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Multi-period Factor Model of a Loan Portfolio

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    0480803 - ÚTIA 2018 CZ eng V - Research Report
    Šmíd, Martin - Dufek, J.
    Multi-period Factor Model of a Loan Portfolio.
    Praha: ÚTIA AV ČR v.v.i, 2017. 45 s. Research Report, 2363.
    Keywords : Credit Risk * Structural Factor Models * Loan Portfolio Management
    http://library.utia.cas.cz/separaty/2017/E/smid-0480803.pdf

    We construct a general dynamic model of losses of a large loan portfolio, secured by collaterals. In the model, the wealth of a debtor and the price of the corresponding collateral depend each on two factors: a common one, having a general distribution, and an individual one, following an AR(1) process. The default of a loan happens if the wealth stops to be su cient for repaying the loan. We show that the mapping transforming the common factors into the probability of default (PD) and the loss given default (LGD) is one-to-one twice continuously differentiable. As the transformation is not analytically tractable, we propose a numerical technique for its computation and demonstrate its accuracy by a numerical study.
    We show that the results given by our multi-period model may differ signi cantly from
    those resulting from single-period models, and demonstrate that our model naturally replicates
    the empirically observed decrease of PDs within a portfolio in time. In addition, we give a formula for the overall loss of the portfolio and, as an example of its application, we formulate a simple optimal scoring decision problem and discuss its solution.
    Permanent Link: http://hdl.handle.net/11104/0276487

     
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