Including Jumps in the Stochastic Valuation of Freight Derivatives

Mathematics

Julia Martínez-Rodríguez¹  Lourdes Gómez-Valle¹ 

[1] Departamento de Economía Aplicada e IMUVA, Facultad de Ciencias Económicas y Empresariales, Universidad de Valladolid, 47011 Valladolid, Spain;

关键词: spot freight rates;    freight options;    stochastic jump-diffusion process;    stochastic delay differential equation;    risk-neutral measure;    arbitrage arguments;   

DOI  :  10.3390/math9020154

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown