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

See all articles by Alois Geyer

Alois Geyer

VGSF / WU

Michael Hanke

University of Liechtenstein

Alex Weissensteiner

Free University of Bolzano Bozen

Date Written: April 16, 2009

Abstract

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

Geyer, Alois and Hanke, Michael and Weissensteiner, Alex, Scenario Trees, Arbitrage, and Multi-Asset ALM Models (April 16, 2009). European Journal of Operational Research, Vol. 206, No. 3, pp. 609-613, 2010. Available at SSRN: https://ssrn.com/abstract=1386222

Alois Geyer

VGSF / WU ( email )

Welthandelsplatz 1
Institute for Financial Research
Vienna, 1020
Austria

HOME PAGE: http://www.wu.ac.at/~geyer

Michael Hanke (Contact Author)

University of Liechtenstein ( email )

Fuerst Franz Josef-Strasse
Vaduz, FL-9490
Liechtenstein

Alex Weissensteiner

Free University of Bolzano Bozen ( email )

Universitätsplatz 1
Bolzano, 39100
+39 0471 013496 (Phone)

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