论文标题
在多资产衍生品市场中检测套利机会
Detection of arbitrage opportunities in multi-asset derivatives markets
论文作者
论文摘要
我们对同等的Martingale措施以及在同时交易多个多资产衍生品的市场中发现套利机会的发现感兴趣。更具体地说，我们考虑了一个具有多个交易资产的金融市场，其边际风险中性分配已知，并假设同时交易了这些资产上的几个衍生品。在这种情况下，在等效的Martingale度量的存在与结束这些边缘的副群体的存在之间存在两者。在存在有关lux和papapantoleon [18]的其他信息的其他信息的情况下，使用这种两次培养和最新结果，对copula的其他信息进行了改进的结果，我们可以将塔文[33]的结果扩展到套利机会，以发现套利机会的结果。更具体地说，我们为缺乏套利而得出了足够的条件，并为检测可能的套利机会提出了优化问题。可以使用数值优化例程有效地解决此问题。最有趣的实际结果是：我们可以构建一个金融市场，在该金融市场中，每个多资产阶级衍生产品都在其自身的无度上间隔内交易，但是当考虑在一起时，可能会出现套利机会。
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.
