Stochastic dynamical modelling of spot freight rates

Abstract

Based on empirical analysis of the Capesize and Panamax indices, we propose different continuous-time stochastic processes to model their dynamics. The models go beyond the standard geometric Brownian motion, and incorporate observed effects like heavy-tailed returns, stochastic volatility and memory. In particular, we suggest stochastic dynamics based on exponential Lévy processes with normal inverse Gaussian distributed logarithmic returns. The Barndorff-Nielsen and Shephard stochastic volatility model is shown to capture time-varying volatility in the data. Finally, continuous-time autoregressive processes provide a class of models sufficiently rich to incorporate short-term persistence of freight rates. Our proposed dynamical models are fitted to market data. Finally, a numerical Value-at-Risk exercise is provided that illustrate the significance of using more sophisticated models than geometric Brownian motion.