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Including Jumps in the Stochastic Valuation of Freight Derivatives

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  • Lourdes Gómez-Valle

    (Departamento de Economía Aplicada e IMUVA, Facultad de Ciencias Económicas y Empresariales, Universidad de Valladolid, 47011 Valladolid, Spain)

  • Julia Martínez-Rodríguez

    (Departamento de Economía Aplicada e IMUVA, Facultad de Ciencias Económicas y Empresariales, Universidad de Valladolid, 47011 Valladolid, Spain)

Abstract

The spot freight rate processes considered in the literature for pricing forward freight agreements (FFA) and freight options usually have a particular dynamics in order to obtain the prices. In those cases, the FFA prices are explicitly obtained. However, for jump-diffusion models, an exact solution is not known for the freight options (Asian-type), in part due to the absence of a suitable valuation framework. In this paper, we consider a general jump-diffusion process to describe the spot freight dynamics and we obtain exact solutions of FFA prices for two parametric models. Moreover, we develop a partial integro-differential equation (PIDE), for pricing freight options for a general unifactorial jump-diffusion model. When we consider that the spot freight follows a geometric process with jumps, we obtain a solution of the freight option price in a part of its domain. Finally, we show the effect of the jumps in the FFA prices by means of numerical simulations.

Suggested Citation

  • Lourdes Gómez-Valle & Julia Martínez-Rodríguez, 2021. "Including Jumps in the Stochastic Valuation of Freight Derivatives," Mathematics, MDPI, vol. 9(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:154-:d:479372
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    1. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2019. "A general framework for time-changed Markov processes and applications," European Journal of Operational Research, Elsevier, vol. 273(2), pages 785-800.
    2. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    3. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    4. 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.
    5. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    6. Ioannis Kyriakou & Panos K. Pouliasis & Nikos C. Papapostolou & Nikos K. Nomikos, 2018. "Income uncertainty and the decision to invest in bulk shipping," European Financial Management, European Financial Management Association, vol. 24(3), pages 387-417, June.
    7. Sigbjørn Sødal & Steen Koekebakker & Roar Adland, 2009. "Value based trading of real assets in shipping under stochastic freight rates," Applied Economics, Taylor & Francis Journals, vol. 41(22), pages 2793-2807.
    8. Adland, Roar & Cullinane, Kevin, 2006. "The non-linear dynamics of spot freight rates in tanker markets," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 42(3), pages 211-224, May.
    9. Bandi, Federico M. & Nguyen, Thong H., 2003. "On the functional estimation of jump-diffusion models," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 293-328.
    10. Marcel Prokopczuk, 2011. "Pricing and hedging in the freight futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(5), pages 440-464, May.
    11. 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.
    12. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    13. Xuemin Yan, 2002. "Valuation of commodity derivatives in a new multi-factor model," Review of Derivatives Research, Springer, vol. 5(3), pages 251-271, October.
    14. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    15. Kavussanos, Manolis G. & Marcoulis, Stelios N., 2004. "4. Cross-Industry Comparisons Of The Behaviour Of Stock Returns In Shipping, Transportation And Other Industries," Research in Transportation Economics, Elsevier, vol. 12(1), pages 107-142, January.
    16. Corsaro, Stefania & Kyriakou, Ioannis & Marazzina, Daniele & Marino, Zelda, 2019. "A general framework for pricing Asian options under stochastic volatility on parallel architectures," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1082-1095.
    17. Jostein Tvedt, 1998. "Valuation of a European futures option in the BIFFEX market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 18(2), pages 167-175, April.
    18. Sødal, Sigbjørn & Koekebakker, Steen & Aadland, Roar, 2008. "Market switching in shipping -- A real option model applied to the valuation of combination carriers," Review of Financial Economics, Elsevier, vol. 17(3), pages 183-203, August.
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