Pricing Loans Using Default Probabilities STUART M. TURNBULL * 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 method- ologies 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 incorpo- rate 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). 1. Introduction What is a reasonable value for a loan? This is a question that must be addressed at origination. If a loan is priced to reflect relationship considera- tions, the determination of a reasonable price is still necessary if transfer pricing is used at the bank originating the loan. It is a question that needs to be addressed if banks are required to mark-to-market their loan portfolios for risk management purposes. For many obligors, especially below invest- ment grade, and for private firm there is no secondary market for their loans, so new loans cannot be readily ‘bench marked’. Large firms will often have debt ratings from one or more of the recognized rating agencies. For the majority of small and private firms, banks must rely on their own internal rate methodology to produce obligor and facility specific ratings. 1 For firms with traded equity and debt securities, estimates of the term * Lehman Brothers Inc., 745 Seventh Avenue, 6th Floor, New York, NY 10019, stuart.turnbull@lehman.com. The views expressed in this paper are those of the author and do not necessarily reflect the position of Lehman Brothers Inc. 1 An obligor rating provides information about the likelihood of the obligor defaulting over some horizon. A facility rating takes into account the expected loss for the particular facility in the event of default by the obligor. # Banca Monte dei Paschi di Siena SpA, 2003. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. Economic Notes by Banca Monte dei Paschi di Siena SpA, vol. 32, no. 2-2003, pp. 197–217