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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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    References listed on IDEAS

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