |

Q (10) | 37.12*** | 116.52*** | 15,881.45*** |

Q2 (10) | 583.12*** | 963.99** | 10,571.71*** |

Note: *, **, ***: showed a significance level of 10%, 5%, and 1%, respectively.

Ljung-Box Q statistic of the sequence itself, the three yield series have different degrees of autocorrelation, and the squared Ljung-Box Q statistic is significant, which indicates that the square of the yield series also has autocorrelation. All yield sequences have significant fluctuation clustering effect.

In order to analyze time series data, stationary of the data is a prerequisite. However, most macroeconomic variables are known to be non-stationary. As such, a unit-root test was first conducted on three variables. To examine this, the Augmented Dicky-Fuller test was used. The results are shown in

In order to analyze time series data, stationary of the data is a prerequisite. However, most macroeconomic variables are known to be non-stationary. As such, a unit-root test was first conducted on the level variables such as the stock price, interest rate, and won/dollar exchange in order to determine the stationary of the time series data. To examine this, the Augmented Dicky-Fuller test was used. The results are shown in

According to Akai Information Criterion (AIC), Likelihood Ratio (LR) and Final Error (FPE), the optimal lag order of VAR model is 7. It can be seen that for the VAR model the mould of unit root is less than 1 so it can be considered robust.

As seen in

Variables | (c,t,p) | ADF Statistics | 1% critical value | 5% critical value | 10% critical value |
---|---|---|---|---|---|

(c,0,0) | −50.06 | −3.44 | −2.86 | −2.57 | |

(c,0,0) | −42.91 | −3.44 | −2.86 | −2.57 | |

(c,0,0) | −3.82 | −3.44 | −2.86 | −2.57 |

Note: (c,t,p) represents the intercept term, the trend term and the lag order, respectively.

RHS | REX | IR7 | |
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RHS (−1) | 0.0317 [1.6305] | −0.0004 [−0.3243] | −0.0059 [−1.4292] |

