Abstract
Previous studies on freight rate dynamics have explored the behavior of freight rates and their characteristics, including unit root, among other factors. However, there are few articles related to the stochastic process characterizing their dynamics. Moreover, to the best of the authors’ knowledge, there are no articles that incorporate seasonality in the freight rate dynamics. In the present article, we propose a factor model for the stochastic behavior of TCE (Time Charter Equivalent) and WS (World Scale) prices where one factor is a seasonal factor. In addition, based on this type of modeling, we study the seasonal behavior of freight rates and find that models allowing for stochastic seasonality outperform models with deterministic seasonality. Therefore, ship owners and charterers can accommodate their business strategies to the facts that (i) freight rates are higher in winter and spring than in the summer and autumn and that (ii) these differences are not deterministic but stochastic. These facts have also important implications in derivatives valuation and hedging.
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Notes
For the sake of brevity we have just presented one route results and we have used the current month forward, FCM, prices. However the rest of the routes and forward prices results are more or less the same and are available upon readers’ requests.
Each seasonal factor is modeled through a complex trigonometric component, whichcan be expressed by means of two real SDE. The SDE for the complex trigonometric component is: da t =−i2πφa t dt+Q α dW at , where a t is a complex factor (a t =α t +iα∗ t ). Equaling real and imaginary components in the previous equation yields the two real SDEs for α t and α∗ t .
Here we assume homoskedasticity in the error terms. Liu and Tang (2011) show evidence of heteroskedasticity in the convenience yield series for WTI and copper, using daily data. However, we have confined ourselves to the constant volatility case for several reasons. First, the residuals of the model show little evidence of heteroskedasticity with weekly data. Second, a stochastic volatility model is probably more realistic, but also more complex so much the Kalman-filter formulae cannot be computed explicitly in an exact way and it is necessary the use of approximations, whereas all the formulae in this article are exact.
As seen by Garcia et al (2012), ραα*=0 and σ α =σα*.
As seasonal factors are not stochastic, they do not need a risk premium.
Detailed accounts of Kalman filtering are given in Harvey (1989).
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Poblacion, J. The stochastic seasonal behavior of freight rate dynamics. Marit Econ Logist 17, 142–162 (2015). https://doi.org/10.1057/mel.2014.37
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DOI: https://doi.org/10.1057/mel.2014.37