| dc.description.abstract | Western Bulk is a shipping company that is interested in generating realistic realisations of five different price series; two freight rates, one interest rate and two oil rates. The realisations should keep the internal correlation-structure.
There should also be possible to introduce a crisis-regime where all the prices are correlated with a downward trend similar to what was observed in 2008.
The prices series modelling is approached through a state-space method. The volatility is modelled by a multivariate stochastic volatility model on the compounded returns. The multivariate model decomposes the five dimensional correlation matrix
into fifteen univariate models; five for the volatilities and ten for the correlation between each of the series. Only the two freight rates and the two oil rates are correlated, but the correlation-structure is not strong enough to create
series in line with what is historically observed. A stochastic trend is therefore also introduced. The stochastic trend is a local linear trend model, where the underlying state-space variable follows an AR(1) model.
To get good simulations on a long time span both simulating directly from the model of the underlying state-space time series as well as bootstrapping them are compared.
For the stochastic volatility models with a trend there is little difference between bootstrapping and simulating, except for the interest rate which tends to diverge when simulated. For the stochastic trend bootstrapping gives more stable
results, most notably on realisations without crisis-regimes. | |
