Scenario tree generation approaches using K-means and LP moment matching methods

We consider in this paper the efficient ways to generate multi-stage scenario trees. A general modified K-means clustering method is first presented to generate the scenario tree with a general structure. This method takes the time dependency of the simulated path into account. Based on the traditio...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 236; no. 17; pp. 4561 - 4579
Main Authors: Xu, Daobao, Chen, Zhiping, Yang, Li
Format: Journal Article
Language:English
Published: Elsevier B.V 01.11.2012
Subjects:
Clustering
Computer simulation
K-means clustering
Matching
Mathematical models
MGARCH
Moment matching
Scenario tree
Series (mathematics)
Simulation
Time series
Trees
Volatility
Scenario tree
Moment matching
Simulation
LP
MGARCH
K-means clustering
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:We consider in this paper the efficient ways to generate multi-stage scenario trees. A general modified K-means clustering method is first presented to generate the scenario tree with a general structure. This method takes the time dependency of the simulated path into account. Based on the traditional and modified K-means analyses, the moment matching of multi-stage scenario trees is described as a linear programming (LP) problem. By simultaneously utilizing simulation, clustering, non-linear time series and moment matching skills, a sequential generation method and another new hybrid approach which can generate the whole multi-stage tree right off are proposed. The advantages of these new methods are: the vector autoregressive and multivariate generalized autoregressive conditional heteroscedasticity (VAR-MGARCH) model is adopted to properly reflect the inter-stage dependency and the time-varying volatilities of the data process, the LP-based moment matching technique ensures that the scenario tree generation problem can be solved more efficiently and the tree scale can be further controlled, and in the meanwhile, the statistical properties of the random data process are maintained properly. What is more important, our new LP methods can guarantee at least two branches are derived from each non-leaf node and thus overcome the drawback in relevant papers. We carry out a series of numerical experiments and apply the scenario tree generation methods to a portfolio management problem, which demonstrate the practicality, efficiency and advantages of our new approaches over other models or methods.
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ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2012.05.020