Checking Default Correlation and Score Correlation in a Breakpoint Model for Rating Classification

This paper, inspired by the efforts of a Canadian bank, discusses Basel preparation and validation issues. A comprehensive outcomes analysis (eg, back-testing) framework is presented, including a simulation-based calibration test. A consistent risk rating philosophy - point-in-time (PIT) or through-the-cycle (TTC) - encompasses both the probability of default (PD) and the default correlations, and the validation needs to be consistent with both. Related arguments are made that not only PD itself, but the correlation of PD used in economic capital models should be rating system specific. We need to use a larger PD correlation under a TTC rating system than under a PIT rating system. Furthermore, Basel loss given default may not be appropriate for commonly used internal models, and accordingly adjustments are proposed.

The main challenge of forecasting credit default risk in loan portfolios may be seen in forecasting the default probabilities and the default correlations. We derive a Merton-style threshold value model for the default probability which treats the asset value of a firm as unknown and uses a factor model instead. In addition, we demonstrate how default correlations can be easily modeled. The empirical analysis is based on a large data set of German firms provided by Deutsche Bundesbank. We find that default probabilities can be forecast given the values of risk drivers known at the point of time at which the forecast is made. In addition, correlations depend on the fit of the estimated default probabilities to the realized default rate for given points in time.

The three drivers in modeling CDOs (collateralized debt obligations) are the probability of default, the recovery rate, and correlation of the underlying pool of credits. In general, the probability of default is by far the most relevant factor and correlation, the least. Unfortunately, an unwarranted amount of attention is currently given to correlation. Worse yet, most models are driven by (or based on) asset correlation assumptions when what is really relevant is the default correlation. There is no assurance that controlling the asset correlation can produce the desired default correlation.

We address the estimation of asset correlation for credit risk assessment in the Italian market and its impact on SME credit access. The empirical evidence demonstrates that assumptions underlying the regulatory capital formula are not substantiated, and benefits received from the respect of granularity could be reduced or even removed. This outcome could depend on the positive relationship between asset correlation and default probability, the negative relationship between asset correlation and size and the positive link between default correlation and default probability. The regulatory impact is that the goal of levelling the playing field could fail, a regulatory arbitrage opportunity could be created and certain firms, clustered by size and industry, could suffer from the credit crunch.

Chapter 11 - Estimating Parameters Required for Credit Risk Modeling

Introduction Three main variables affect the credit risk of a financial asset: (i) the probability of default (PD), (ii) the ‘loss given default’ (LGD), which is equal to one minus the recovery rate in the event of default (RR), and (iii) the exposure at default (EAD). While significant attention has been devoted by the credit risk literature on the estimation of the first component (PD), much less attention has been dedicated to the estimation of RR and to the relationship between PD and RR. This is mainly the consequence of two related factors. First, credit pricing models and risk management applications tend to focus on the systematic risk components of credit risk, as these are the only ones that attract risk-premia. Second, credit risk models traditionally assumed RR to be dependent on individual features (e.g. collateral or seniority) that do not respond to systematic factors, and therefore to be independent of PD. This traditional focus only on default analysis has been partly reversed by the recent increase in the number of studies dedicated to the subject of RR estimation and the relationship between the PD and RR (Fridson et al . 2000, Gupton et al . 2000, Altman et al . 2001, Altman et al . 2003, 2005, Frye 2000a, 2000b, 2000c, Hu and Perraudin 2002, Hamilton et al . 2001, Jarrow 2001 and Jokivuolle and Peura 2003). This is partly the consequence of the parallel increase in default rates and decrease of recovery rates registered during the 1999–2002 period.

The use of stress testing for risk monitoring has increased considerably over the last decade. Stress testing – a simulation technique used to assess the strength of a portfolio or a financial institution under unusual economic conditions – emerged as a powerful tool that was originally used in market risk. Its use has subsequently been extended into credit risk. To stress test a credit risk portfolio, practitioners focus on the key parameters that allow the risk of a credit portfolio to be assessed. These parameters, also known as Basel II parameters, are probability of default, loss given default, exposure at default and asset correlation. In this paper, using a time series approach (specifically, an error correction model), we focus on the probability of default parameter that is related to macroeconomic factors. Such an approach involves dealing with the nonstationarity of economic time series and cointegration issues. Hence, when the model is estimated, the probability of default can be simulated by measuring the effects of macroeconomic shocks applied to the model. In turn, these probabilities of default can be used to measure the impact on the probability of default under a given macroeconomic scenario, and then to improve the credit risk monitoring. The results of our study suggest that error correction models are well-suited to macroeconomic stress testing. Indeed, the fitting of the historical probability of default and the results under the stress scenarios considered here are satisfactory.

