Measure-invariance of copula functions as tool for testing no-arbitrage assumption

Measure-invariance of copula functions as tool for testing no-arbitrage assumption Copulas, which are invariant under margins’ transforms induced by some change of measure, are investigated. It is emphasized that this particular kind of transforms induced by some change of measure, largely used in pricing techniques, preserves the invariance of the aggregation operator and a sufficient condition to assure it is proved. The discussion is extended to the time-preserving of measure-invariance; a characterization of its stability in time for multivariate stationary processes, based on the dynamic copula representation (see Cherubini et al., 2011), is provided. Finally a measure invariance-based statistical test for the absence of arbitrage opportunity assumption and its preservation in time is proposed and an empirical experiment based on quotes of S&P 500 futures and options traded on the Chicago Mercantile Exchange (CME) is discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Computational and Applied Mathematics Elsevier

Measure-invariance of copula functions as tool for testing no-arbitrage assumption

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Publisher
Elsevier
Copyright
Copyright © 2018 Elsevier B.V.
ISSN
0377-0427
eISSN
1879-1778
D.O.I.
10.1016/j.cam.2018.02.001
Publisher site
See Article on Publisher Site

Abstract

Copulas, which are invariant under margins’ transforms induced by some change of measure, are investigated. It is emphasized that this particular kind of transforms induced by some change of measure, largely used in pricing techniques, preserves the invariance of the aggregation operator and a sufficient condition to assure it is proved. The discussion is extended to the time-preserving of measure-invariance; a characterization of its stability in time for multivariate stationary processes, based on the dynamic copula representation (see Cherubini et al., 2011), is provided. Finally a measure invariance-based statistical test for the absence of arbitrage opportunity assumption and its preservation in time is proposed and an empirical experiment based on quotes of S&P 500 futures and options traded on the Chicago Mercantile Exchange (CME) is discussed.

Journal

Journal of Computational and Applied MathematicsElsevier

Published: Aug 15, 2018

References

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