RHS (−2) | −0.0286 [−1.4720] | 0.0015 [1.3976] | 0.0006 [0.1442] |

RHS (−3) | 0.0191 [0.9801] | 0.0007 [0.6696] | −0.0079* [−1.9071] |

RHS (−4) | 0.0715*** [3.6842] | −0.0005 [−0.4186] | 0.0002 [0.0497] |

RHS (−5) | 0.0041 [0.2118] | −0.0001 [−0.1354] | −0.0035 [−0.8378] |

RHS (−6) | −0.0620*** [−3.1939] | 0.0012 [1.091] | 0.0006 [0.1439] |

RHS (−7) | 0.0268 [1.3782] | 0.0006 [0.51407] | 0.0016 [0.3840] |

REX (−1) | 0.5193 [1.5059] | 0.1863*** [9.5748] | 0.0108 [0.1469] |

REX (−2) | −0.2857 [−0.8150] | −0.0076 [−0.3838] | −0.0459 [−0.6126] |

REX (−3) | 0.2703 [0.7714] | 0.0101 [0.5133] | 0.0289 [0.3869] |

REX (−4) | −0.1571 [−0.4475] | 0.0158 [0.7956] | −0.0330* [−1.9395] |

REX (−5) | −0.2200 [−0.6265] | −0.0381* [−1.9228] | −0.0178 [−0.2376] |

REX (−6) | 0.0374 [0.1066] | −0.0089 [−0.4532] | 0.0163 [0.2176] |

REX (−7) | −1.2753*** [−3.6882] | 0.0682*** [3.4958] | −0.0893 [−1.2074] |

IR7 (−1) | −0.0824 [−0.9072] | −0.0007 [−0.1332] | 1.0063*** [51.7755] |

IR7 (−2) | −0.1176 [−0.9161] | 0.0066 [0.9066] | −0.1179*** [−4.2942] |

IR7 (−3) | 0.1953* [1.8272] | −0.0113 [−1.5449] | 0.0063 [0.23014] |

IR7 (−4) | 0.0074 [0.0575] | −0.0004 [−0.0600] | 0.0365 [1.3262] |

IR7 (−5) | −0.0966 [−0.7501] | 0.0177*** [2.4413] | −0.0606** [−2.2003] |

IR7 (−6) | 0.1899 [1.4773] | −0.0239*** [−3.3019] | 0.1511*** [5.4958] |

IR7 (−7) | −0.1343 [−1.4763] | 0.0103** [2.0135] | −0.0727*** [−3.7354] |

Constant | 0.1490 [1.4913] | −0.0009 [−0.1591] | 0.1498*** [7.0121] |

Note: *, **, ***: showed a significance level of 10%, 5%, and 1%, respectively.

have a significant impact on the current period, the lag 1, 2, 5, 6 and 7 period of the money market interest rate have significant effects on the current period, indicating that there are different degree of autocorrelation in all market yields. From the point of view of the significance level of the variables, for the stock market equation, the lag 7 of exchange rate is significant at 1% level, and the lag 3 of money market yield is significant at the level of 10%. For the exchange rate equation, the lag 5, 6 and 7 of money market rate were significant at 1%, 1% and 5% respectively. For the money market interest rate equation, the lagged 3 stock return and the lagged 4 foreign exchange market at 10% level

As seen in

Analysis of Mean Spillover Effect of Equity Returns | Exchange rate yield equation mean spillover effect test | Monetary Market Interest Rate Equations Mean Spillover Effect Test |
---|---|---|

The Mean Spillover Effect of Exchange Market to the Stock Market | The Mean Spillover Effect of Stock Market to Foreign Exchange Market | The Mean Spillover Effect of Stock Market to Money Market |

The Mean Spillover Effect of Money Market To Stock Market | The Mean Spillover Effect of Money Market To Exchange Market | The Mean Spillover Effect of Money Market To Exchange Market |

Note: *, **, ***: showed a significance level of 10%, 5%, and 1%, respectively.

H 0 : κ 2 , 1 = κ 2 , 2 = κ 2 , 3 = κ 2 , 4 = κ 2 , 5 = κ 2 , 6 = κ 2 , 7 = 0 was refused, which shows there was mean spillover effect from money market return to exchange rate yield. Under the 10% and 5% significant level, null hypothesis H 0 : θ 3 , 1 = θ 3 , 2 = θ 3 , 3 = θ 3 , 4 = θ 3 , 5 = θ 3 , 6 = θ 3 , 7 = 0 and H 0 : κ 3 , 1 = κ 3 , 2 = κ 3 , 3 = κ 3 , 4 = κ 3 , 5 = κ 3 , 6 = κ 3 , 7 = 0 was refused respectively, which indicate that there was mean spillover effect from exchange return and stock market yield to money market yield.

In this paper, we use the maximum likelihood estimation to estimate the parameters of the GARCH-BEKK (1,1) model. Given that the log-likelihood function is nonlinear, we use the BFGS algorithm and Wald test. Winrats 8.0 was chosen.

As shown at

As shown in

Based on the high frequency daily data of China’s stock market, foreign exchange market and money market interest rate from July 2005 to December 2016, this paper chooses VAR (7)-GARCH (1,1)-BEKK model to study the mean spillover effect and volatility spillover effect between the three markets. Results

