In this note, we provide a simple example of regulation risk. The idea is that, in certain situations, the very prudential rules (or, rather, some of them) imposed by the regulator in the framework of the Basel II/III Accords or Solvency II directive are themselves the source of a systemic risk. The instance of regulation risk that we bring to light in this work can be summarised as follows: wrongly assuming that prices evolve in a continuous fashion when they may in fact display large negative jumps, and trying to minimise Value at Risk (VaR) under a constraint of minimal volume of activity leads in effect to behaviours that will maximise VaR. Although much stylised, our analysis highlights some pitfalls of model-based regulation.

A class of continuous-time models is developed for modelling data with heavy tails and long-range dependence. These models are based on the Green function solutions of fractional differential equations driven by Lévy noise. Some exact results on the second- and higher-order characteristics of the equations are obtained. Applications to stochastic volatility of asset prices and macroeconomics are provided.