THE "MAXIMUM ACCEPTABLE CORRELATION" FOR A DEFAULTABLE GUARANTEE

Abstract

In the broader context of the measures decided for restoring confidence in the banking sector, this thesis analyses government guarantees on bank liabilities especially with relation to their financial valuation. The pricing of these government guarantees can be decided in three different ways: the first is “ex lege”, or calculated with a pricing formula determined by regulatory frameworks; the second is “mark to market”, which is determined by the market; the third is “mark to model”, which is the topic of this thesis. The European Commission has indicated the methodology for calculating fees for banks that benefit from such guarantees; it has also asked that they should be in line with what can be considered their “market price” as much as possible. It is precisely this aspect of the Commission’s request (the alignment of the pricing to the market) that is the objective of this study. Indeed, from the market point of view, both the State and the bank that issues the bonds guaranteed, are at risk of failure, and these risks are correlated. In particular, for financial market this defaultable guarantee can be interpreted as defaultable single name Credit Default Swap (CDS). It follows that in our financial valuation analysis the reference defaultable guarantee will be valued under the standard Gaussian copula model (G), which is the benchmark for such credit derivative. The main reason for the widespread use in the industry of the G model is the easy interpretation of its linear correlation parameter. However, as we will show, for some levels of correlation, the model gives incoherent results in terms of guarantee’s value. This causes a reduction on the natural domain of the model’s correlation parameter. In this work we call maximum acceptable correlation the maximum level of the copula’s correlation parameter for which the model works appropriately. In order to provide a model that allows to determine “realistic” results in terms of the guarantees “mark-to-model” value when the standard Gaussian copula model does not work, we suggest a “modified” standard Gaussian copula model, so-called Modified Gaussian model (MG). It is obtained by combining the stan dard Gaussian copula with default time distributions of the parties where the default intensities of the guarantor is appropriately modified by an “adjustment term”. As for calibration purpose of the MG model, we use the “maximum ac ceptable correlation” of the G model to produce MG values of the guarantee contract as close as possible to those of the G model.