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Differential equations --- Classical mechanics. Field theory --- Differential equations, Nonlinear --- Nonlinear mechanics --- Équations différentielles non linéaires. --- Mécanique non linéaire. --- Differential equations, Nonlinear. --- Nonlinear mechanics. --- Mathematical Sciences --- Applied Mathematics --- Complex Analysis --- General and Others --- non-linear phenomena --- computational techniques --- differential equations --- Mechanics, Nonlinear --- Mechanics, Analytic --- Nonlinear differential equations --- Nonlinear theories --- Équations différentielles non linéaires. --- Mécanique non linéaire. --- Chaos Theory. --- Differential Equations. --- Mathematics --- Calculus --- Équations différentielles non linéaires --- Mécanique non linéaire

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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.

Credit -- Management -- Mathematical models. --- Electronic books. -- local. --- Financial services industry -- State supervision. --- Finance --- Business & Economics --- Credit, Debt & Loans --- Credit --- Financial services industry --- Management --- Mathematical models. --- State supervision. --- Services, Financial --- Borrowing --- Service industries --- Money --- Loans --- Banks and Banking --- Econometrics --- Money and Monetary Policy --- Portfolio Choice --- Investment Decisions --- Financial Institutions and Services: General --- Banks --- Depository Institutions --- Micro Finance Institutions --- Mortgages --- Mathematical Methods and Programming: General --- Computational Techniques --- Monetary Policy, Central Banking, and the Supply of Money and Credit: General --- Time-Series Models --- Dynamic Quantile Regressions --- Dynamic Treatment Effect Models --- Diffusion Processes --- Financing Policy --- Financial Risk and Risk Management --- Capital and Ownership Structure --- Value of Firms --- Goodwill --- Monetary economics --- Econometrics & economic statistics --- Financial services law & regulation --- Vector autoregression --- Credit risk --- Financial risk management