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Time-Consistent Evaluation of Credit Risk with Contagion

Author

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  • Ketelbuters, John John

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

A time-consistent evaluation is a dynamic pricing method according to which a risk that will be almost surely cheaper than another one at a future date should already be cheaper today. Common actuarial pricing approaches are usually not time-consistent. Pelsser and Ghalehjooghi (2016) derived time-consistent valuation principles from time-inconsistent ones. The aim of this paper is twofold. Firstly, we propose a model for credit insurance portfolios taking into account the contagion risk via self-exciting jump processes. Secondly, we extend the approach of Pelsser and Ghalehjooghi to credit insurance in this framework. Starting from classical time-inconsistent actuarial pricing methods, we derive partial integro-differential equations (PIDE) for their time-consistent counterparts. We discuss numerical methods for solving these PIDE and their results. We draw two conclusions from these results. On the one hand, we show that working with time-consistent evaluations in the absence of a risk of contagion does not make a significant difference compared to time-inconsisent evaluations. On the other hand, our results show that the time-consistency of evaluations allows to better take into acount the risk of contagion in credit insurance, if such a risk exists.

Suggested Citation

  • Ketelbuters, John John & Hainaut, Donatien, 2021. "Time-Consistent Evaluation of Credit Risk with Contagion," LIDAM Discussion Papers ISBA 2021004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2021004
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    References listed on IDEAS

    as
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    Keywords

    Credit risk ; Self-exciting processes ; Time-consistency;
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