A Valuation of Options to Extend the Time Charter Period: The Application of Artificial Neural Networks

Abstract

Options in the shipping market consist of paper freight options and physicaloptions attached to charterparties or newbuilding contracts. The options most frequently associated with the physical shipping market are options to extend the charter period on time charters and additional shipment options attached to contracts of affreightment. In both the paper market and the physical market, the value of

freight options, in practice, is estimated mostly by referring to the forward curves of freight derivatives. The option on freight has different properties from its financial

counterparts, and the straightforward adoption of theoretical models like the Black-Sholes option pricing model (BSM) has not produced promising results. So far, academic research in this field has also hardly made a meaningful contribution to practice and is in need of further elaboration.

This research focuses on the period extension options attached to time charter contracts. In this paper, extension options, which have the property of options on futures, were conceptually transformed into regular European call options before the BSM was applied. The efficient market hypothesis (EMH), which justifies the parity of the performance of a long-term charter to that of repetitive short-term charters for the same period, worked as the basis of the conversion.

The option values determined by the BSM were compared with the actual realized values to verify the applicability of the model. Additionally, a robust relationship mapping model, artificial neural networks (ANN), was employed to

derive the option values, and then the results were compared with those of the BSM. The ANN is recently expanding its application to business, finance, and

management, and is drawing attention in the areas of discrimination, pattern recognition, and forecasting.

This study is meaningful as the first-time application of both the closed-form solution and the ANN to the valuation of physical freight options. In particular, the application of the ANN is expected to lead the active adoption of machine learning tools in the analysis of shipping market behavior. The result of this research can contribute to enhancing the quality of chartering decisions by providing criteria to determine option values. The decision rationality to be achieved by the model can be contrasted with the fact that, so far, decisions have been made with a ‘rule-ofthumb’

valuation of options. The extension option, in reality, tends to be granted to charterers with better credit, even free of charge when the market is at its trough.

Hence, the results could also be used as a tool to quantify counterparty risk. This analysis is limited to the Panamax bulk market, which has long-term data consistency. The extension of the study to other segments of bulk shipping such as Cape, Supramax and even to wet bulk markets will help generalize the model’s performance. The result also implies the ‘forecasting’ performance of the ANN because the value of the extension options contains the information required to make freight market forecasts. Therefore, the study can be extended to the area of

forecasting. In that case, the performances can be tested with additional input variables, such as forward market features, to the BSM input variables.