Jumps in intensity models: investigating the performance of Ornstein-Uhlenbeck processes in credit risk modeling

This work presents intensity-based credit risk models where the default intensity of the point process is modeled by an Ornstein-Uhlenbeck type process completely driven by jumps. Under this model we compute the default probability over time by linking it to the characteristic function of the integrated intensity process. In case of the Gamma and the Inverse Gaussian Ornstein-Uhlenbeck processes this leads to a closed-form expression for the default probability and to a straightforward estimate of credit default swaps prices. The model is calibrated to a series of real-market term structures and then used to price a digital default put option. Results are compared with the well known cases of Poisson and CIR dynamics. Possible extensions of the model to the multivariate setting are finally discussed.     

Assessment of time-varying systemic risk in credit default swap indices: Simultaneity and contagiousness

This study assesses systemic risk inherent in credit default swap (CDS) indices using empirical and statistical analyses. We define systemic risk in two perspectives: the possibilities of simultaneous and contagious defaults, and then quantify them separately across benchmark models. To do so, we employ a Marshall-Olkin copula model to measure simultaneous default risk, and an interacting intensity-based model to capture contagious default risk. For an empirical test, we collect daily data for the iTraxx Europe CDS index and its tranche prices in the period from 2005 to 2014, and calibrate model parameters varying across time. In addition, we select forecasting models that have minimal prediction errors for the calibrated time series. Finally, we identify significant changes in each dynamic of systemic risk indicator before and after default and downgrade-related episodes that have occurred in the global financial crisis and European sovereign debt crisis.     

Time series estimation of the bond default risk premium

The bond default risk premium, measured by the spread between higher and lower grade bond returns, is often estimated with univariate time series procedures and used as an input in financial models. In this paper, time series properties of the historical default risk premium are analyzed and forecasting results from univariate time series models are compared. An autoregressive model with an overreaction component provides the best statistical fit for the bond default risk premium series. A random walk model exhibits the worst fit. The findings are robust over a variety of model specifications and measurement choices. For all forms of the time series process the univariate time series models explain a small percentage of the variation in the default risk premium, raising questions about traditional approaches to estimating the expected default risk premium.     

基于省域视角的信用风险模型适应性分析

巴塞尔新资本协议在鼓励银行采用内部评级法评估信用风险以提取资本准备的同时也强化了各国监管机构对内部评级模型绩效检验与审查的要求.CreditMetrics和CreditRisk+是银行业信用风险评估的基准模型.从建模的数学方法看,CreditRisk+是基于违约的判断,而CreditMetrics则是根据等级变化评价.利用江苏省银监局的相关统计数据对信用风险评估模型进行参数特性审查与绩效检验,结果显示这两类常用模型都可以在江苏的商业银行经营实践中稳定地实现根据信贷组合的实际风险状况进行内部资本配置这一目标.     

信息不完全的信用风险定价模型及其在我国的应用

基于信息不完全的信用风险定价模型与传统的结构化模型和约化模型的最大区别在于它将信息不完全这一前提引入了以信息完全为前提的结构化模型,同时它又考虑了约化模型中强度的优点,引入短期信用风险的度量,成为当前最切合现实的信用风险定价模型。本文认为,应用基于信息不完全的信用风险定价模型来测度信用风险,将具有十分重要的现实意义。     

A mixture model for credit card exposure at default using the GAMLSS framework

The Basel II and III Accords propose estimating the credit conversion factor (CCF) to model exposure at default (EAD) for credit cards and other forms of revolving credit. Alternatively, recent work has suggested it may be beneficial to predict the EAD directly, i.e.modelling the balance as a function of a series of risk drivers. In this paper, we propose a novel approach combining two ideas proposed in the literature and test its effectiveness using a large dataset of credit card defaults not previously used in the EAD literature. We predict EAD by fitting a regression model using the generalised additive model for location, scale, and shape (GAMLSS) framework. We conjecture that the EAD level and risk drivers of its mean and dispersion parameters could substantially differ between the debtors who hit the credit limit (i.e.“maxed out” their cards) prior to default and those who did not, and thus implement a mixture model conditioning on these two respective scenarios. In addition to identifying the most significant explanatory variables for each model component, our analysis suggests that predictive accuracy is improved, both by using GAMLSS (and its ability to incorporate non-linear effects) as well as by introducing the mixture component.     

The role of banking regulation in an economy under credit risk and liquidity shock

This paper develops a Dynamic Stochastic General Equilibrium model which includes a financial sector to analyze the effects of liquidity shock and credit risk in the Brazilian economy. Banks use equity capital and deposits from agents to finance investments of the productive sector. The sources of financial frictions are default rate and liquidity shock, due to deposits withdrawn in advance. The banking supervisor injects liquidity in the deposit market. Using data for the Brazilian economy in the period from 1995 to 2009, the structural parameters are estimated by Bayesian methods. Impulse response functions are computed to describe the dynamic effects of exogenous shocks. The major results show that credit risk is pro-cyclical and default risk depends on structural features. The banking regulator is able to set up a policy to promote financial stability and efficiently reduce fluctuations in the output.     

