Chinese Academy of International Trade and Economic Cooperation of MOC, Beijing 100710, China

1 Introduction

The great volatility in international agricultural prices since 2006 has drawn the attention of all countries. At the G20 summit held in Seoul, South Korea in November 2010, under the theme of "Multi-year Development Action Plan: Pillar of Food Security", the G20 leaders proposed that the international organizations and relevant agencies should work together to help members of the G20 to seek measures to better manage and mitigate the risks associated with price volatility of agricultural products. Soybean is not only an important grain and oil product, but also an important strategic material. It has both commodity and financial attributes. Its price fluctuates frequently and greatly. For example, the international soybean futures price rose from $5.27/bushel (1 539.39 yuan/t) on September 12, 2006 to $16.58/bushel (4 173 yuan/t) on July 3, 2008, an increase of 214.61%, but then it quickly fell to $7.84/bushel (1 979.08 yuan/t) on December 5, 2008, down by 52.71%. The domestic soybean futures market price soared from 2 388 yuan/t on September 12, 2006 to 5 749 yuan/t on June 7, 2008, up 140.74%, but it rapidly dropped to 3 287 yuan/t on October 16, 2008, a decrease of 42.82 %. China is a major importer of soybeans, and since the late 1990s, the imports have increased year by year, and China’s soybean imports from 2014 to 2015 reached 78.35 million t, and the import dependence was as high as 86.6%.

With the increasing import of soybeans, the soybean price volatility on international market has a deepening impact on China’s soybean market through trade channels or information transmission. At the same time, with the development of the domestic futures market, the connection between the domestic futures market and the spot market is also constantly strengthened. If there is price volatility spillover between different markets, then the policy changes in one market will have an impact on other markets[1]. So how does the price volatility interact between the international soybean market and the domestic soybean market, between the domestic futures market and the spot market? The answer to this question is directly related to the price risk management decisions related to soybean production, processing and trade, and also affects the performance of government policy control over the price of agricultural products.

In this paper, we analyze the price volatility spillover effects of soybeans in the international market, domestic futures market and domestic spot market, with the aim of providing the basis for the government to introduce the corresponding price control policy, and for the domestic soybean producers and processing traders to make risk management decisions.

2 Literature review

The price volatility spillover refers to the link between the conditional variances of price return series, and it is also considered the linkage of uncertainty between the markets[2]. The research on the spillover effect of price volatility of agricultural products in foreign countries began in the 1990s, but it mainly focuses on the research of agricultural products in Europe and the United States. The research areas focus on the price volatility spillover between the upstream and downstream products of the agricultural product chain[1-4], between different agricultural products[5-6]. The main research method is to use the vector autoregression model (VAR model), generalized autoregressive conditional heteroskedasticity model (GARCH model) and its extended form (EGARCH, Spline-GARCH,etc.) as well as multivariate GARCH model. The domestic research on the price volatility spillover of soybeans started late, and the research mainly focuses on two aspects.

(i) The volatility spillover effect between the domestic futures market and the spot market. Liu Qingfu and Wang Haimin use the binary EGARCH model, and find that there is a two-way volatility spillover relationship between the soybean futures market and spot market, but the volatility spillover effects of futures market on spot market is significantly greater than the volatility spillover effects of spot market on futures market[7]. Zhong Weijun and Dai Yang think that there is a symmetrical two-way volatility spillover effect between China’s soybean futures and spot prices[8]. (ii) The volatility spillover effect between the international market and the domestic market. Hua Renhai and Liu Qingfu use the dual parameter AR-EGARCH (t) model to analyze the volatility spillover of soybean futures price, and believe that the influence of international market on domestic market is significantly greater than the influence of domestic market on international market[9]. Xiao Xiaoyongetal. and Li Guangsietal. use the binary BEKK-GARCH model to study, and find that there is two-way volatility spillover effect between the domestic soybean spot prices[10-11].

It can be seen that the domestic and foreign scholars have made a useful research from different perspectives on the volatility spillover effects of soybean market price, but there are the following shortcomings.

(i) It does not put the three interconnected markets (international market, one country’s domestic futures market, domestic spot market) into one system for analysis, while the putting the three markets together for analysis can better help us to understand the mutual influence among different markets. (ii) Although using the binary BEKK-GARCH model overcomes the shortcoming that the GARCH model and its extended form do not consider the influence of conditional covariance between the variables when analyzing the volatility spillover, the domestic literature mainly analyzes the volatility spillover based on monthly data, lacking the analysis of high frequency data such as daily price data, and the use of high frequency data for volatility spillover analysis can better capture the short-term volatility characteristics and meet the investment needs of hedgers for price risk aversion or market transactions. (iii) Most of the research literature lacks the statistical test on the validity of the model estimation, so the validity of the conclusions is debatable.

In order to make up for the drawbacks of the above research, we use the daily futures and spot price data, to extend the binary VAR-BEKK-GARCH model to the multivariate VAR-BEKK-GARCH model, and on the basis of the statistical test on the validity of the model estimation, we analyze the volatility spillover effect among the international soybean market, domestic soybean futures market, and domestic soybean spot market.

3 Data and model

3.1DatadescriptionIn this study, we choose the daily soybean transaction prices from December 22, 2004 to December 19, 2014. The domestic spot price of soybeans is the spot wholesale price of yellow soybean in Dalian market. The domestic futures price of soybeans is the No. 1 yellow soybean futures price of Dalian Commodity Exchange. The international soybean price is the soybean futures price of Chicago Board of Trade (CBOT). The above futures price data are based on the closing prices of continuous futures contracts for the most recent delivery month. The advantage of choosing a continuous contract price for a contract of the recent delivery month is that the resulting futures data are relatively close to the last trading day, and thus the futures price is relatively close to the spot price while also overcoming the disadvantages of small volume of transactions and unstable data in the delivery month[7]. All of the above price data are from the Datastream database at Thomson Reuters.

In order to unify the pricing unit, the international market price of soybean is converted into RMB, and the exchange rate of USD to RMB is from the RMB central rate of the State Foreign Exchange Trading Center. In addition, in order to match the transaction time of the domestic and international market sample data, the time point (segment) where there is no transaction data in the international market or the domestic market on the same date is deleted. Finally, we get 2 290 sample points.

3.2ModelsettingIn this study, we use the multivariate VAR-BEKK-GARCH model (hereinafter referred to as VAR-BEKK model) for the modeling of volatility spillover effects among the domestic spot market, domestic futures market and international futures market price of soybeans, to analyze the volatility spillover effect between the various markets. The advantage of the VAR-BEKK model is that it can guarantee the positive definite property of conditional covariance matrix under weaker conditions[12], so the volatility spillover effect between soybean markets can be well examined. The model is set as follows:

Let the domestic spot market, domestic futures market and international futures market prices of soybeans in thetperiod bep1t,p2t,p3t, respectively, and its return series can be expressed asr1t,r2t,r3t, respectively, whererit=100×ln(pit/pit-1),i=1, 2, 3.

Using the soybean return series, the VAR-BEKK (1, 1) model is built, and its expression is as follows:

(1)

(2)

(3)

Among them, formula (1) is the conditional mean equation, andRtis 3×1 dimensional vector, namelyRt=(r1t,r2t,r3t)′;mis the largest lag order;μis 3×1 dimensional constant vector,φiis 3×3 dimensional parameter matrix;εtis the 3×3 dimensional conditional residual vector;Ft-1is the information set in timet-1. In formula (2),ηtis 3×1 the dimensional independent and identically distributed random vector,Htis the conditional variance covariance matrix ofRt. Formula (3) is the conditional variance equation,C,A,Bare all the 3×3 dimensional parameter matrix,Cis the upper triangular matrix,Arepresents the coefficient matrix of ARCH term,Brepresents the coefficient matrix of GARCH term.

In formula (3), it can be expressed as follows:

whereh11, t,h22, t,h32, t,, represent the conditional variance of domestic spot market, domestic futures market, and international futures market of soybeans, respectively;h12, t(h21, t),h13, t(h31, t),h23, t(h32, t), , represent the conditional covariance between domestic spot market and domestic futures market, between domestic spot market and international futures market, between domestic futures market and international futures market, respectively.

