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"Credit Management Mathematical models"
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Credit risk
Modelling credit risk accurately is central to the practice of mathematical finance. This volume of the Mastering Mathematical Finance series offers a comprehensive and accessible introduction to the subject tailored specially for master's students. The book focuses on the two mainstream modelling approaches to credit risk, namely structural models and reduced form models, and on pricing selected credit risk derivatives. Balancing rigorous theory with real-world examples from the post-credit crisis financial markets, it takes readers through a natural development of mathematical ideas and financial intuition. Students, practitioners and researchers alike will benefit from the compact presentation and detailed worked examples, exercises and solutions.
Book
Review and Implementation of Credit Risk Models of the Financial Sector Assessment Program (FSAP)
The paper presents the basic Credit Risk+ model, and proposes some modifications. This model could be useful in the stress-testing financial sector assessments process as a benchmark for credit risk evaluations. First, we present the setting and basic definitions common to all the model specifications used in this paper. Then, we proceed from the simplest model based on Bernoulli-distributed default events and known default probabilities to the fully-fledged Credit Risk+ implementation. The latter is based on the Poisson approximation and uncertain default probabilities determined by mutually independent risk factors. As an extension we present a Credit Risk+ specification with correlated risk factors as in Giese (2003). Finally, we illustrate the characteristics and the results obtained from the different models using a specific portfolio of obligors.
eBook
Recent Advances in Credit Risk Modeling
As is well known, most models of credit risk have failed to measure the credit risks in the context of the global financial crisis. In this context, financial industry representatives, regulators and academics worldwide have given new impetus to efforts to improve credit risk modeling for countries, corporations, financial institutions, and financial instruments. The paper summarizes some of the recent advances in this regard. It considers modifications of structural models, including of the classical Merton model, and efforts to reconcile the structural and the reduced-form models. It also discusses the reassessment of the default correlations using copulas, the pricing of credit index options, and the determination of the prices of distressed debt and estimation of recovery values.
eBook
Semi-Markov migration models for credit risk
Credit risk is one of the most important contemporary problems for banks and insurance companies. Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with substantial economic, social and financial tools, building stochastic models is nevertheless necessary to complete this descriptive orientation. This book presents a complete presentation of such a category of models using homogeneous and non-homogeneous semi-Markov processes developed by the authors in several recent papers.
Book
Counterparty Credit Risk, Collateral and Funding
\"The book's content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book however also looks at quite practical problems, linking particular models to particular 'concrete' financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity. The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price counterparty credit and funding risk, to develop a 'feel' for applying sophisticated mathematics and stochastic calculus to solve practical problems. The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with. The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation. Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered\"--provided by publisher.
eBook
Feature selection strategies: a comparative analysis of SHAP-value and importance-based methods
In the context of high-dimensional credit card fraud data, researchers and practitioners commonly utilize feature selection techniques to enhance the performance of fraud detection models. This study presents a comparison in model performance using the most important features selected by SHAP (SHapley Additive exPlanations) values and the model’s built-in feature importance list. Both methods rank features and choose the most significant ones for model assessment. To evaluate the effectiveness of these feature selection techniques, classification models are built using five classifiers: XGBoost, Decision Tree, CatBoost, Extremely Randomized Trees, and Random Forest. The Area under the Precision-Recall Curve (AUPRC) serves as the evaluation metric. All experiments are executed on the Kaggle Credit Card Fraud Detection Dataset. The experimental outcomes and statistical tests indicate that feature selection methods based on importance values outperform those based on SHAP values across classifiers and various feature subset sizes. For models trained on larger datasets, it is recommended to use the model’s built-in feature importance list as the primary feature selection method over SHAP. This suggestion is based on the rationale that computing SHAP feature importance is a distinct activity, while models naturally provide built-in feature importance as part of the training process, requiring no additional effort. Consequently, opting for the model’s built-in feature importance list can offer a more efficient and practical approach for larger datasets and more intricate models.
Journal Article
OBSERVATION-DRIVEN MIXED-MEASUREMENT DYNAMIC FACTOR MODELS WITH AN APPLICATION TO CREDIT RISK
We propose an observation-driven dynamic factor model for mixed-measurement and mixed-frequency panel data. Time series observations may come from a range of families of distributions, be observed at different frequencies, have missing observations, and exhibit common dynamics and cross-sectional dependence due to shared dynamic latent factors. A feature of our model is that the likelihood function is known in closed form. This enables parameter estimation using standard maximum likelihood methods. We adopt the new framework for signal extraction and forecasting of macro, credit, and loss given default risk conditions for U.S. Moody's-rated firms from January 1982 to March 2010.
Journal Article