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.
Highlights
From its modest origins, the freight transportation has progressed immeasurably in terms of size and complexity
In the international shipping markets, freight derivatives are very useful instruments to deal with risk, and of interest to market practitioners as well as to academics
The main contribution of this paper is to offer a new framework for pricing both forward freight agreements (FFA) contracts and freight options, when the spot freight rate follows a jump-diffusion stochastic process
Summary
The freight transportation has progressed immeasurably in terms of size and complexity. The main contribution of this paper is to offer a new framework for pricing both FFA contracts and freight options, when the spot freight rate follows a jump-diffusion stochastic process. We obtain a closed-form solution in a part of its domain for the geometric Brownian motion with jumps to be added as a boundary condition when numerical discretization schemes are designed to approximate the price With this framework, we contribute with a new, fast, and accurate analytical method for pricing freight derivatives when jumps are considered.
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