The method of estimating the above VAR-BEKK model: under the assumption of the conditional residual vectorεtfollowing the normal distribution, the parameter estimation is performed by maximizing the following log-likelihood function:

whereθis the parameter to be estimated;Tis the number of observed samples;Nis the number of series in the model.

After the model is estimated, in order to ensure the rationality of the model, the residuals of the model estimation need to be diagnosed and tested. This study uses the Ljung-Box Q statistics and Engle’s ARCH effect test[13]to test the sequence correlation of normalized residuals and conditional heteroskedasticity, respectively. If there is no sequence correlation and conditional heteroskedasticity in the normalized residuals of the model, the estimated model can be considered as reasonable.

To test whether there is volatility spillover effect in the soybeans among the three markets, the estimated model obtained is used to set the following null hypothesis, and the Wald test method is used for volatility spillover effect test:

H1: Ifa12=b12=0, there is no volatility spillover effect from the domestic spot market to the domestic futures market;

H2: Ifa13=b13=0, there is no volatility spillover effect from the domestic spot market to the international futures market;

H3: Ifa21=b21=0, there is no volatility spillover effect from the domestic futures market to the domestic spot market;

H4: Ifa23=b23=0, there is no volatility spillover effect from the domestic futures market to the international futures market;

H5: Ifa31=b31=0, there is no volatility spillover effect from the international futures market to the domestic spot market;

H6: Ifa32=b32=0, there is no volatility spillover effect from the international futures market to the domestic futures market.

4 Model estimation and result analysis

To ensure the validity of the estimation results of VAR-BEKK model, we need to test the stability of different variables included in the model analysis and ARCH effects. The results are shown in Table 1. The ADF method is used to conduct the unit root test on the return series in three markets of soybeans, and the results show that all variables are stationary. The ARCH effect test of lag order 1 and 4 shows that there is ARCH effect in the gains of the domestic and international soybean markets. Therefore, the VAR-BEKK model can be used to model and conduct the volatility spillover effect analysis.

Table1Theunitroottestonthesoybeanreturns

VariableTestform1Lagorder2StatisticLM(1)LM(4)r1C5-14．5727???43．317???99．685???r2C0-49．5381???57．770???74．124???r3C0-50．1900???16．116???37．532???

Note:Cin the test form indicates that the estimation equation includes the intercept term, indicates the lag order selected according to the SIC indicator;***indicates that it is statistically significant at the 1% level; LM (1), LM (4) represent the chi-square test statistic of ARCH effects of lag order 1, 4, respectively;r1,r2,r3represent the domestic soybean spot return, domestic soybean futures return, and international soybean futures return series, respectively.

The specific steps of AR-BEKK model estimation are as follows: firstly, the mean equation VAR model is estimated, and the optimal lags of the VAR model are selected according to SIC indicator; secondly, the pseudo maximum likelihood estimation method is used to estimate the VAR-BEKK (1, 1) model, and the rationality of the model estimation results is tested; finally, the Wald test is conducted on the coefficients of the model passing the residual test, and the volatility spillover effects between different soybean markets are investigated.

Table 2 shows the estimated results of the VAR (2)-BEKK model of soybean returns. It can be found that most of the coefficients of most cross terms in the variance equation are statistically significant, and the test results of normalized residuals of the model show that there is no ARCH effect in the model, therefore, the estimated model is reasonable, and it can be used for volatility spillover effect analysis.

Table2VAR(2)-BEKKmodelestimationresults

MeanequationVariableCoefficientStandarderrorVarianceequationVariableCoefficientStandarderrorr1--r1(1)0．1619???0．0577C(1，1)-0．02150．0574r1(2)-0．1004???0．0273C(2，1)-0．27720．5583r2(1)-0．00200．0128C(2，2)-0．7080?0．4266r2(2)-0．02160．0149C(3，1)-0．3518???0．1152r3(1)-0．0316???0．0072C(3，2)-0．15970．4496r3(2)-0．00790．0049C(3，3)-0．00311．2390r2- -A(1，1)-0．2727???0．0382r1(1)-0．03680．1059A(1，2)-0．12370．1463r1(2)-0．03770．0398A(1，3)-0．27467???0．0968r2(1)-0．11570．0796A(2，1)-0．0713??0．0278r2(2)-0．01710．0643A(2，2)-0．6324???0．0958r3(1)-0．14250．0245A(2，3)-0．01770．0819r3(2)-0．02380．0188A(3，1)-0．0486???0．0141r3- -A(3，2)-0．0682???0．0182r1(1)-0．13520．1130A(3，3)-0．24013???0．0552r1(2)-0．06490．0668B(1，1)-0．8729???0．0352r2(1)-0．05970．0490B(1，2)-0．17940．2197r2(2)-0．01530．0476B(1，3)-1．20030．1541r3(1)-0．01480．0352B(2，1)-0．02140．0474r3(2)-0．01620．0238B(2，2)-0．32290．5119B(2，3)-0．19980???0．0191B(3，1)-0．07879???0．0098B(3，2)-0．19110???0．0468B(3，3)-0．87960???0．0272LogL-9042．4136AIC7．944BIC8．05NormalizedresidualtestMVQ(4)40．1134LM(4)130．02LM(8)209．88

Note: The variables are the same as in Table 1, the number in brackets after variables represents the lag; LogL represents the log-likelihood function value; MVQ (4) represents the multivariate Ljung-Box Q statistic of lag order 4; LM (4), LM (8) represent the chi-squared statistic value of ARCH test of order 4, 8, respectively; the standard error is the robust standard error calculated according to the pseudo maximum likelihood estimation method of Bollerslev and Wooldridge[14];***,**,*indicate that it is statistically significant at the 1%, 5%, 10% level, respectively.

Due to the nonlinear structure of VAR-BEKK model, as for the understanding of the estimated coefficients of the model, we can not rely on the significance of single coefficient to simply explain the volatility spillover effects between markets, therefore, in this study, we use the Wald test for joint test on the model coefficients. The results in Table 3 show that there are no one-way volatility spillover effects in the soybeans from the domestic futures market to the domestic spot market; there are two-way volatility spillover effects between the domestic futures market and the international futures market; there are two-way volatility spillover effects between the domestic spot market and the international futures market.

4 Conclusions and discussions

Using the VAR-BEKK-GARCH model, we investigate the volatility spillover effect in the soybean prices among the domestic spot market, domestic futures market, and international futures market. Research findings show that for both the domestic spot market and futures market of soybeans, the domestic market is greatly affected by the international market price volatility, and the soybean price volatility can be passed from the international market to the domestic market through trade channels or information channels. There is a very close volatility link between the domestic market and the international market of soybeans. China is the world’s largest soybean importer, and from 2014 to 2015, China’s soybean imports accounted for 62.2% of global soybean exports, and China’s importing price of soybeans is mainly determined with reference to the international futures market price, therefore, the changes in the international market price of soybeans are directly reflected in the importing price of soybeans, and the changes in the importing price of soybeans will lead to the volatility of domestic market price of soybeans by affecting the domestic soybean demand. The changes in China’s soybean market price can have an important impact on the international soybean market through the market information transmission or direct import trade. In addition, after nearly 30 years of development, China’s soybean futures market has become one of the major trading places of soybeans in the world. There is obvious interaction in the price volatility between the domestic and international futures market. The market risk is directly related to the market price volatility, and the price volatility spillover from the international soybean market to the domestic market means that the price volatility risk is transferred from the international soybean market to the domestic market.

Table3TheWaldtestresultsontheVAR(2)-BEKKmodelcoefficients

NullhypothesisChi?squarestatisticsConclusionsa12=b12=01．5585Thereisnospilloverfromthedomesticspotmarkettothedomesticfuturesmarketa21=b21=013．4449???Thereisspilloverfromthedomesticfuturesmarkettothedomesticspotmarketa13=b13=063．1449???Thereisspilloverfromthedomesticspotmarkettotheinternationalfuturesmarketa31=b31=084．8894???Thereisspilloverfromtheinternationalfuturesmarkettothedomesticspotmarketa23=b23=026．9864???Thereisspilloverfromthedomesticfuturesmarkettotheinternationalfuturesmarketa32=b32=034．6134???Thereisspilloverfromtheinternationalfuturesmarkettothedomesticfuturesmarket

Data source: It is calculated based on the VAR(2)-BEKK model estimation results.

