Pricing in Offshore Shipping Markets : A Two-Regime Mean Reverting Jump Diffusion Model with Seasonality

Abstract

The academical research on o shore shipping markets is very limited. This thesis is an attempt to improve our understanding of the spot rates for o shore shipping markets and consequently our ability to do more accurate pricing. I perform an empirical analysis of the most signi cant characteristics of the spot rates for Platform Supply Vessels (PSV) and Anchor Handling Tug Supply (AHTS) vessels and propose a model able to capture these dynamics. The proposed spot rate model is an extension to the simple geometric mean reversion model, incorporating two-regime mean reversion, jumps and a deterministic seasonal function. Parameters are estimated based on the historical spot rates and the model is calibrated for the North Sea market. Using modern derivatives techniques I derive the risk adjusted spot rate process and adopt Tvedt's [30] approach to pricing vessels as a spot rate contingent claim on cash ows, where the pay-o structure can be described as a continuous American call option. The proposed spot rate model is then applied to the problem and the partial di erential equation satisfying the value function of a vessel is derived.