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Economic Capital. Loss Identification Point. Leverage Ratio. Point In Time. Liquidity Coverage Ratio. Pre—Provision Net Revenue. Low Default Portfolio. Risk—Adjustment Performance Measurement. Loss Given Default.

Risk—Adjusted Return on Capital. Replacement Cost. Liquidity Valuation Adjustment. Risk Not In Value—at—Risk. Monte Carlo. Return on Risk Weighted Assets. Margin Valuation Adjustment. Regulatory Technical Standards. Net Interest Income SA. Standardised Approach NIM. Systematically Important Financial Institu-. Net Present Value.

Netting Set SMA. Standardized Measurement Approach M. Maturity SREP. Supervisory Review and Evaluation Process. Recovery Rate. Stressed Value—at—Risk. Through the Cycle. Office of the Comptroller of the Currency. Unexpected Loss. Probability of Default.

Value Creation. Profit and Loss.

Wrong—Way Risk. Potential Future Exposure. X—Valuation Adjustments. 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 dissertation 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 Riemannian 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 alternative, 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 the 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.

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The results of this thesis are addressed to both practitioners and scientists. With regard to the academic society, this thesis should contribute to the scientific analysis of the complex problem of model risk and introduce differential geometry and information theory into financial modelling.

On the other hand, the 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, model limits, weaknesses and gaps can be assessed quantitatively and so managed constructively and proportionally. The model risk stemming from usage of a model can be communicated. As such, a strong model risk management with objective assessment of model risk can act as a competitive advantage for an institution..

Los resultados de esta tesis pueden ser de utilidad tanto a profesionales como a investigadores. Os resultados desta tese poden ser de utilidade tanto a profesionais como a investigadores. The current practice of finance heavily relies on a high level of sophistication, quantitative analysis and models to assist with decision making, thereby improving efficiency, enabling the ability to better understand, manage and oversee various risks as well as the capability to synthesize complex issues and centralize modelling infrastructure.

As a consequence of that very sophistication and complexity, risks have emerged that are unpredictable, global and difficult to hedge and measure. Model risk is an eminent example of such risks since it arises as the result of technological progress, innovations or attempt at managing other risks in a more effective way; it is difficult to manage and account for; it is hard to measure and often difficult to comprehend.

The latter aspect implies not only that no model can be judged out of context, as its performance may completely differ depending on what asset or portfolio it is applied to, but besides, its particular usage, be it capital, pricing or hedging, will determine the ultimate financial impact of any inaccuracy or error. Model error encompasses phenomena such as simplifications of or approximations to reality, inadequate data, incorrect or missing assumptions, incorrect design process, and measurement or estimation error, among many other. On the other hand, model misuse includes applying models outside the use for which they were intended.

First, the risk related to the underestimation of own funds requirements by regulatory approved models e.

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Model risk, in a broader business and regulatory context, incorporates the exposure from making poor decisions based on inaccurate model analyses or forecasts and, in either context, can arise from any model in active use [85]. Decisions based on incorrect or misleading model outputs may lead to financial losses to the bank and its customers, inferior business decisions or ultimately reputation damage. Model risk may be particularly Future changes and evolution of model risk are to be expected in the mid term both by regulatory demands and institutions best practices.

Any source of model risk of an individual model may in addition be propagated, cumulated or amplified as model outputs are used both directly and as inputs into other models.

In other words, a model may provide input to, or use the output from, other models. In such a chain of models, understanding the interconnections upstream and downstream dependencies to other models between different models and clear identification of potential sources of model risk are crucial and an important mitigant of model risk.

Financial institutions use a wide range of models designed to meet regulatory requirements and to achieve business needs that are subject to governance and model risk management see Figure 1. Quantitative analysis and models are central to the operation within and across financial institutions; they are employed for a variety of purposes including exposure calculations, trading e.

They are integral to financial reporting e. Furthermore, more models are being developed in order to comply with 1 Loss. Segmentation approaches can range from expert judgement, statistical methods and data mining techniques, including logistic and linear regression, decision trees to advanced cluster modelling, factor segmentation, machine learning or neural networks. An appropriate segmentation is fundamental to achieving a thorough identification of risks. Each of these metrics is quantified using a variety of stochastic, market comparative and statistical approaches, and in some instances by deriving volatility from historical or implied means.

For instance, modelling LGD requires consideration of the seniority of the assets, the industry, the issuer, historical recoveries and trends, and an evaluation of the current climate, as well as the assets and liabilities of the issuer; estimation of EAD involves the modelling of the investment value that in turn depends on the evolution of the market factors upon which the value of the investment depends.. Figure 1: Examples of models subject to governance and model risk management of a large global bank..

Models range from simple formulae to complex models that require simulations and optimization routines, some are internally developed and some may be sourced through consultants and vendors. Models may run standalone on desktops or deployed onto serves. In general, financial models are simplifying mappings of reality to serve a specific purpose aimed at applying mathematical, financial and economic theories to available data.

They deliberately focus on specific aspects of the reality and degrade or ignore the rest, certainly, within the level of precision required by the specific usage and application. Most of the models are quantitative approaches, including the complex manipulations of expert judgements, or systems that apply mathematical techniques and assumptions to process input information— often containing distributional information— into quantitative estimates that drive decisions.

Input data may be of economic, financial or statistical nature, partially or entirely qualitative or based on expert judgement, but in all cases, the model outputs are quantitative and subject to interpretation. For instance, econometric models specify a probability measure in order to capture the historical evolution of market price, pricing models use a risk—neutral probability measure to specify a pricing rule, or risk models aim at estimating the probability distribution of future losses.

The risk of using such models comes, among many others, from the potential failure in devising a realistic and plausible representation of the factors influencing the value of security, the inaccuracy in the estimation of the relevant probability distribution that translates into smaller or larger losses depending on the way such distribution is used and the subsequent incorrect decisions this may entail. For example, a credit or market risk measure may be used for computing economic and regulatory capital, pricing, provisioning, assessing the eligibility of a transaction or a counterpart, for establishing a portfolio, counterpart or other limits, among others.

Subsequent imprecision in each of these estimates, in turn, may have financial consequences and so, financial models require a certain fundamental prudence in their interpretation and usage.