从货币汇率报价到字符串和膜世界场景
From the currency rate quotations onto strings and brane world scenarios
摘要：
在本文中，我们数值研究了实际汇率动态的弦状拓扑的投影。我们的方法受到当代弦理论运动的启发。通过边界条件、特征长度、实值和信息重分布方法定义了数据串映射。作为一个实际问题，该图代表了去趋势和数据标准化过程。我们引入了映射到1-端点和2-端点开弦，满足Dirichlet和Neumann边界条件。讨论了额外维数的选择、对称性、对偶性以及部分紧化的方法等问题。随后，我们将转向更高维度和更复杂的对象。2D膜被建议，其中包括买卖价差。通过价差的极化被认为是承认分析套利机会的市场上的交易成本考虑。旋转弦的模型，自然产生角动量的计算是适合于跟踪几个货币对。系统的方式，它允许一个建议更结构化的地图适合于同时研究的几个货币对进行了分析，通过Gâteaux广义微分。通过比较弦映射和膜映射的平均统计特性，研究了弦映射和膜映射对测试数据的影响。该研究揭示了拓扑结构之间的显著差异。我们回顾的特征字符串长度，平均波动和字符串内统计的属性的依赖。研究弦振幅与波动率的耦合。
英文摘要：
In the paper, we study numerically the projections of the real exchange rate dynamics onto the string-like topology. Our approach is inspired by the contemporary movements in the string theory. The string map of data is defined here by the boundary conditions, characteristic length, real valued and the method of redistribution of information. As a practical matter, this map represents the detrending and data standardization procedure. We introduced maps onto 1-end-point and 2-end-point open strings that satisfy the Dirichlet and Neumann boundary conditions. The questions of the choice of extra-dimensions, symmetries, duality and ways to the partial compactification are discussed. Subsequently, we pass to higher dimensional and more complex objects. The 2D-Brane was suggested which incorporated bid-ask spreads. Polarization by the spread was considered which admitted analyzing arbitrage opportunities on the market where transaction costs are taken into account. The model of the rotating string which naturally yields calculation of angular momentum is suitable for tracking of several currency pairs. The systematic way which allows one suggest more structured maps suitable for a simultaneous study of several currency pairs was analyzed by means of the Gâteaux generalized differential calculus. The effect of the string and brane maps on test data was studied by comparing their mean statistical characteristics. The study revealed notable differences between topologies. We review the dependence on the characteristic string length, mean fluctuations and properties of the intra-string statistics. The study explores the coupling of the string amplitude and volatility.
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