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Time-varying copula models in the shipping derivatives market


  • Wenming Shi

    () (Shanghai Jiao Tong University)

  • Kevin X. Li

    () (Chung-Ang University)

  • Zhongzhi Yang

    () (Shanghai Jiao Tong University)

  • Ganggang Wang

    () (Shanghai Jiao Tong University)


In this paper, we provide an alternative hedging method based on a popular risk indicator relating to value at risk (VaR) for shipowners to hedge spot freight rate volatility in the tanker market. To achieve this, we use a univariate generalized autoregressive conditional heteroskedasticity model to capture the volatility characteristics of freight derivative returns and apply time-varying copula models to describe the nonlinear dependence between returns of spot and freight derivatives. Using quotes of spot freight rate and forward freight agreement (FFA) in the tanker market from January 3, 2006 to December 23, 2011, we derive the minimum VaR hedge ratios. Our main findings are as follows: First, we found significant evidence for the presence of volatility persistence in freight rate returns. Second, for dependence, we suggested that a time-varying t-copula performs best in describing how returns of spot freight rates relate to 1-month FFA returns, whereas a time-varying Gumbel copula performs much better for the description of nonlinear dependence between returns of spot freight rates and 2 and 3-month FFA returns. Third, the derived hedge ratios are associated with shipowners’ risk preferences and freight rate dynamics, which have important implications for shipowners in determining the optimal number of FFA contracts. The results provide some insights into the modeling of freight derivatives for risk management.

Suggested Citation

  • Wenming Shi & Kevin X. Li & Zhongzhi Yang & Ganggang Wang, 2017. "Time-varying copula models in the shipping derivatives market," Empirical Economics, Springer, vol. 53(3), pages 1039-1058, November.
  • Handle: RePEc:spr:empeco:v:53:y:2017:i:3:d:10.1007_s00181-016-1146-9
    DOI: 10.1007/s00181-016-1146-9

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    References listed on IDEAS

