Pricing Loans Using Default Probabilities

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Abstract

This paper examines the pricing of loans using the term structure of the probability of default over the life of the loan. We describe two methodologies for pricing loans. The first methodology uses the term structure of credit spreads to price a loan, after adjusting for the difference in recovery rates between bonds and loans. In loan origination, it is common practice to estimate the probability of default for a loan over a specified time horizon and the loss given default. The second methodology shows how to incorporate this information into the arbitrage free pricing of a loan. We also show how to derive an estimate of the credit spread due to liquidity risk. For both methodologies, we show how to calculate a break–even credit spread, taking into account the fee structure of a loan and the costs associated with the term structure of marginal economic capital. The break–even spread is the minimum spread for the loan to be EVA neutral in a multi–period setting.

(J.E.L.: G12, G33).

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