Modeling frailty-correlated defaults using many macroeconomic covariates

We propose a novel time series panel data framework for estimating and forecasting time-varying corporate default rates subject to observed and unobserved risk factors. In an empirical application for a U.S. dataset, we find a large and significant role for a dynamic frailty component even after controlling for more than 80% of the variation in more than 100 macro-financial covariates and other standard risk factors. We emphasize the need for a latent component to prevent a downward bias in estimated default rate volatility and in estimated probabilities of extreme default losses on portfolios of U.S. debt. The latent factor does not substitute for a single omitted macroeconomic variable. We argue that it captures different omitted effects at different times. We also provide empirical evidence that default and business cycle conditions partly depend on different processes. In an out-of-sample forecasting study for point-in-time default probabilities, we obtain mean absolute error reductions of more than forty percent when compared to models with observed risk factors only. The forecasts are relatively more accurate when default conditions diverge from aggregate macroeconomic conditions.     

Benchmarking regression algorithms for loss given default modeling

The introduction of the Basel II Accord has had a huge impact on financial institutions, allowing them to build credit risk models for three key risk parameters: PD (probability of default), LGD (loss given default) and EAD (exposure at default). Until recently, credit risk research has focused largely on the estimation and validation of the PD parameter, and much less on LGD modeling. In this first large-scale LGD benchmarking study, various regression techniques for modeling and predicting LGD are investigated. These include one-stage models, such as those built by ordinary least squares regression, beta regression, robust regression, ridge regression, regression splines, neural networks, support vector machines and regression trees, as well as two-stage models which combine multiple techniques. A total of 24 techniques are compared using six real-life loss datasets from major international banks. It is found that much of the variance in LGD remains unexplained, as the average prediction performance of the models in terms of R² ranges from 4% to 43%. Nonetheless, there is a clear trend that non-linear techniques, and in particular support vector machines and neural networks, perform significantly better than more traditional linear techniques. Also, two-stage models built by a combination of linear and non-linear techniques are shown to have a similarly good predictive power, with the added advantage of having a comprehensible linear model component.     

Premia for correlated default risk

Using data on corporate default experience in the U.S. and market rates of CDX index and tranche swaps of various maturities, we estimate reduced-form models of correlated default timing in the CDX High Yield and Investment Grade portfolios under actual and risk-neutral probabilities. The striking contrast between the estimated processes followed by the actual and risk-neutral arrival intensities of defaults, and between the parameters governing the actual and risk-neutral dynamics of the risk-neutral intensities, indicates the presence of substantial default risk premia in CDX swap market rates. The effects of risk premia on swap rates covary strongly across maturities, and depend on general stock market volatility and several measures of credit spreads. Large moves in the effects of these premia on swap rates have natural interpretations in terms of economic and financial market developments during the sample period, April 2004 to October 2007. Our results suggest that a large portion of the movements in CDX swap market rates observed during the sample period may be caused by changing attitudes toward correlated default risk rather than changes in the economic factors affecting the actual risk of clustered defaults, which ultimately governs swap payoffs.     

Homogeneous semi-Markov reliability models for credit risk management*

Abstract The credit risk problem is one of the most important issues of modern financial mathematics. Fundamentally it consists in computing the default probability of a company going into debt. The problem can be studied by means of Markov transition models. The generalization of the transition models by means of homogeneous semi-Markov models is presented in this paper. The idea is to consider the credit risk problem as a reliability problem. In a semi-Markov environment it is possible to consider transition probabilities that change as a function of waiting time inside a state. The paper also shows how to apply semi-Markov reliability models in a credit risk environment. In the last section an example of the model is provided. Mathematics Subject Classification (2000): 60K15, 60K20, 90B25, 91B28 Journal of Economic Literature Classification: G21, G33     

A mixed PDE-Monte Carlo approach for pricing credit default index swaptions

Abstract The problem of numerically pricing credit default index swaptions on a large number of names is considered. We place ourselves in a stochastic intensity framework, where Ornstein-Uhlenbeck-type correlated processes are used to model both firms’ distance to default and a macroeconomic state variable. Here the default of the firms’ follows the reduced-form approach and the (random) intensity of the default depends on the behavior of the diffusion processes. We propose here a numerical method based on both a Monte Carlo and a deterministic approach for solving PDEs by finite differences. Numerical tests demonstrate the efficiency and the robustness of the proposed procedure.     

To pool or not to pool: What is a good strategy for parameter estimation and forecasting in panel regressions?

This paper considers estimating the slope parameters and forecasting in potentially heterogeneous panel data regressions with a long time dimension. We propose a novel optimal pooling averaging estimator that makes an explicit trade‐off between efficiency gains from pooling and bias due to heterogeneity. By theoretically and numerically comparing various estimators, we find that a uniformly best estimator does not exist and that our new estimator is superior in nonextreme cases and robust in extreme cases. Our results provide practical guidance for the best estimator and forecast depending on features of data and models. We apply our method to examine the determinants of sovereign credit default swap spreads and forecast future spreads.     

