The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis

Abstract

In the aftermath of the 2007-2008 fi nancial crisis, there has been criticism of mathematics and the mathematical models used by the fi nance industry. We answer these criticisms through a discussion of some of the actuarial models used in the pricing of credit derivatives. As an example, we focus in particular on the Gaussian copula model and its drawbacks. To put this discussion into its proper context, we give a synopsis of the fi nancial crisis and a brief introduction to some of the common credit derivatives and highlight the diffi culties in valuing some of them.We also take a closer look at the risk management issues in part of the insurance industry that came to light during the fi nancial crisis. As a backdrop to this, we recount the events that took place at American International Group during the fi nancial crisis. Finally, through our paper we hope to bring to the attention of a broad actuarial readership some "lessons (to be) learned" or "events not to be forgotten".

Taming Uncertainty: The Limits to Quantification

“…It has been argued that the crisis revealed an intellectual failure of a monocultural economics and modelling, which focused exclusively on risk, ignoring epistemological and ontological uncertainties (Bronk, 2011). The use of Gaussian copulas in credit risk management is an instructive example (Donnelly and Embrechts, 2010): the emphasis on calculating default probability of a credit derivative like a CDO (risk) came at the cost of using models that were too simple, internally inconsistent, and did not capture tail dependencies appropriately (epistemological uncertainty). Such disregard of uncertainty was not because of naivety on behalf of modellers, who were perfectly aware of the limitations of the Gaussian copula model.…”

Copula-based multivariate input modeling

“…The limitation of this multivariate copula in representing positive tail dependence becomes apparent in modeling investor's default risk [75,76]. For further discussion on the limitations of the multivariate normal copula, we refer the reader to Lipton and Rennie [77], Donnelly and Embrechts [78] and Brigo et al [79].…”

Univariate conditioning of vine copulas

“…In all three cases, we shrink the neighbourhoods towards respectively the vertex, the face or the union of faces, and we study the limiting properties of copulas (compare [25][26][27]8] for the first approach, [28,29,13,21,37] for the second one, [4,5,33,34] for both first and second and [32,36,39] for the first and third one).…”