The value of options for time charterparty extension: an artificial neural networks (ANN) approach

The most frequently associated options in the physical shipping market are options to extend the charter period on time charters and additional shipment options on contracts of affreightment. The value of freight options, in practice, is estimated mostly by referring to forward curves. An option on freight has different properties from its financial counterparts, and the straightforward adoption of theoretical models does not produce promising results. In this paper, extension options, which have the property of options on futures, were transformed into regular European options before the application of the Black-Scholes model (BSM). The efficient market hypothesis, which justifies the parity of the performance of a long-term charter to that of repetitive short-term charters, worked as the basis for the transformation. The option values determined by the BSM were compared with actual realized values. Additionally, the artificial neural networks (ANN) was employed to derive the option values. 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. The research results can contribute to the quality of chartering decisions. The results could also be used in quantifying credit risk, as extension options tend to be granted to charterers with more creditability.