Credit Risk and Risk Neutral Default Probabilities: Information About Rating Migrations and Defaults

Авторы: Ксения Михайловна Тотьмянина НИУ ВШЭ totmyanina.k@gmail.com
 Рост объемов и снижение качества корпоративных кредитных портфелей банков актуализирует вопрос совершенствования подходов к оценке вероятности дефолта данных заемщиков. Более того, кризис 2007-2009 гг. показал, что корпоративный кредитный портфель в значительной степени подвержен системным рискам и оценка кредитного риска корпоративных заемщиков должна основываться на комплексном анализе не только заемщика, но отраслевой и макроэкономической конъектуры.В данной статье предлагается один из подходов к моделированию вероятности дефолта промышленных компаний на примере компаний строительной отрасли, которые представляют значительную долю кредитования среди крупнейших российских банков и наиболее подвержены системным рискам. Для этого в рамках данной работы решаются следующие задачи: формируется репрезентативная выборка для построения модели на основе данных по российским компаниям строительной отрасли и российской экономике;выделяются ключевые финансовые и макроэкономические показатели, позволяющие наилучшим образом разделять анализируемые компании с точки зрения вероятности дефолта;на основе выделенных показателей строятся модели оценки вероятности дефолта заемщиков, а также проводится анализ качества полученных моделей.Основой для информационной базы исследования послужили несколько источников: 1) данные официальной публикуемой отчетности предприятий корпоративного сектора, размещенные в информационной аналитической системе FIRA PRO 2) данные о макроэкономических показателях, размещенные на сайтах Банка России, Международного валютного фонда и Банка международных расчетов и другие информационные общедоступные источники.На основе общедоступных данных о российских предприятиях корпоративного сектора (на примере строительной отрасли) предложены подходы к отбору риск-доминирующих показателей и многофакторному моделированию вероятности дефолта. Проведен статистический анализ качества полученной модели, теоретически и эмпирически обоснована необходимость включения макроэкономических факторов, предложено несколько альтернативных подходов к отбору риск-доминирующих показателей для включения в многофакторную модель.

Abstract. The objective of this article is theoretical and methodological justifying of determining algorithm of the cost of debt capital for enterprises functioning in emerging markets (EM). The methods of research: analysis and synthesis, system analysis, comparative analysis, empirical and statistical methods, factor analysis. Results. In this article key determinants of interest rates on debt capital for enterprises and their impact on the procedure of discount rate calculation are determined. The issue of the cost of debt calculation of enterprises in condition of absence of complete information concerning systematic and non-systematic crediting risks is studied. Differences between interest rate on the loan fixed in credit agreement and expected by creditors the cost of debt are identified. It is determined that the key factor impacting the deviation level of market value of debt capital from the nominal, and respectively, deviation of the cost of debt from the cost of capital is probability of default (PD). At the minimum values of PD, the contract interest rate corresponds to the rate of cost of debt and it is advisable to use it for discount rate calculation. Critical analysis of alternative methodological approaches of the cost of debt calculation is made. Ways of integrating of market information concerning credit default swaps into the process of expected cost of debt calculation are justified. Factors of shadowing of rates of the cost of debt and ways of reducing of shadow transactions’ level in the credit market are identified. Conclusions. At high PD values, expected by market premium for default risk may exceed the contract interest rate, which necessitates constant monitoring of credit risks and appropriate adaptation of interest rates. In the paper the algorithm of such adaptation are proposed. It is shown that in the case of non-use of interest rates adjustment taking into account changes in PD, CDS and LGD, premium for creditors’ systematic risk can differ significantly from market values of similar enterprises (peer-group), and estimated value of the cost of debt can acquire negative values. Contract (promised) interest rate should be set in such way that the premium for systematic risk of providing debt capital will be at the level of similar companies and does not change significantly as a result of probability of default changes. If in practice the opposite situation occurs, it is the evidence of contract interest rate shadowing, absence of effective system of assessment and management of credit risks. For solving the problem of interest rate transparency and filling of information gaps concerning PD borrowers in EM countries, should intensify CDS market. Keywords: debt capital, default probability, non-performing loans, credit default swap, credit spread, debt capital premium, shadow economy. JEL Classification E47 Formulas: 16; fig.: 0; tabl.: 3; bibl.: 15.

