A Conditional Equity Risk Model for Regulatory Assessment

We define and study in this work a simple model allowing for a prudential valuation of solvency capital requirement while avoiding over-assessment specifically after market disruption. The main idea is to include a dampener component in charge of refining risk assessment after a market failure. Rather than aiming at a realistic, and thus complex, description of equity prices movements, our model concentrates on minimal features enabling accurate computation of regulatory capital requirements. The model 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. We believe that our approach offers an attractive alternative for insurance and reinsurance companies to assess their 1 year equity-risk solvency capital requirement with an internal model and their ORSA capital.