Scenario Generation Employing Copulas

stochastic programs are effective for solving long-term planning problems under uncertainty. Such programs are usually based on scenario generation model about future environment developments. In the present paper, the scenario model is developed for the case when enough data paths can be generated, but due to solvability of stochastic program the scenario tree has to be constructed. The proposed strategy is to generate multistage scenario tree from the set of individual scenarios by bundling scenarios based on cluster analysis. The K-means clustering approach is modified to capture the interstage dependencies. Such generation of scenario tree can be useful in cases when it is difficult to construct the adequate scenario tree from the stochastic differential equations or time-series models, and the sampled paths can be obtained by sampling or resampling techniques. While generating the initial fan of individual scenarios, the copula is employed for modeling the dependence between stochastic variables in a multivariate structure. This allows to model nonlinear dependencies between non-elliptically distributed stochastic variables. While investigating the copula effect on the scenario tree structure, we will try to answer the question: does the copula features are captured in the approximate representation of uncertainty in the form of scenario tree. The proposed scenario tree generation method is implemented on sampled data of discount bond yields. The Gaussian copula and Student's t-copula are employed while generating the set of individual scenarios in the multivariate structure.