Default Risk and its Greeks under an Objective Probability Measure

Abstract

This paper investigates default probabilities and their comparative statics (default Greeks) in the Black and Scholes, Merton framework, using the objective or real probability measure. First we show how a risk neutral default probability can be transformed into an objective probability. The difference between the two is analysed numerically. Risk neutral probabilities appear to be accurate only when they are not useful, and to be too inaccurate for normal credit risk management. Several sensitivity measures for default probability are derived. Default probability is shown to decrease with the value and the drift of assets and to increase with asset volatility, while debt maturity has an ambigous effect. The approach in this paper facilitates the use of the BSM framework for risk management purposes and provides a theoretical basis for empirical analyses of default probability.