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A Framework for Pricing and Risk Management of Loans with Embedded Options

by Bernd Engelmann of Quantsolutions

May 30, 2012

Abstract: A framework for the pricing and risk management of retail loans with embedded options is developed. For retail customers there is in general no market information related to their ability to pay (bond or CDS spreads) available. In this case a bank has to rely on statistical data to judge the credit quality of a debtor. For the pricing of a loan with embedded options like prepayment rights in this context, a model is proposed that combines a stochastic interest rate model with statistical information like a term structure of default probabilities or a one-year transition matrix and recovery rate estimations. By defining a suitable notion of risk, it is shown how the concepts of credit risk management can be transferred to this framework. It turns out that this modeling approach unifies the theories of derivatives pricing and credit risk modeling in the sense that derivatives pricing theory measures the costs for hedging optional components in loans while credit risk modeling measures the risk that these hedging costs turn out to be inadequate. This risk does depend not only on the single loan’s risk characteristics but also on the dependence structure and the granularity of the total loan portfolio.

JEL Classification: G12, G13.

Keywords: Loan Pricing, Prepayment Options, Interest Rate Derivatives Pricing, Credit Risk Modeling, Risk Management of Loans.

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