Mathematics and Financial Economics

, Volume 12, Issue 4, pp 541–559 | Cite as

Sensitivity analysis for marked Hawkes processes: application to CLO pricing

  • Guillaume Bernis
  • Kaouther Salhi
  • Simone ScottiEmail author


This paper deals with a model for pricing Collateralized Loan Obligations, where the underlying credit risk is driven by a marked Hawkes process, involving both clustering effects on defaults and random recovery rates. We provide a sensitivity analysis of the CLO price with respect to the parameters of the Hawkes process using a change of probability and a variational approach. We also provide a simplified version of the model where the intensity of the Hawkes process is taken as the instantaneous default rate. In this setting, we give a moment-based formula for the expected survival probability.


Change of probability Credit derivatives Poisson processes Hawkes processes Self-exciting structure Sensitivity analysis 

Mathematics Subject Classification

C02 C63 



The opinions and views expressed in this document are those of the authors and do not necessarily reflect those of Natixis Asset Management. The authors wish to thank Nicolas Bouleau for fruitful discussions on the sensitivity analysis for Poisson processes. The research of the third author is supported by Institut Europlace de Finance within the project “Clusters and Information Flow: Modeling, Analysis and Implications”.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Ostrum Asset ManagementParisFrance
  2. 2.LPMA - Université Paris 7ParisFrance

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