In this paper, we present a new approach for estimating the drift of the risk neutral spot freight rate process, which is not observable, directly from Forward Freight Agreement (FFA) prices without requiring knowledge of some prior closed-form model solution. We demonstrate our approach is robust by means of numerical simulations. We make empirical experiments which involve the estimation of two standard parametric models from the relevant literature and a non-parametric model using data from the Baltic Capesize, Panamax and Supramax indices. We find that our proposed methodology with a non-parametric estimation approach yields the lowest pricing errors across different maturities. Finally, we obtain the market price of risk as the difference between the drift under the physical and risk neutral measures and analyze its behaviour in the in-sample and out-sample periods, and find that the market price of risk estimated with a non-parametric approach evolves consistently with the considered indices.