A Framework for Pricing and Risk Management of Loans with Embedded Options (Engelmann B.)

Bank Lending Investment Banking Risk-taking and Risk Management

Abstract A framework for the pricing and risk management of retail loans with embedded options is developed. For retail costumers 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. The pricing of a loan in this context can be done by combining 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. In this framework embedded options that are typically included in loan contracts like prepayment rights can be valued using a tree algorithm. The pricing model combines risk-neutral probabilities with real-world probabilities which makes a perfect replication of contingent claims in this framework in general not possible. By defining a suitable notion of risk, we show how the concepts of credit risk measurement can be transferred to this framework. We find 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.
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Libref/ Engelmann B. (2011) "A Framework for Pricing and Risk Management of Loans with Embedded Options", pp. 1 - 23
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