On pricing risky loans and collateralized fund obligations

Ernst Eberlein, Helyette Geman, Dilip B. Madan

Abstract

ABSTRACT

Loan spreads are analyzed for two types of loans. The first type takes losses at maturity only; the second follows the formulation of collateralized fund obligations, with losses registered over the lifetime of the contract. In both cases, the implementation requires the choice of a process for the underlying asset value and the identification of the parameters. The parameters of the process are inferred from the option volatility surface by treating equity options as compound options with equity itself being viewed as an option on the asset value with a strike set at the debt level following Merton. Using data on the stock of General Motors during 2002-3, we show that the use of spectrally negative Lévy processes is capable of delivering realistic spreads without inflating debt levels, deflating debt maturities or deviating from the estimated probability laws.