Arbitrage-free scenario trees for financial optimization


Type Research Project

Duration Dec. 1, 2010 - Dec. 31, 2013

  • Institute for Financial Research IN (Details)

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  • Geyer, Alois (Details) Project Head
 

Abstract (German)

This paper presents a method which is designed to generate arbitrage-free scenario trees representing multivariate return distributions. We derive bounds on expected excess returns required to achieve this objective. Our approach is embedded in the setting of arbitrage pricing theory (APT), and asset returns are assumed to be driven by orthogonal factors. We derive no-arbitrage bounds for the least possible number of scenarios (i.e. the smallest dimension of the discrete state-space) necessary to match the first two moments and to exclude arbitrage at the outset. This not only safeguards against the curse of dimensionality: Numerical results from solving two-stage asset allocation problems show that highly accurate results can be obtained with the smallest possible scenario tree.


Abstract (English)

This paper presents a method which is designed to generate arbitrage-free scenario trees representing multivariate return distributions. We derive bounds on expected excess returns required to achieve this objective. Our approach is embedded in the setting of arbitrage pricing theory (APT), and asset returns are assumed to be driven by orthogonal factors. We derive no-arbitrage bounds for the least possible number of scenarios (i.e. the smallest dimension of the discrete state-space) necessary to match the first two moments and to exclude arbitrage at the outset. This not only safeguards against the curse of dimensionality: Numerical results from solving two-stage asset allocation problems show that highly accurate results can be obtained with the smallest possible scenario tree.

Publications

Journal article

2014 Geyer, Alois, Hanke, Michael, Weissensteiner, Alex. 2014. No-arbitrage bounds for financial scenarios. European Journal of Operational Research (EJOR) 236 (2): 657-663. open access (Details)
  Geyer, Alois, Hanke, Michael, Weissensteiner, Alex. 2014. No-Arbitrage ROM Simulation. Journal of Economic Dynamics & Control 45, 66-79. (Details)
2013 Geyer, Alois, Hanke, Michael, Weissensteiner, Alex. 2013. Scenario Tree Generation and Multi-Asset Financial Optimization Problems. Operations Research Letters 41 (5): 494-498. open access (Details)

Working/discussion paper, preprint

2011 Geyer, Alois, Hanke, Michael, Weissensteiner, Alex. 2011. Arbitrage-free Scenario Trees for Financial Optimization. (Details)