On the Mechanism of CDOs behind the Current Financial Crisis and Mathematical Modeling with Levy Distributions

Abstract

This paper aims to reveal the mechanism of Collateralized Debt Obligations (CDOs) and how CDOs extend the current global financial crisis. We first introduce the concept of CDOs and give a brief account of the de-velopment of CDOs. We then explicate the mechanism of CDOs within a concrete example with mortgage deals and we outline the evolution of the current financial crisis. Based on our overview of pricing CDOs in various existing random models, we propose an idea of modeling the random phenomenon with the feature of heavy tail dependence for possible implements towards a new random modeling for CDOs

A detection algorithm for the first jump time in sample trajectories of jump-diffusions driven byα-stable white noise

“…The self-similarity property of stable distributions has drawn more and more attention from both theoretical and practical view points, i.e (Campbell, Lo, and MacKinlay, 1997;Mandelbrot, 1960) and (Zolotarev, 1986;Leland, Taqqu, Willinger, and Wilson, 1993;Shlesinger, Zaslavsky, and Frisch, 1995). We refer the reader to (Du, Wu, and Yang, 2010) for discussions of utilising α-stable distributions to model the mechanism of Collateralised Debt Obligations (CDOs) in mathematical finance.…”

Critical link of self-similarity and visualisation for jump-diffusions driven by $α$-stable noise

“…The self-similarity property of stable distributions has drawn more and more attention from both theoretical and practical view points, i.e [2,14] and [19,10,18]. We refer the reader to [6] for discussions of utilising α-stable distributions to model the mechanism of Collateralised Debt Obligations (CDOs) in mathematical finance.…”

Valuation of synthetic CDOs with affine jump-diffusion processes involving Lévy stable distributions

“…In [23], we have proposed to incorporate Lévy stable distributions in an intensity based model to price CDOs. In the intensity based model, default is defined as the first jump of a pure jump process, and it is assumed that the jump process has an intensity process.…”