Affiliations: [a] Department of Mathematical Sciences, Clemson University, Clemson, SC, USA | [b] Senior Managing Director, Guggenheim Partners, New York, NY, USA | [c] Research Affiliate, Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
Abstract: A large portion of Macroeconomic and Financial research is built upon classical applications of Linear Algebra (such as regression analysis) and Stochastic Calculus (such as valuation models). As a result, most Macroeconomic and Financial research has inherited a focus on geometric locations rather than logical relations. Ideally, Econometric models could be complemented with Topological and Graph-Theoretical tools that recognize the hierarchy and relationships between system constituents. Stochastic Flow Diagrams (SFDs) are topological representations of complex dynamic systems. We construct a network of financial instruments and show how SFDs allow researchers to monitor the flow of capital across the financial system. Because our approach is dynamic, it models how and for how long a financial shock propagates through the system. Practical applications include stress-testing of investment portfolios under user-defined scenarios, and the discovery of Macro trading opportunities. SFDs add Topology to the Econometric toolkit used by Macroeconomists, and may enlighten perennial controversies, such as the one involving Keynesians and Austrian-school economists. Our findings have important implications for regulators, market designers and Macro investors.
Keywords: 90C35, 90B15, 05C21, 62P05, 37M10
Keywords: Time series, graph theory, topology, financial flows, macro trading
