No-Arbitrage ROM Simulation

29 Pages Posted: 15 Apr 2012 Last revised: 30 Jan 2018

See all articles by Alois Geyer

Alois Geyer


Michael Hanke

University of Liechtenstein

Alex Weissensteiner

Free University of Bolzano Bozen

Date Written: January 16, 2014


Ledermann et al. (2011) propose random orthogonal matrix (ROM) simulation for generating multivariate samples matching means and covariances exactly. Its computational efficiency compared to standard Monte Carlo methods makes it an interesting alternative. In this paper we enhance this method's attractiveness by focusing on applications in finance. It is well known that many financial applications require simulated asset returns to be free of arbitrage opportunities. We analytically derive no-arbitrage bounds for expected excess returns to be used in the context of ROM simulation, and we establish the theoretical relation between the number of states (i.e., the sample size) and the size of (no-)arbitrage regions. Based on these results, we present a No-Arbitrage ROM simulation algorithm, which generates arbitrage-free random samples by purposefully rotating a simplex. Hence, the proposed algorithm completely avoids any need for checking samples for arbitrage. Compared to the alternative of (potentially frequent) re-sampling followed by arbitrage checks, it is considerably more efficient. As a by-product, we provide interesting geometrical insights into affine transformations associated with the No-Arbitrage ROM simulation algorithm.

Keywords: scenario trees, financial optimization, no-arbitrage

JEL Classification: C61, G11

Suggested Citation

Geyer, Alois and Hanke, Michael and Weissensteiner, Alex, No-Arbitrage ROM Simulation (January 16, 2014). Journal of Economic Dynamics and Control, 2014, 45, 66-79, Available at SSRN: or

Alois Geyer

VGSF / WU ( email )

Welthandelsplatz 1
Institute for Financial Research
Vienna, 1020


Michael Hanke (Contact Author)

University of Liechtenstein ( email )

Fuerst Franz Josef-Strasse
Vaduz, FL-9490

Alex Weissensteiner

Free University of Bolzano Bozen ( email )

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

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