Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds

Lourdes Gómez-Valle,Miguel Angel López-Marcos,Julia Martínez-Rodríguez

doi:10.3390/math8040620

Abstract

Freight derivative prices have been modeled assuming that the spot freight follows a particular stochastic process in order to manage them, like freight futures, forwards and options. However, an explicit formula for pricing freight options is not known, not even for simple spot freight processes. This is partly due to the fact that there is no valuation equation for pricing freight options. In this paper, we deal with this problem from two independent points of view. On the one hand, we provide a novel theoretical framework for pricing these Asian-style options. In this way, we build a partial differential equation whose solution is the freight option price obtained from stochastic delay differential equations. On the other hand, we prove lower and upper bounds for those freight options which enables us to estimate the option price. In this work, we consider that the spot freight rate follows a general stochastic diffusion process without restrictions in the drift and volatility functions. Finally, using recent data from the Baltic Exchange, we compare the described bounds with the freight option prices.

Highlights

In this global economy, the transport of every kind of goods around the world has become of great importance
We provide a novel partial differential equation whose solution is the freight option price
In order to obtain the equation that verifies the freight option price, we introduce a new variable which is a delay of the spot freight rate along a time period d

Summary

Introduction

The transport of every kind of goods around the world has become of great importance. Traded freight options are contracts whose payoffs are the difference between the average of freight rates in a settlement period and the strike price. That is, they are arithmetic Asian-style options. We provide a novel partial differential equation whose solution is the freight option price This PDE depends on three independent state variables: the spot freight rate, its delay and the continuous version of the average of the spot freight rate over a time period. This framework opens a new way to address this valuation problem.

The Option Pricing Model

Valuation Partial Differential Equation

Lower and Upper Bounds for Freight Options

Empirical Application

Findings

Discussion and Conclusions