In order to reduce the impact of international soybean market price volatility on the domestic market, on the one hand, it is necessary to strengthen the supply and demand analysis, price monitoring and forecasting on the international soybean market, establish the soybean price volatility early warning mechanism, comprehensively use various trade policies to regulate the soybean imports, and timely prevent the impact of international soybean market risk on the domestic soybean market. On the other hand, the domestic futures market should further perfect the soybean futures contract and transaction risk management mechanism, improve the information disclosure system, regulate the speculation of major players, prevent market manipulation, and reduce the impact of international market volatility risk on the domestic market. At the same time, the domestic soybean producers, spot importers, soybean processors and soybean traders should make full use of the domestic and international soybean futures market for hedging to avoid the risk of price volatility. It is a job with high technical requirements to use the futures market for hedging. There is not only the basis risk caused by different changes in the spot price and futures price, but also the liquidity risk in the need for financial resources, which requires the soybean hedgers to fully understand the volatility characteristics and correlation changes about the spot and futures soybean prices, strengthen the management of fund utilization, and formulate a reasonable hedging strategy, to effectively avoid the risks brought by price volatility.

[1] BUGUK C, HUDSON D, HANSON D. Price volatility in agricultural markets: An examination of U.S. catfish markets[J]. Journal of Agricultural and Resource Economics, 2003, 28(1):86-99.

[2] APERGIS N, REZITIS A. Agricultural price volatility spillover effects: The case of Greece[J]. European Review of Agricultural Economics, 2003, 30(3): 389-406.

[3] KHAN MA, HELMERS GA. Causality, input price variability and structural changes in the U.S. livestock-meatindustry[J]. Western Journal of Agricultural Economics, 1997, 22(2):392.

[4] REZITIS AN, STAVROPOULOS KS. Greek meat supply response and price volatility in a rational expectationsframework: A multivariate GARCH approach[J]. European Review of Agricultural Economics,2012, 39(2):309-333.

[5] ZHAO J, GOODWIN BK. Volatility spillovers in agricultural commodity markets: an application involving implied volatilities from options markets[A]. Proceedings of the 2011 AAEA & NAREA Joint Annual Meeting[C], Pittsburgh, Pennsylvania, 2011.

[6] BECKMANN J, CZUDAJ R. Volatility transmission in agricultural futures markets[J]. Economic Modelling, 2014, 36(1): 541-546.

[7] LIU QF, WANG HM. Price discovery in the spot-futures markets： An empirical analysis in Chinese agricultural products[J]. Research on Financial and Economic Issues，2006(4)：44-53．(in Chinese).

[8] ZHONG WJ, DAI Y. An analysis on volatility relationship in China’s soybean spot-futures markets[J]. Journal of Southeast University(Philosophy and Social Science )，2007，9(3)：23-27. (in Chinese).

[9] HUA RH, LIU QF. Vitality spillovers between Chinese and overseas future markets[J].The Journal of World Economy，2007,30(6)：64-74. (in Chinese).

[10] XIAO XY, LI CG, LI J. Analysis on spillover effects of international food prices on grain prices in China[J]. Chinese Rural Economy，2014(2)： 42-55. (in Chinese).

[11] LI GS, CAO BM, MA XL. The opening of Chinese grain market and the fluctuation of international grain price [J]. Chinese Rural Economy，2015(8)：44-52，66. (in Chinese).

[12] ENGLE RF, KRONER KF. Multivariate simultaneous generalized ARCH[J]. Econometric Theory, 1995,11(1): 122-150.

[13] ENGLE RF. Autoregressive conditional heterodasticity with estimate of variance of United Kingdom inflation[J]. Econometrica,1982,50(4): 987-1007.

[14] BOLLERSLEV T, WOOLDRIDGE JM. Quasi maximum likelihood estimation and inference in dynamic models with time varying covariances[J]. Econometric Reviews,1992, 11(2):143-172.