Default Propensity Implicit in Pulled to Par V@r for Bonds

Abstract

Using the pulled to par returns, proposed by [27] for computing historical V@R of bonds, we develop a way of extracting – at any reference date before maturity – implicit default propensities from observed bond quotes. This method is new to the literature and it has the advantage on focusing directly on loss given default. To illustrate the method we present two examples of actual computation with real data – on German and Portuguese bonds. The market data seems to support the proposed method. In the case of a very concrete simple Gaussian model, we establish the connection between our implicit default propensity and the more traditional notions of default probability and recovery given default of a bond.

Keywords: value-at-risk, bonds, default probability, recovery given default

JEL Classification: G29