    1. Donald Lien & Yiu Kuen Tse, 2000. "Hedging downside risk with futures contracts," Applied Financial Economics, Taylor & Francis Journals, vol. 10(2), pages 163-170.
    2. Sergio H. Lence, 1995. "The Economic Value of Minimum-Variance Hedges," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 77(2), pages 353-364.
    3. Leland L. Johnson, 1960. "The Theory of Hedging and Speculation in Commodity Futures," Review of Economic Studies, Oxford University Press, vol. 27(3), pages 139-151.
    4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    5. Howard, Charles T. & D'Antonio, Louis J., 1984. "A Risk-Return Measure of Hedging Effectiveness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(1), pages 101-112, March.
    6. Robert J. Myers & Stanley R. Thompson, 1989. "Generalized Optimal Hedge Ratio Estimation," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 71(4), pages 858-868.
    7. Cecchetti, Stephen G & Cumby, Robert E & Figlewski, Stephen, 1988. "Estimation of the Optimal Futures Hedge," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 623-630, November.
    8. Jui-Cheng Hung & Chien-Liang Chiu & Ming-Chih Lee, 2006. "Hedging with zero-value at risk hedge ratio," Applied Financial Economics, Taylor & Francis Journals, vol. 16(3), pages 259-269.
    9. Lai, YiHao & Chen, Cathy W.S. & Gerlach, Richard, 2009. "Optimal dynamic hedging via copula-threshold-GARCH models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2609-2624.
    10. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 130-168.
    11. Patton, Andrew J, 2001. "Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula," University of California at San Diego, Economics Working Paper Series qt01q7j1s2, Department of Economics, UC San Diego.
    12. Zhiguang Cao & Richard D.F. Harris & Jian Shen, 2010. "Hedging and value at risk: A semi‐parametric approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(8), pages 780-794, August.
    13. Xun Lu & Kin Lai & Liang Liang, 2014. "Portfolio value-at-risk estimation in energy futures markets with time-varying copula-GARCH model," Annals of Operations Research, Springer, vol. 219(1), pages 333-357, August.
    14. Chang, Chia-Lin & McAleer, Michael & Tansuchat, Roengchai, 2011. "Crude oil hedging strategies using dynamic multivariate GARCH," Energy Economics, Elsevier, vol. 33(5), pages 912-923, September.
    15. Richard D. F. Harris & Jian Shen, 2006. "Hedging and value at risk," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(4), pages 369-390, April.
    16. Haim Shalit, 1995. "Mean‐Gini hedging in futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 15(6), pages 617-635, September.
    17. C. Sherman Cheung & Clarence C. Y. Kwan & Patrick C. Y. Yip, 1990. "The hedging effectiveness of options and futures: A mean‐gini approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 10(1), pages 61-73, February.
    18. Massimiliano Barbi & Silvia Romagnoli, 2014. "A Copula‐Based Quantile Risk Measure Approach to Estimate the Optimal Hedge Ratio," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(7), pages 658-675, July.
    19. Huang, Jen-Jsung & Lee, Kuo-Jung & Liang, Hueimei & Lin, Wei-Fu, 2009. "Estimating value at risk of portfolio by conditional copula-GARCH method," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 315-324, December.
    20. Ederington, Louis H, 1979. "The Hedging Performance of the New Futures Markets," Journal of Finance, American Finance Association, vol. 34(1), pages 157-170, March.
    21. Kavussanos, Manolis G. & Visvikis, Ilias D. & Batchelor, Roy A., 2004. "Over-the-counter forward contracts and spot price volatility in shipping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 40(4), pages 273-296, July.
    22. Chen, Sheng-Syan & Lee, Cheng-few & Shrestha, Keshab, 2003. "Futures hedge ratios: a review," The Quarterly Review of Economics and Finance, Elsevier, vol. 43(3), pages 433-465.
    23. Rolfo, Jacques, 1980. "Optimal Hedging under Price and Quantity Uncertainty: The Case of a Cocoa Producer," Journal of Political Economy, University of Chicago Press, vol. 88(1), pages 100-116, February.
    24. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    25. Lu Jing & Peter B. Marlow & Wang Hui, 2008. "An analysis of freight rate volatility in dry bulk shipping markets," Maritime Policy & Management, Taylor & Francis Journals, vol. 35(3), pages 237-251, June.
    26. Batchelor, Roy & Alizadeh, Amir & Visvikis, Ilias, 2007. "Forecasting spot and forward prices in the international freight market," International Journal of Forecasting, Elsevier, vol. 23(1), pages 101-114.
    27. Kavussanos, Manolis G. & Dimitrakopoulos, Dimitris N., 2011. "Market risk model selection and medium-term risk with limited data: Application to ocean tanker freight markets," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 258-268.
    28. Kuang-Liang Chang, 2011. "The optimal value-at-risk hedging strategy under bivariate regime switching ARCH framework," Applied Economics, Taylor & Francis Journals, vol. 43(21), pages 2627-2640.
    29. Manolis G. Kavussanos & Ilias D. Visvikis, 2006. "Shipping freight derivatives: a survey of recent evidence," Maritime Policy & Management, Taylor & Francis Journals, vol. 33(3), pages 233-255, July.
    30. Chollete, Lorán & de la Peña, Victor & Lu, Ching-Chih, 2011. "International diversification: A copula approach," Journal of Banking & Finance, Elsevier, vol. 35(2), pages 403-417, February.
    31. Lence, Sergio H., 1996. "Relaxing The Assumptions Of Minimum-Variance Hedging," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 21(1), pages 1-17, July.
    32. Manolis Kavussanos & Ilias Visvikis & Dimitris Dimitrakopoulos, 2010. "Information linkages between Panamax freight derivatives and commodity derivatives markets," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 12(1), pages 91-110, March.
    33. Chin‐Wen Hsln & Jerry Kuo & Cheng‐Few Lee, 1994. "A new measure to compare the hedging effectiveness of foreign currency futures versus options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 14(6), pages 685-707, September.
    34. Yung-Shun Chen & Shiu-Tung Wang, 2004. "The empirical evidence of the leverage effect on volatility in international bulk shipping market," Maritime Policy & Management, Taylor & Francis Journals, vol. 31(2), pages 109-124, April.
    35. Osvaldo C. Silva Filho & Flavio A. Ziegelmann & Michael J. Dueker, 2014. "Assessing dependence between financial market indexes using conditional time-varying copulas: applications to Value at Risk (VaR)," Quantitative Finance, Taylor & Francis Journals, vol. 14(12), pages 2155-2170, December.
    36. Chih‐Chiang Hsu & Chih‐Ping Tseng & Yaw‐Huei Wang, 2008. "Dynamic hedging with futures: A copula‐based GARCH model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(11), pages 1095-1116, November.
    37. Wei, Yu & Wang, Yudong & Huang, Dengshi, 2011. "A copula–multifractal volatility hedging model for CSI 300 index futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4260-4272.
    38. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    39. Yuki Toyoshima & Tadahiro Nakajima & Shigeyuki Hamori, 2013. "Crude oil hedging strategy: new evidence from the data of the financial crisis," Applied Financial Economics, Taylor & Francis Journals, vol. 23(12), pages 1033-1041, June.
    40. Pok, Wee Ching & Poshakwale, Sunil S. & Ford, J.L., 2009. "Stock index futures hedging in the emerging Malaysian market," Global Finance Journal, Elsevier, vol. 20(3), pages 273-288.
    41. Yang, Lu & Hamori, Shigeyuki, 2014. "Dependence structure between CEEC-3 and German government securities markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 29(C), pages 109-125.
    Full references (including those not matched with items on IDEAS)


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    More about this item


    Forward freight agreement; Value-at-risk; Time-varying copula models; Hedge ratio;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • R49 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Other


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