Dynamic Models of Portfolio Credit Risk

International Journal of Applied Management …, 2010

The aim of this paper is to study the impact of structure of dependency on the pricing of multi-name credit derivatives such as collateralised debt obligations (CDO). The correlation between names defaulting has an effect on the value of the basket credit derivatives. We present a copula based simulation procedure for pricing CDO under different structure of dependency and assessing the influence of different price drivers (correlation, hazard rates and recovery rates) on modelling portfolio losses. Gaussian copulas and Monte Carlo simulation are widely used to measure the default risk in basket credit derivatives. Many studies have shown that many distributions have fatter tails than those captured by the normal distribution. We use distributions with fat tails such as the t-student distribution. The paper has several practical implications that are of value for financial hedgers and engineers, financial regulators, central banks, and financial risk managers.

SSRN Electronic Journal, 2000

Banks' internal credit risk assessment may take into account not only publicly available ratings but also internal measures of credit risk. We present a credit rating model of credit risk that permits banks to employ their own risk assessment in addition to public rating information.

Journal of …, 2006

The multivariate modeling of default risk is a crucial aspect of the pricing of credit derivative products referencing a portfolio of underlying assets, and the evaluation of Value at Risk of such portfolios. This paper proposes a model for the joint dynamics of credit ratings of several firms. Namely, individual credit ratings are modeled by univariate continuous time Markov chain, while their joint dynamic is modeled using copulas. A by-product of the method is the joint laws of the default times of all the firms in the portfolio. The use of copulas allows us to incorporate our knowledge of the modeling of univariate processes, into a multivariate framework. The Normal and Student copulas commonly used in the literature as well as by practitioners do not produce very different estimates of default risk prices. We show that this result is restricted to these two two basic copulas. That is, for any other family of copula, the choice of the copula greatly affects the pricing of default risk.

1. Introduction 2. Structural Approach 2.1. Basic Assumptions 2.2. Classic Structural Models 2.3. Stochastic Interest Rates 2.4. Credit Spreads: A Case Study 2.5. Comments on Structural Models 3. Intensity-Based Approach 3.1. Hazard Function 3.2. Hazard Processes 3.3. Martingale Approach 3.4. Further Developments 3.5. Comments on Intensity-Based Models 4. Dependent Defaults and Credit Migrations 4.1. Basket Credit Derivatives 4.2. Conditionally Independent Defaults 4.3. Copula-Based Approaches 4.4. Jarrow and Yu Model 4.5. Extension of the Jarrow and Yu Model 4.6. Dependent Intensities of Credit Migrations 4.7. Dynamics of Dependent Credit Ratings 4.8. Defaultable Term Structure 4.9. Concluding Remarks References

Social Science Research Network, 2007

We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return distributions can substantially deviate from the asymptotic Gaussian limit for very long horizons. We introduce the notion of correlation surface as a convenient tool for comparing portfolio credit loss generating models and pricing synthetic CDO tranches. Analyzing alternative specifications of the underlying dynamics, we conclude that the asymmetric models with TARCH volatility specification are the preferred choice for generating significant and persistent credit correlation skews. The characteristic dependence of the correlation skew on term to maturity and portfolio hazard rate in these models has a significant impact on both relative value analysis and risk management of CDO tranches.

Copula functions have proven to be extremely useful in describing joint default and survival probabilities. We overview the state of the art and point out some modelling issues, such as the choice of a speci…c copula and of the amount of dependence, as well as re-mapping of models. We also discuss how to simplify credit models using factors. The survey leads us to focus on historical versus risk neutral dependence. We present an original methodology for inferring risk neutral dependence without using a single factor, provide an application to market data and explore its impact on the fees of some credit derivatives. The …rst part of the paper is a review of the copula techniques developed so far in order to evaluate credit risk in default-no default models. The review proceeds as follows: we …rst resume some basics about structural and intensity- based models, then recall how and under which conditions two models of these classes can be re-mapped into each other, using the latent va...

Control and Cybernetics, 2015

Abstract: In this paper we present a new arbitrage-free bottomup model of correlated defaults, based on a special approach to systematic and idiosyncratic risks for individual obligors. The model admits several attractive features, like consistency with currency and interest rate models, as well as numerical tractability and flexibility, making it capable to fit the market for practically all self-consistent CDO tranche prices. Its background is rather remote from other approaches, like copulas and point processes, so our presentation is detailed.

European Actuarial Journal, 2011

The recent credit crisis has focused attention on the models used for pricing and assessing risk of structured credit transactions including synthetic CDOs. The market standard one factor Gaussian copula model has been criticized for its unrealistic constant correlation assumption. In this paper, a range of market models that allow a positive relationship between default correlation and default probability, including the correlation mapping methods and the implied copula models, are compared with the Gaussian copula model, based on their relative performance in hedging credit spread risk and pricing bespoke CDOs. The models assessed are calibrated to the traded CDO tranche spreads prior to the credit crisis and then compared based on the mean absolute pricing errors over a time period including the credit crisis. The results of the analysis highlight a number of issues including the accuracy of ''mark-to-model'' valuations of bespoke CDOs, the value of including past information in pricing and hedging, and the relative performance of the base correlation Gaussian copula model compared to the other market models in this study.

2011

In the last decade, a considerable growth has been added to the volume of the credit risk derivatives market. This growth has been followed by the current financial market turbulence. These two periods have outlined how significant and important are the credit derivatives market and its products. Modelling-wise, this growth has parallelised by more complicated and assembled credit derivatives products such as m th to default Credit Default Swaps (࣭ࣝࣞ), m out of n (࣭ࣝࣞ) and collateralised debt obligation (ࣩࣝࣞ). In this thesis, the Lévy process has been proposed to generalise and overcome the Credit Risk derivatives standard pricing model's limitations, i.e. Gaussian Factor Copula Model. One of the most important drawbacks is that it has a lack of tail dependence or, in other words, it needs more skewed correlation. However, by the Lévy Factor Copula Model, the microscopic approach of exploring this factor copula models has been developed and standardised to incorporate an endless number of distribution alternatives those admits the Lévy process. Since the Lévy process could include a variety of processes structural assumptions from pure jumps to continuous stochastic, then those distributions who admit this process could represent asymmetry and fat tails as they could characterise symmetry and normal tails. As a consequence they could capture both high and low events' probabilities. Subsequently, other techniques those could enhance the skewness of its correlation and be incorporated within the Lévy Factor Copula Model has been proposed, i.e. the TABLE OF CONTENTS III

Aiming to solve the difficulty in describing the high dimensional dependency structure of credit assets, we construct pair copula VaR model to evaluate the credit portfolio risk. The empirical study which takes the publicly traded companies in Shanghai stock exchanges and Shenzhen stock exchanges shows that the Clayton copula with Canonical vine structure is the most appropriate function to describe the high dimensional low tail dependency structure. Meanwhile, the Monte Carlo simulation result proves that the pair copula VaR model can accurately measure the credit portfolio risk both in calm period and crisis period. Additionally, we acquired the optimal weights of the different credit assets in portfolio according to the simulation results of pair copula VaR models. Based on the research results, the commercial banks can dynamically adjust their credit asset allocation, so as to alleviate the credit portfolio risk and conduct more efficient credit risk management. JEL Classifications: G21