Including Jumps in the Stochastic Valuation of Freight Derivatives

Lourdes Gómez-Valle and Julia Martínez-Rodríguez
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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

Mathematics, 2021, vol. 9, issue 2, 1-17

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.

Keywords: spot freight rates; freight options; stochastic jump-diffusion process; stochastic delay differential equation; risk-neutral measure; arbitrage arguments; partial integro-differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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