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Forward pricing in the shipping freight market

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Abstract

In this paper, we derive the price of the forward freight contract using spot-forward relationship framework. We base our pricing on six different stochastic models which can capture many stylized facts of spot freight rates such as heavy-tailed logreturns, time-varying volatility and mean reversion. The models are analytically tractable which allows for pricing of forwards. We also examine the shape of forward curve for all continuous-time forward pricing formulas and find various shapes being the combination of fixed and stochastically dependent terms. Finally, this paper discusses the effect of different time to delivery and the maturity effect to the forward curve.

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References

  1. Barndorff-Nielsen, O.E.: Processes of normal inverse Gaussian type. Financ. Stoch. 2(1), 41–68 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barndorff-Nielsen, O.E., Shephard, N.: Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics. J. R. Stat. Soc. B 63(Part 2), 167–241 (2001)

  3. Barndorff-Nielsen, O.E., Shiryaev, A.: Change of Time and Change of Measure. World Scientific, Singapore (2010)

    Book  MATH  Google Scholar 

  4. Benth, F.E., Šaltytė, Benth J.: The normal inverse Gaussian distribution and spot price modelling in energy markets. Int. J. Theor. Appl. Financ. 7(2), 177–192 (2004)

    Article  MATH  Google Scholar 

  5. Benth, F.E., Šaltytė, Benth J., Koekebakker, S.: Stochastic Modelling of Electricity and Related Markets. World Scientific, Singapore (2008)

    Google Scholar 

  6. Benth, F.E.: The stochastic volatility model of Barndorff-Nielsen and Shephard in commodity markets. Math. Financ. 21(4), 595–625 (2011)

    MathSciNet  MATH  Google Scholar 

  7. Benth, F.E., Sgarra, C.: The risk premium and the Esscher transform in power markets. Stoch. Anal. Appl. 30, 20–43 (2012)

  8. Benth, F.E., Koekebakker, S., Taib, C.M.I.C.: Stochastic dynamical modelling of spot freight rates. IMA J. Manag. Math. (2014). doi:10.1093/imaman/dpu001

  9. Borovkova, S., Geman, H.: Seasonal and stochastic effects in commodity forward curves. Rev. Deriv. Res. 9, 167–186 (2006)

    Article  MATH  Google Scholar 

  10. Brockwell, P.J.: Lévy-driven CARMA process. Ann. Inst. Stat. Math. 53(1), 113–124 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  11. Esscher, F.: On the probability function in the collective theory of risk. Skand. Aktuarietidskr. 15, 175–195 (1932)

    Google Scholar 

  12. Gerber, H.U., Shiu, E.S.W.: Option pricing by Esscher transforms. Trans. Soc. Actuar. 46, 99–191 (1994). (with discussion)

    Google Scholar 

  13. Hardle, W.K., Lopez Cabrera, B.: The implied market price of weather risk. Appl. Math. Financ. 19(1), 59–95 (2009)

    Article  MathSciNet  Google Scholar 

  14. Kavussanov, M., Alizadeh, M.A.H.: Seasonality patterns in tanker spot freight rate markets. Econ. Model. 19, 747–782 (2002)

  15. Kavussanov, M., Nomikos, N.: The forward pricing function of the shipping freight futures market. J. Futur. Mark. 19, 353–376 (1999)

    Article  Google Scholar 

  16. Kavussanov, M., Nomikos, N.: Futures hedging when the structure of the underlying asset changes: the case of the BIFFEX contract. J. Futur. Mark. 20, 776–801 (2000)

    Google Scholar 

  17. Koekebakker, S., Ådland, R.O.: Modelling forward freight rate dynamics-empirical evidence from time charter rates. Marit. Policy Manag. 31(4), 319–335 (2004)

    Article  Google Scholar 

  18. Prokopczuk, M.: Pricing and hedging in the freight futures market. J. Futur. Mark. 31, 440–464 (2011)

    Article  Google Scholar 

  19. Schwartz, E.S.: The stochastic behaviour of commodity prices: implications for valuation and hedging. J. Financ. 52(3), 923–973 (1997)

    Article  Google Scholar 

  20. Zhang, S., Zhang, X.: Exact simulation of IG-OU processes. Methodol. Comput. Appl. Probab. 10, 337–355 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

Author acknowledges financial support from the project “Managing Weather Risk in Electricity Markets (MAWREM)” funded by the Norwegian Research Council under Grant RENERGI 216096. Fred Espen Benth is thanked for his suggestions and valuable comments in improving the paper.

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Authors and Affiliations

  1. School of Informatics and Applied Mathematics, University Malaysia Terengganu, 21030, Kuala Terengganu, Terengganu, Malaysia

    Che Mohd Imran Che Taib

  2. Centre of Mathematics for Applications, University of Oslo, PO Box 1053, Blindern, 0316, Oslo, Norway

    Che Mohd Imran Che Taib

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  1. Che Mohd Imran Che Taib
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Correspondence to Che Mohd Imran Che Taib.

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Taib, C.M.I. Forward pricing in the shipping freight market. Japan J. Indust. Appl. Math. 33, 3–23 (2016). https://doi.org/10.1007/s13160-015-0204-6

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  • DOI: https://doi.org/10.1007/s13160-015-0204-6

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