New approaches to quantification and management of model risk

Abstract

The present contribution facuses on the problem of an objective assessment of model risk in practice. In spite of the awareness of model risk significance and the regulatory requirements for its proper management, there are no globally defined industry or market standards on its exact definition and quantification. The main objective of this díssertation is to address this issue by designing a general framework for the quantification of model risk, taking into account both internal policies and regulatory issues, applicable to most modelling techniques currently under usage in financial institutions. We address the quantification of model risk through differential geometry and information theory, by the calculation of the norm of an appropriate function defined on a Riemannian manifold endowed with a proper Riemanruan metric. Pulling back the model manifold structure, we further introduce a consistent Riemannian structure on the sample space that allows us to investigate and quantify model risk by working merely with the samples. This offers primarily practical advantages such as a computational altemative, easier application of business intuition, and easier way to assign the uncertainty in the data. Additionally, one gains the insight on model risk from both the data and the model perspective. The proposed framework has the following properties: provides a systematic and repeatable procedure to identify and assess model risk, allows for the quantification of risk materiality, incorporates most of tbe relevant aspects of model risk management, such as usage, model performance, mathematical foundations, data and model calibration, and facilitate establishing a control environment around the use of models. The theoretical analysis is completed with practical applications to a credit risk model used for capital calculation, currently employed in the financial industry. As another application of the proposed framework, we emphasize the importance of the geometry of the underlying space in financial models and apply curvature not only to control and reduce the inherent model risk but also to improve the overall performance of a model. These ideas are exemplified through the P&L explanation of digital options with the Black-Scholes model and demonstrate the improvement by comparing results under Euclidean and non-Euclidean geometries. The results of this thesis are addressed to botb practitioners and scientists. With regard to the academic society, tlris thesis should contribute to the scientific analysis of tbe complex problem of model risk and introduce differential geometry and infonnation theory into financial modelling. On the other hand, tbe proposed approach gives direct benefits in practice, for the management and the use of models inside financial institutions: The confidence in the model can be quantified, modellimits, weaknesses and gaps can be assessed quantitatively and so managed constructively and proportionally. The model risk sternming from usage of a model can be communicated transparently and consistently to users, managers and regulators, communicating model credibility, setting controls systematically, anrl focusing on morlel management. As such, a strong model risk management with objective assessment of model risk can act as a competitive advantage for an institution.