No-Arbitrage ROM simulation

Alois Geyer, Michael Hanke and Alex Weissensteiner

Journal of Economic Dynamics and Control, 2014, vol. 45, issue C, 66-79

Abstract: 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. 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: Financial scenario generation; ROM simulation; No-arbitrage bounds; Simplex; Rotation matrix (search for similar items in EconPapers)
JEL-codes: C63 G11 G12 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:45:y:2014:i:c:p:66-79

DOI: 10.1016/j.jedc.2014.05.017

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