Variables | Coefficient | Std | T Statistic | P value |
---|---|---|---|---|

C (1,1) | 0.2939*** | 0.0303 | 9.7171 | 0.0000 |

C (2,1) | −0.0086*** | 0.0011 | −8.1369 | 0.0000 |

C (2,2) | 0.0010 | 0.0011 | 0.9487 | 0.3428 |

C (3,1) | −0.0052 | 0.0053 | −0.9901 | 0.3221 |

C (3,2) | 0.0398*** | 0.0037 | 10.7378 | 0.0000 |

C (3,3) | 0.0000 | −0.0472 | 0.0000 | 1.0000 |

A (1,1) | 0.2931*** | 0.0146 | 20.0349 | 0.0000 |

A (1,2) | −0.0044*** | 0.0006 | −6.9576 | 0.0000 |

A (1,3) | −0.0037** | 0.0016 | −2.3031 | 0.0213 |

A (2,1) | 0.9476*** | 0.2149 | 4.4102 | 0.0000 |

A (2,2) | 0.2261*** | 0.0117 | 19.3120 | 0.0000 |

A (2,3) | 0.0029 | 0.0168 | 0.1724 | 0.8631 |

A (3,1) | 0.0276 | 0.0701 | 0.3931 | 0.6942 |

A (3,2) | 0.0082** | 0.0032 | 2.5416 | 0.0110 |

A (3,3) | 0.5619*** | 0.0265 | 21.1826 | 0.0000 |

B (1,1) | 0.9439*** | 0.0050 | 188.2448 | 0.0000 |

B (1,2) | 0.0025*** | 0.0002 | 15.2582 | 0.0000 |

B (1,3) | 0.0013** | 0.0005 | 2.5293 | 0.0114 |

B (2,1) | −0.4804*** | 0.0979 | −4.9058 | 0.0000 |

B (2,2) | 0.9704*** | 0.0033 | 293.9139 | 0.0000 |

B (2,3) | −0.0047 | 0.0082 | −0.5698 | 0.5688 |

B (3,1) | −0.0147 | 0.0254 | −0.5764 | 0.5644 |

B (3,2) | −0.0043*** | 0.0012 | −3.6130 | 0.0003 |

B (3,3) | 0.8693*** | 0.0104 | 83.8755 | 0.0000 |

Note: *, **, ***: showed a significance level of 10%, 5%, and 1%, respectively.

of analyses conducted in this study show that firstly, between currency market and stock market there is only unidirectional mean spillover effect from currency market to stock market; secondly, however, there exists asymmetrical bidirectional mean spillover effect both between stock market and money market and currency market and money market, which exhibits time-varying variance and volatility persistence; thirdly, there exists bidirectional volatility spillover effect between currency market and money market, however there is only unidirectional volatility spillover effect from stock market to money market, which is demonstrated from money market to currency market.

Thus, the results of this study can provide us with the following policy implications for a more stable and efficient management of financial asset prices.

First, the reason for the volatility spillover of financial market is that the coordinated movement happens in the price or volatility within the financial market. Owing to China’s financial market with linkage characteristics, it is necessary to construct a coordinated interaction mechanism between different markets to

Test item | Hypotheses Testing 1 | Hypotheses Testing 2 | Hypotheses Testing 3 |
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Stock and exchange market | no one-way volatility spillover from stock market to exchange market | no one-way volatility spillover from exchange market to stock market | no volatility spillover between stock market and exchange market |

Stock and money market | no one-way volatility spillover from stock market to money market | no one-way volatility spillover from money market to stock market | no volatility spillover between stock market and money market |

Exchange and money market | no one-way volatility spillover from exchange market to money market | no one-way volatility spillover from money market to exchange market | no volatility spillover between exchange market and money market |

Note: *, **, ***: showed a significance level of 10%, 5%, and 1%, respectively.

mitigate the risk in markets.

Second, between China’s stock market, exchange market and money market interest rates, there exits significant market conductivity, and the spillover effect is obvious. Thus, there need to take more reasonable and effective regulation steps and pay close attention to market volatility and mutual influence so that government can prevent financial risks spreading.

Although this paper analyzes the spillover effect among stock, money and foreign exchange market, it is still not perfect. Broadly speaking, in addition to the three main markets discussed in the paper, financial markets also include the gold market, which could lead to fluctuation stock, money and foreign exchange market. For the deeply research, gold market should be considered.

What’s more, the robustness test examines the robustness of the empirical method and the explanatory. In other words, when changing certain parameters, the empirical results still maintain a consistent and stable. In order to ensure the robustness of empirical results, robustness test should be taken for further study.

Yu, Y.L. and Liao, D. (2017) Empirical Research on Spillover Effect among Stock, Money and Foreign Ex- change Market of China. Modern Economy, 8, 655-666. https://doi.org/10.4236/me.2017.85047