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A CONDITIONAL EQUITY RISK MODEL FOR REGULATORY ASSESSMENT

Published online by Cambridge University Press:  23 November 2018

A. Floryszczak ,
J. Lévy Véhel  and
M. Majri
A. Floryszczak
Affiliation:
Groupe SMA, 8 rue Louis Armand, CS 71201, 75738 Paris Cedex 15, France E-Mail: anthony_floryszczak@groupe-sma.fr
J. Lévy Véhel*
Affiliation:
Anja team, INRIA & Université de Nantes, 2 rue de la Houssiniere, BP 92208, 44322 Nantes cedex 3, France E-Mails: jacques.levy-vehel@inria.fr, jacques.levy.vehel@caselawanalytics.com
M. Majri
Affiliation:
Groupe SMA, 8 rue Louis Armand, CS 71201, 75738 Paris Cedex 15, France E-Mail: mohamed_majri@groupe-sma.fr
*
E-Mails: jacques.levy-vehel@inria.fr, jacques.levy.vehel@caselawanalytics.com
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Abstract

We define and study in this work a simple model designed for managing long-term market risk of financial institutions with long-term commitments. It allows the assessment of solvency capital requirements and the allocation of risk budgets. This model allows one to avoid over-assessment of solvency capital requirements specifically after market disruptions. It relies on a dampener component in charge of refining risk assessment after market failures. Rather than aiming at a realistic and thus complex description of equity prices movements, this model concentrates on minimal features enabling accurate computation of capital requirements. It is defined both in a discrete and continuous fashion. In the latter case, we prove the existence, uniqueness and stability of the solution of the stochastic functional differential equation that specifies the model. One difficulty is that the proposed underlying stochastic process has neither stationary nor independent increments. We are however able to perform statistical analyses in view of its validation. Numerical experiments show that our model outperforms more elaborate ones of common use as far as medium-term (between 6 months and 5 years) risk assessment is concerned.

Keywords

Risk budget allocationsolvency capital requirementvalue-at-riskpro-cyclicalitystochastic functional differential equationnon-stationary processmarket risk allocation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 1 , January 2019 , pp. 217 - 242
Copyright
Copyright © Astin Bulletin 2018 

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