The recent crises have emphasized how crucially important it is for financial companies to assess in a sound way various types of risks including credit, liquidity, equity or interest rate risk.
The current prudential regulations (Basel III, Solvency 2) explicitly require that mathematical models be used for evaluating most of these risks, for instance for the evolution of assets or interest rates. However, any model is a simplification of reality: the very fact of using a model-based procedure for risk computation entails a new type of risk, often called model risk: typically, the parameters may be wrongly estimated, or the model itself may be a bad approximation, at least under certain circumstances (for instance in case of a crisis),… Provisions computed from models should then be considered with caution. Even when the model is essentially correct, the tools that are used to evaluate, for instance, prudential amounts of own funds are themselves prone to performative effects: as an example, turning from a calibration based on Value at Risk to one based on Expected Shorfall entails consequences which are not precisely enough assessed.
Our work builds on two aspects:
- propose realistic models for asset movements. Such models are typically not semimartingales, which means that specific tools must be developped in order to use them in financial engineering;
- measure the performative effects of economical policies and prudential regulations, and conduct counterfactual analyses, based in particular on causality theory.
Selected associated references:
Sylvain Corlay, Joachim Lebovits, Jacques Lévy Véhel. Multifractional Stochastic volatility models. Mathematical Finance, Wiley, 2014, 24 (2), pp.364-402.
Hicham El Mekeddem, Jacques Lévy Véhel. Value at Risk with tempered multistable motions. 30th International French Finance Association Conference, May 2013, Lyon, France. 2013.
Jacques Lévy Véhel. Financial modelling with tempered multistable motions. International Workshop on Statistical modeling, financial data analysis and applications, Nov 2013, Venise, Italy. 2013.