An asset protection scheme for banks exposed to troubled loan portfolios

We examine a specific portfolio credit derivative, an Asset Protection Scheme (APS), and its applicability as a discretionary regulatory tool to reduce asymmetric information and help restore the capital base of troubled banks. The APS can be a fair-valued contract with an appropriate structure of incentives. We apply two alternative multivariate structural default risk models: the classical Gaussian Merton model and a model based on Normal Inverse Gaussian processes. Using a data set on annual farm level data from 1996 to 2009, we use the Danish agricultural sector as a case study and price an APS on an agricultural loan portfolio. We compute the economic capital for this loan portfolio with and without an APS. Moreover, we illustrate how model risk in the form of parameter uncertainty is reduced when an APS is attached to the loan portfolio.     

Commercial mortgage underwriting: How well do lenders manage the risks?

Loan-to-value ratio and debt service coverage ratios have long been viewed as the two most important quantitative measures of the default risk of commercial mortgages. Option-based models of default provide strong theoretic support for the importance of original loan-to-value ratio. The same theoretical predictions have found strong empirical support in residential single-family mortgage analyses. However, recent empirical studies of commercial mortgage default have raised questions about the role of loan-to-value ratio in assessing the riskiness of commercial mortgages. These studies generally either find no relationship or a puzzling negative relationship between loan-to-value ratio and default. This paper uses a very large database of commercial loan histories to thoroughly investigate this issue. It finds strong evidence that loan-to-value and debt service coverage ratios are endogenous to the underwriting process. Lenders react to other—unmeasured—risk factors with credit rationing and pricing. As a result, unusually low loan-to-value ratio loans appear to have above average risk in other dimensions and their default probabilities are equal to or higher than average. The results show that the pricing spread that lenders establish as part of the underwriting process serves as an excellent summary measure of the riskiness of the loan. A test of lenders’ ability to appropriately price loan-to-value risk finds that, while there is some unpriced effect of loan-to-value ratio after controlling for the lender’s pricing, introducing lender pricing into the model removes the otherwise puzzling negative loan-to-value and default relationship previously observed in the literature.     

Forecasting and stress testing credit card default using dynamic models

We present discrete time survival models of borrower default for credit cards that include behavioural data about credit card holders and macroeconomic conditions across the credit card lifetime. We find that dynamic models which include these behavioural and macroeconomic variables provide statistically significant improvements in model fit, which translate into better forecasts of default at both account and portfolio levels when applied to an out-of-sample data set. By simulating extreme economic conditions, we show how these models can be used to stress test credit card portfolios.     

Market perception of sovereign credit risk in the euro area during the financial crisis

We study market perception of sovereign credit risk in the euro area during the financial crisis. In our analysis we use a parsimonious CDS pricing model to estimate the probability of default (PD) and the loss given default (LGD) as perceived by financial markets. In our empirical results the estimated LGDs perceived by financial markets stay comfortably below 40% in most of the samples. Global financial indicators are positively and strongly correlated with the market perception of sovereign credit risk; whilst macroeconomic and institutional developments were at best only weakly correlated with the market perception of sovereign credit risk.     

Measuring Credit Risk of a Bank's Corporate Loan Portfolio Using Advanced Internal Ratings Base Approach

Abstract

The use of technical and advanced approaches in the measurement of credit risk of banks' portfolios has nowadays become a very hot issue. The most recent technical report issued by the Basel Committee in May 2003 has concentrated heavily on the measurement of credit risk using either foundation or advanced Internal Ratings Base (IRB) approaches. This empirical research study attempts to measure credit risk of a bank's corporate loan portfolio, including firms from 10 different Turkish sectors. The monthly observations of the total amount of corporate loans and the total amount of corporate loans at default across various sectors are downloaded from the web page of Central Bank of Turkey (CBT) in a period of 1999-2002. This period covers 47 monthly observations since CBT has captured sectoral corporate loans beginning of 1999. Therefore, the observed sectoral default rates are needed to be simulated to obtain a nicely shaped distribution. Monte Carlo simulation is applied for 1,000 times. Based on the simulated default rates, the expected sectoral default rates are computed. Next, a credit quality rating scale is fitted into sectoral default rates distributions. Finally, the sectoral weights in the whole loan portfolio are multiplied by the expected sectoral default rates matrix, considering cross-sectoral correlations to get the total amount of the bank's credit risk and capital requirement. It is assumed that sectoral monthly default rates are a good representative of the default risk of a sample bank's corporate loan portfolio since no publicly available data on any particular bank's corporate loan portfolio composition exists. Nevertheless, this research may be a good application for measuring the credit risk of banks' corporate loan portfolios using advanced IRB approach.     

Recovering default risk from CDS spreads with a nonlinear filter

We propose a nonlinear filter to estimate the time-varying default risk from the term structure of credit default swap (CDS) spreads. Based on the numerical solution of the Fokker–Planck equation (FPE) using a meshfree interpolation method, the filter performs a joint estimation of the risk-neutral default intensity and CIR model parameters. As the FPE can account for nonlinear functions and non-Gaussian errors, the proposed framework provides outstanding flexibility and accuracy. We test the nonlinear filter on simulated spreads and apply it to daily CDS data of the Dow Jones Industrial Average component companies from 2005 to 2010 with supportive results.