Default Greeks Under an Objective Probability Measure
by Tom E. S. Farmen of the Norwegian School of Science and Technology Management,
July 9, 2004
Abstract: Correct estimation of default probabilities are becoming an increasingly important element of financial institution's measurement and management of credit exposures. Growing stress on proper rating systems driven by regulators also motivates for a better understanding of these issues. This article focus on the use of option based models in credit risk management. We present a framework to derive an objective probability of default directly, and its comparative statics (or socalled "Greeks") based on the BlackScholesMerton model. We then demonstrate the use of these concepts with several numerical examples. In special, we elucidate the difference between risk neutral and objective (or real) probabilities of default and its implication for credit risk management and capital allocation strategies. Effort should though be put on the transformation of the risk measures as wrong estimates of expected default frequencies could lead to a situation where to little capital is allocated to less risky project and as a consequence destroy shareholder value.
Keywords: Default probability, Option theory, Risk Management.