LARGE DEVIATIONS IN MULTIFACTOR PORTFOLIO CREDIT RISK

We consider the problem of calculating tail loss probability and conditional excess for the Bernoulli mixture model of credit risk. This is an important problem as all credit risk models proposed in literature can be represented as Bernoulli mixture models. Thus, we deviate from the efficient simulation of credit risk literature in that we propose an efficient simulation algorithm for this general Bernoulli mixture model in contrast to previous works that focus on specific credit risk models like CreditRisk\(^+\) or Credit Metrics. The algorithm we propose is a combination of stratification, importance sampling based on cross-entropy, and inner replications using the geometric shortcut method. We evaluate the efficiency of our general method considering three different examples: CreditRisk\(^+\) and two of the latent variable models, the Gaussian and the t-copula model. Numerical results suggest that the proposed general algorithm is more efficient than the benchmark methods for these specific models.

The Gaussian copula model, with all of its flaws, has become the most common approach for estimating the loss distribution of a portfolio of risky credits. In general, extensive calculations are still required, although simplification is often obtained by using an asymptotic single factor model. The model assumes idiosyncratic risks are fully diversified and dependence across names comes entirely from their joint dependence on a single common factor. However, credit risk exposure in a portfolio, such as one held by a bank, does not depend only on the probability of default, but also on uncertainty over loss given default (LGD) and even uncertainty over face amounts, or the exposure at default (EAD), in the case of revolving credits. This article extends the asymptotic model by formally introducing creditors’ draw rates and recoveries in case of default, both of which are tied to the same common factor. A closed-form asymptotic solution incorporating all three components of risk is obtained when distributions are continuous. The author also derives an approximate solution for the discrete distribution case and uses it to show how the overall loss distribution is affected by the properties of the LGD, in particular, its skewness.

In portfolio credit risk models, correlated credit events are often modelled by means of correlated latent variables. The latent variables are interpreted as the firms’ asset values, and assumed to follow a normal distribution. A procedure is described that uses the information embodied in rating transition matrices to infer the shape of the latent variable distribution. Applying the approach to transition matrices of different origin yields consistent results. Compared to the normal distribution, the implied asset value distributions are fat-tailed, leading to a substantial increase of portfolio credit risk relative to the one under normality. The results are thus highly relevant for the design of credit risk measurement systems.

Notable changes in financial markets have required the development of a standard structure for risk measurement, and obtaining an appropriate risk measurement from historical data is the challenge that is addressed in this article. In recent years, insurance and investment experts are interested in focusing on the use of the tail conditional expectation (TCE) because it has usable and desirable features in different situations. It is well-known that the tail conditional expectation as a risk measurement provides information about the mean of the tail of the loss distribution, while the tail variance (TV) measures the deviation of the loss from this mean along the tail of the distribution. In this paper, we present a theorem that extends the tail variance formula from the elliptical distributions to a rich class of Generalized Skew-Elliptical (GSE) distributions. We develop this theory for the four main classes of skew-elliptical distributions, including the Skew-Normal, Skew-Student-t, Skew-Logistic and Skew-Laplace distributions and obtain the proposed TV measure for them.

An integrated inverse adaptive neural fuzzy system with Monte-Carlo sampling method for operational risk management

Risk factor contributions in portfolio credit risk models

Mean-risk models have been widely used in solving portfolio selection problems in the last years. Since the mean-variance theory of Markowitz, an enormous amount of papers have been published extending or modifying the basic model in several directions like the simplification of the type and amount of input data, the introduction of alternative measures of risk, the incorporation of additional criteria or constraints. Recently, risk measures concerned with the left tails of distributions that evaluate the extremely unfavourable outcomes are used. The most used risk measure for such purposes is Value-at-Risk (VaR). In this paper we concentrate on the second direction of incorporating of a new risk measure in portfolio modeling. We define a new risk measure, which take into consideration the values exceeding a certain threshold in the extreme tail of the loss distribution, called Limited Value-at-Risk (LVaR). We study the properties of this risk measure. We build a new model for portfolio selection, named mean-LVaR model, in which risk is evaluated using LVaR risk measure. We study the properties of the new mean-risk model and compare it with the classical mean-VaR model. We derive the analytical form of LVaR risk measure in the case of normal distribution. We provide computational results and analyze the implications of using the mean-LVaR risk model in portfolio optimization problem.

This article reviews and analyzes the emerging approaches to capital management under risk by financial institutions. Included are discussions of recent developments in the measurement and modeling of credit risk and other sources of risk, and comparisons of the regulatory environment for capital adequacy under the old versus the proposed New Basel Accord. The relationships for agricultural finance are considered in terms of the uniqueness of agriculture, current institutional capital positions and practices, risk measures, and recent experiences in developing risk‐based approaches to determining capital adequacy in agricultural finance.

The modeling of dependence structures (or copulas) is undoubtedly one of the key challenges for modern financial engineering. First applied to credit-risk modeling, copulas are now widely used across a range of derivatives transactions, asset pricing techniques, and risk models, and are a core part of the financial engineer's toolkit. However, by their very nature, copulas are complex and their applications are often misunderstood. Incorrectly applied, copulas can be hugely detrimental to a model or algorithm. Financial Engineering with Copulas Explained is a reader-friendly, yet rigorous introduction to the state-of-the-art regarding the theory of copulas, their simulation and estimation, and their use in financial applications. Starting with an introduction to the basic notions, such as required definitions and dependence measures, the book looks at statistical issues comprising parameter estimation and stochastic simulation. The book will show, from a financial engineering perspective, how copula theory can be applied in the context of portfolio credit-risk modeling, and how it can help to derive model-free bounds for relevant risk measures. The book will cover numerous different market applications of copulas, and enable readers to construct stable, high-dimensional models for asset pricing and risk modeling. Written to appeal to quantitatively minded practitioners across the trading floors and in risk management, academics and students, Financial Engineering with Copulas Explained will be a valuable, accessible and practical guide to this complex topic.

Parameterizing Credit Risk Models

Race Across Mud: The Best Choice for Measuring Credit Risk

Chapter 10 - New Challenges in Credit Risk Modeling and Measurement

Chapter 24 - Large-Scale Credit Risk Loss Simulation

Internal ratings systems, implied credit risk and the consistency of banks’ risk classification policies

Standard market risk optimization tools, based on assumptions of normality, are ineffective for evaluating credit risk. In this article, the authors develop three scenario optimization models for portfolio credit risk. They first create the trading risk profile and find the best hedge position for a single asset or obligor. The second model adjusts all positions simultaneously to minimize the regret of the portfolio subject to general linear restrictions. Finally, a credit risk‐return efficient frontier is constructed using parametric programming. While scenario optimization of quantile‐based credit risk measures leads to problems that are not generally tractable, regret is a relevant and tractable measure that can be optimized using linear programming. The three models are applied to optimizing the risk‐return profile of a portfolio of emerging market bonds.