Scenario Trees, Arbitrage, and Multi-Asset ALM Models
European Journal of Operational Research, Vol. 206, No. 3, pp. 609-613, 2010
17 Pages Posted: 16 Apr 2009 Last revised: 15 Sep 2011
Date Written: April 16, 2009
Many numerical optimization methods use scenario trees as a discrete approximation for the true (multi-dimensional) probability distributions of the problem's random variables. Realistic specifications in asset-liability management (ALM) models can lead to tree sizes that quickly become computationally intractable. In this paper we focus on the two main approaches proposed in the literature to deal with this problem: scenario reduction and state aggregation. We first state necessary conditions for the node structure of a tree to rule out arbitrage. However, currently available scenario reduction algorithms do not take these conditions explicitly into account. State aggregation excludes arbitrage opportunities by relying on the risk-neutral measure. This is, however, only appropriate for pricing purposes but not for optimization. Both limitations are illustrated by numerical examples. We conclude that neither of these methods is suitable to solve ALM or related problems.
Keywords: Finance, Uncertainty modelling, Scenario trees, Sparse trees, Asset-liability management
JEL Classification: C61, G11
Suggested Citation: Suggested Citation