A Top-down Model for Cash CLO

We propose a top-down model for cash CLO. This model can consistently price cash CLO tranches both within the same deal and across different deals. Meaningful risk measures for cash CLO tranches can also be defined and computed. This method is self-consistent, easy to implement and computationally efficient. It has the potential to bring the much needed pricing transparency to the cash CLO markets; and it could also greatly improve the risk management of cash instruments.Comment: 14 pages, 12 figure

European Stock Market Contagion during Sovereign Debt Crisis and the Effects of Macroeconomic Announcements on the Correlations of Gold,Dollar and Stock Returns

The first part of this dissertation examines the presence of the financial contagion across European stock markets with respect to the Greece sovereign debt crisis by estimating the time-varying conditional correlations of stock returns between Greece and other European countries over 2001 to 2012. We find that the correlations vary over time and reach the peaks in the late 2008 during theU.S.subprime crisis, and in the beginning of 2010 of the height of European debt crisis. Further, the correlations between stock index returns of Greece and Spain, France, Ireland, Netherlands are significantly increased by Greek sovereign credit rating downgrade announcements. The second part of this dissertation examines the correlations of gold, dollar and U.S. stock returns over 2001 to 2012 using ADCC-GARCH model. The conditional correlations of gold-dollar returns are negative during all sub-sample periods and significantly increase in magnitude during both subprime crisis and sovereign debt crisis. The conditional correlations of gold-stock returns are positive on average over time. However, gold-stock correlation falls below zero during subprime crisis and sovereign debt crisis. Gold-stock correlation is significantly negatively affected by positive CPI announcements. And gold-dollar correlation is significantly negatively affected by negative GDP announcements and positive unemployment announcements. The effects of macroeconomic announcements are stronger during economic recessions

Fractal dimensions for deterministic and random substitution graph systems

Based on [19], this paper aims to introduce fractal geometry into graph theory. To do so, we construct and study the fractal-like graphs by the method of substitution, called deterministic or random substitution graph systems. Though the idea of substitution is common in terms of fractal geometry and dynamical systems, the analysis of fractals regarding graph theory remains an immature field. By investigating the properties of the systems such as diameter and distal, we obtain two main results in this paper. The first of which, for deterministic substitution graph systems, the box-counting dimension and Hausdorff dimension are analytically coincidental by explicit formulae. Another finding is, for random substitution graph systems, that we prove almost surely every graph limit has the same box-counting and Hausdorff dimensions numerically by their Lyapunov exponents. Through these conclusions, the substitution graph system will potentially lead to new research directions

On the scale-freeness of random colored substitution networks

Extending previous results in the literature, random colored substitution networks are introduced and are proved to be scale-free under natural conditions. Furthermore, the asymptotic node degrees, arc cardinalities and node cardinalities for these networks are derived. These results are achieved by proving stronger results regarding stochastic substitution processes, which form a new stochastic model that is here introduced.Comment: The following article has been submitted to Chaos. After it is published, it will be found at https://aip.scitation.org/journal/ch