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Pricing freight rate options

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  • Koekebakker, Steen
  • Adland, Roar
  • Sødal, Sigbjørn

Abstract

In this paper we set up the theoretical framework for the valuation of the Asian-style options traded in the freight derivatives market. Assuming lognormal spot freight dynamics, we show that Forward Freight Agreements (FFA) are also lognormal prior to the settlement period, but that this lognormality subsequently breaks down. We suggest approximate dynamics in the settlement period for the FFA that leads to closed-form option pricing formulas for Asian call and put options written on the spot freight rate indices in the Black [Black, F., 1976. The pricing of commodity contracts. Journal of Financial Economics 3, 167-179] framework. In a Monte Carlo experiment we show that our formula gives very accurate prices, in particular for forward-starting freight options.

Suggested Citation

  • Koekebakker, Steen & Adland, Roar & Sødal, Sigbjørn, 2007. "Pricing freight rate options," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(5), pages 535-548, September.
    • Handle: RePEc:eee:transe:v:43:y:2007:i:5:p:535-548
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    9. Nomikos, Nikos K. & Kyriakou, Ioannis & Papapostolou, Nikos C. & Pouliasis, Panos K., 2013. "Freight options: Price modelling and empirical analysis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 51(C), pages 82-94.
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    11. Lourdes Gómez-Valle & Miguel Angel López-Marcos & Julia Martínez-Rodríguez, 2020. "Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds," Mathematics, MDPI, vol. 8(4), pages 1-12, April.
    12. Fred Espen Benth & Jūratė Šaltytė Benth & Steen Koekebakker, 2008. "Stochastic Modeling of Electricity and Related Markets," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6811, December.
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    14. Lourdes Gómez‐Valle & Ioannis Kyriakou & Julia Martínez‐Rodríguez & Nikos K. Nomikos, 2021. "Estimating risk‐neutral freight rate dynamics: A nonparametric approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1824-1842, November.
    15. Tvedt, Jostein, 2019. "Transport services and the valuation of flexibility over business cycles," Transportation Research Part A: Policy and Practice, Elsevier, vol. 130(C), pages 517-528.
    16. Murthy Mudrageda & Frederic H. Murphy, 2008. "OR PRACTICE---An Economic Equilibrium Model of the Market for Marine Transportation Services in Petroleum Products," Operations Research, INFORMS, vol. 56(2), pages 278-285, April.
    17. Wolfgang Drobetz & Tim Richter & Martin Wambach, 2012. "Dynamics of time-varying volatility in the dry bulk and tanker freight markets," Applied Financial Economics, Taylor & Francis Journals, vol. 22(16), pages 1367-1384, August.
    18. Georgios I. Papayiannis, 2022. "Static Hedging of Freight Risk under Model Uncertainty," Papers 2207.00862, arXiv.org.
    19. Mhd Ruslan, Siti Marsila & Mokhtar, Kasypi, 2020. "An Analysis of Price Disparity: Peninsular Malaysia and Sabah," Jurnal Ekonomi Malaysia, Faculty of Economics and Business, Universiti Kebangsaan Malaysia, vol. 54(2), pages 53-66.
    20. Wang, He & Huang, Simin & Liu, Zhen & Zheng, Li, 2013. "Optimal tanker chartering decisions with spot freight rate dynamics considerations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 51(C), pages 109-116.
    21. Fred Espen Benth & Steen Koekebakker, 2016. "Stochastic modeling of Supramax spot and forward freight rates," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 18(4), pages 391-413, December.
    22. Sercan Erol, 2017. "Calculation of the freight revenues in Turkey-focused maritime transportation," Maritime Policy & Management, Taylor & Francis Journals, vol. 44(7), pages 815-824, October.
    23. Tezuka, Koichiro & Ishii, Masahiro & Ishizaka, Motokazu, 2012. "An equilibrium price model of spot and forward shipping freight markets," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(4), pages 730-742.

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