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Time-consistent evaluation of credit risk with contagion

Author

Listed:
  • 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 PIDEs and their results. We draw two conclusions from these results. On the one hand, we show that time-consistent evaluations tend to give higher prices, compared to time-inconsistent evaluations. On the other hand, our results show that the time-consistency of evaluations allows to better take into account the risk of contagion in credit insurance, if such a risk exists. Finally, we propose a method to calibrate our model and use it in practice.

Suggested Citation

  • Ketelbuters, John-John & Hainaut, Donatien, 2021. "Time-consistent evaluation of credit risk with contagion," LIDAM Reprints ISBA 2021045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2021045
    DOI: https://doi.org/10.1016/j.cam.2021.113848
    Note: In: Journal of Computational and Applied Mathematics, 2022, vol. 403, 113848
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