A Conditional Equity Risk Model For Regulatory Assessment

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.