A Markov random model of interbank dynamics with filtering and adaptive learning techniques

Most of Basel II and III financial regulations are based on data, treated in a statistical mindset. While regulators call for forward-looking risk management, they suggest no time-based modeling approach. In macroeconomic catastrophes modeling, this is a great setback. This paper reports the experimental application of combined forward looking methods, specifically, filtering techniques, like Sequential Monte Carlo, or Interactive Particles systems, with stress testing causal scenarios in systemic context. We first show how Basel II framework and models leave out temporal dynamics in risk management processes in banks. Next, we suggest how to introduce stochastic equations to solves deficiencies of existing, risk non-sensitive, models. The new models are proposed as value-based, time varying, functions of rare catastrophic scenarios allowing arbitrage between risk mitigation decisions. Next, affiliation is established from Stochastic Optimal Control foundations, through Reinforcement Learning and Temporal Differences Learning, to this toy model set of equations. We use this theoretical approach to introduce a prediction process in a Bayesian framework, and to model economic forecast and rationalized control (e.g. by a Central bank). Some parts of this framework also borrow from Hidden Markov Model and the related Bayesian inference techniques that underlie Interactive particle systems filters. As an illustration, we examine the impact of exogenous shocks on a toy model of a banking system in an exposed economy. The system obeys a neokeynesian dynamics, augmented with a Blinder-Bernanke type of money vs. securities arbitrage. The national banks, characterized by their stylized balance sheet reduced to a vector of ratios, have interbank borrowing and lending relationships. This constitutes the mechanism for spreading risks. Propagation is simulated through markov chains of random processes. We observe the consequences of stressed perturbations in 2 directions: •Credit default (counterparty risk) •Liquidity (lack of confidence and lending) risk We show how a model can evolve from a dynamic framework as previously shown, to one that also encompasses adaptive learning (by establishing a common mutual interbank fund at an optimal level as buffer capital). We conclude by showing how Basel II and Basel III regulations on macroprudential systemic risks (liquidity and default) can benefit from this new, exploratory, rather than statistical, approach to Risk Capital.