Youngna Choi

Financial Crisis Dynamics: Attempt to Define a Market Instability Indicator

The impact of increasing leverage in the economy produces hyperreaction of market participants to variations of their revenues. If the income of banks decreases, they mass-reduce their lendings; if corporations sales drop, and they cannot adjust their liquidities by further borrowing due to existing debt, then they must immediately reduce their expenses, lay off staff, and cancel investments. This hyperreaction produces a bifurcation mechanism, and eventually a strong dynamical instability in capital markets that is commonly called systemic risk. In this article, we show that this instability can be monitored by measuring the highest eigenvalue of a matrix of elasticities. These elasticities measure the reaction of each sector of the economy to a drop in its revenues from another sector. This highest eigenvalue—the spectral radius—of the elasticity matrix can be used as an early indicator of market instability and potential crisis. Grandmont and subsequent research showed the possibility that the ‘invisible hand’ of markets becomes chaotic, opening the door to uncontrolled swings. Our contribution is to provide an actual way of measuring how close to chaos the market is. Estimating elasticities and actually generating the indicators of instability will be the topic of forthcoming research.

Modeling Contagion in the Eurozone Crisis via Dynamical Systems

We recently (Castellacci and Choi, 2013) formulated a theoretical framework for the modeling of financial instability contagion using the theories of dynamical systems. Here, our main goal is to model the Eurozone financial crisis within that framework. The underlying system comprises many economic agents that belong to several subsystems. In each instantiation of this framework, the hierarchy and nesting of the subsystems is dictated by the nature of the problem at hand. We describe in great detail how a suitable model can be set up for the Eurozone crisis. The dynamical system is defined by the evolution of the wealths of the individual agents and can be estimated by solving a nonlinear programming problem that incorporates features of prospect theory. Contagion is formulated in terms of how the market instability indicators for the different subsystems and the global system behave. We present several scenarios tailored to recent financial developments in the Eurozone and discussed within our model. These all point to the key role played by the elasticity coefficients of the wealth dynamical system. Accordingly, we put forward general recommendations on how regulators or other super-systemic agents may act to prevent and forestall the spreading of financial distress.

Financial Instability Contagion: A Dynamical Systems Approach

We build a multi-agent dynamical system for the global economy to investigate and analyse financial crises. The agents are large aggregates of a subeconomy, and the global economy is a collection of subeconomies. We use well-known theories of dynamical systems to represent a financial crisis as propagation of a negative shock on wealth due the breakage of a financial equilibrium. We first extend the framework of the market instability indicator, an early warning signal defined for a single economy as the spectral radius of the Jacobian matrix of the wealth dynamical system. Then, we formulate a quantitative definition of instability contagion in terms thereof. Finally, we analyse the mechanism of instability contagion for both single and multiple economies. Our contribution is to provide a methodology to quantify and monitor the level of instability in sectors and stages of a structured global economic model and how it may propagate through its components.

Topology of attractors from two-piece expanding maps

In this paper we study the topology of the invariant sets derived from two-piece expanding maps. We classify the conditions under which the invariant sets are topological attractors, and show that the set of attractors is open and dense in the set of invariant sets derived by two-piece expanding maps.

Undergraduate Research: Mathematical Modeling of Mortgages

Abstract In this article, we study financing in the real estate market and show how various types of mortgages can be modeled and analyzed. With only an introductory level of interest theory, finance, and calculus, we model and analyze three types of popular mortgages with real life examples that explain the background and inevitable outcome of the current financial crisis.

Topological dynamics of two-piece eventually expanding maps

In this work we show that two-piece eventually expanding maps have the same topological dynamics as two-piece expanding maps. A two-piece eventually expanding map possesses an invariant set that is either a topological attractor or can be perturbed to become one.