Detection of arbitrage opportunities in multi-asset derivatives markets
Abstract
We are interested in the existence of equivalent martingale measures and the detection of arbitrage opportunities in markets where several multi-asset derivatives are traded simultaneously. More specifically, we consider a financial market with multiple traded assets whose marginal risk-neutral distributions are known, and assume that several derivatives written on these assets are traded simultaneously. In this setting, there is a bijection between the existence of an equivalent martingale measure and the existence of a copula that couples these marginals. Using this bijection and recent results on improved Fréchet-Hoeffding bounds in the presence of additional information on functionals of a copula by Lux and Papapantoleon [18], we can extend the results of Tavin [33] on the detection of arbitrage opportunities to the general multi-dimensional case. More specifically, we derive sufficient conditions for the absence of arbitrage and formulate an optimization problem for the detection of a possible arbitrage opportunity. This problem can be solved efficiently using numerical optimization routines. The most interesting practical outcome is the following: we can construct a financial market where each multi-asset derivative is traded within its own no-arbitrage interval, and yet when considered together an arbitrage opportunity may arise.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2020
- DOI:
- 10.48550/arXiv.2002.06227
- arXiv:
- arXiv:2002.06227
- Bibcode:
- 2020arXiv200206227P
- Keywords:
-
- Quantitative Finance - Pricing of Securities;
- Mathematics - Probability;
- 91G20;
- 62H05;
- 60E15
- E-Print:
- 25 pages, 4 figures. Forthcoming in Dependence Modeling