Default risk is one of the most important and fastest growing areas in derivatives. Single-name credit default swaps are now well established, and markets for contracts based on the default experience of a credit portfolio, like collateralized debt obligations (CDOs) and basket default swaps, are developing rapidly. Portfolio credit risk requires default correlation as a critical input. But defaults are rare, so default correlation must be estimated in another way, typically from correlations in stock returns. In a „structural” credit risk model, a credit event occurs when the net asset value of the firm falls below a critical threshold. Transitions among credit rating classes can be modeled with a set of thresholds corresponding to the different ratings. The widely used „normal copula” model treats the default probability for a single issuer, and default correlations among pairs of issuers, as arising from exposure to a set of common stochastic risk factors plus an idiosyncratic term. The resulting models are intuitive, but calibration to (implied) correlations embedded in market CDO prices can be difficult, especially as the number of factors increases. In this article, Overbeck and Schmidt offer an alternative structural approach that produces similar values to the normal copula model, with considerably less difficulty. Their trick is to alter the time scales of the Wiener processes driving the underlying asset values, which is equivalent to allowing time-varying volatilities, and permits a much easier calibration of the correlations.

The quality of bank loan portfolios and the incurred credit risk loss is determined by the development of the economy of the country as well as the financial state of the debtors. With loans accounting for the largest share of the assets of Lithuanian banks, the credit risk is the main individual source of risk. With the current recession of the world economy and the respective situation in Lithuania, when the economy of the country started to recede at the end of 2008, it is obvious that in the future the processes of development of economy of Lithuania will surely be a major influence on the credit risk and results of activities of the bank system of the country, therefore evaluation of this effect under current conditions becomes critical. The importance of research of the influence of macroeconomic processes on the sorts of risks incurred by the bank sector is also proved by the abundance of theoretical research. Testing of the credit risk of the Lithuanian bank sector upon change of risk factors is carried out combining the models used in research performed by M. Sorge (2004), M. A. Segoviano Basurto, P. Padilla (2007) and other scientists. The research covers five phases: the first phase – modeling of macroeconomic scenarios performing an analysis of the current macroeconomic situation of the country, analyzing expert evaluations and establishing the main risk factors. During the second phase indicators describing the quality of bank loan portfolio are evaluated performing an evaluation of the current quality of loan portfolio and calculating the probability of default according to loan sectors. The third phase covers the establishment of macroeconomic indicators influencing the change of the probability of default and the net profit of banks by selecting macroeconomic indicators that can influence the change of the probability of default according to loan sectors and the net profit of banks, by eliminating the seasonal fluctuations of the selected indicators, by evaluating correlation between macroeconomic indicators and the probability of default as well as the net profit, by defining the parameters of explanatory macroeconomic variables, by employing the model of linear regression and verifying reliability. The fourth phase is the research of the influence of macroeconomic scenarios on the credit risk of the bank sector by providing a prognosis of explanatory macroeconomic variables under the formulated macroeconomic scenarios and evaluating the influence of the macroeconomic scenarios on the probability of default according to loan sectors and the net profit of banks. The research is completed with a prognosis of the reserves accumulated by banks for covering the probable losses on the basis of different scenarios: scenario 1– expensive loans, i.e. the rate of interest for loans in litas remains very high, scenario 2 – dropping real estate prices. Evaluation of the credit risk of the bank sector combining the models created by M. Sorge (2004) & M. A. Segoviano Basurto, P. Padilla (2007) helps to raise the most relevant questions of the macroeconomic state for the current period, and the integration of the analysis of the indicators of financial stability into the critical testing of the bank system and drawing up of macroeconomic prognosis helps to form an efficient future activity strategy for the bank sector or an individual financial institution. The results of the research showed that in case the macroeconomics of the country develops according to scenario 2 the Lithuanian bank system would face deficit of capital for covering the probable losses, therefore the banks of the country should accumulate more capital in order to be able to avoid such risk in the future.

Beating market expectations and the pricing of firms’ probability of default

Introduction: Adolescence is marked by increased risk-taking behaviors and challenges engaging in optimal type 1 diabetes (T1D) treatment. We developed the Diabetes-Specific Risk-Taking Inventory (DSRI) to assess risky adolescent T1D self-management behaviors. In the current study, we conducted confirmatory factor analyses (CFAs) for the DSRI and examined model fit. Methods: We surveyed a national sample of 224 adolescents (age 15-18 years; M age 16.9 ± 1.1 years; 49% female, 11% identified as Black, Indigenous, or Persons of Color; 76.8% used insulin pumps; M HbA1c= 8.5% ± 1.3); from the T1D Exchange registry in a cross-sectional design. Participants completed the DSRI, and we collected the most recent HbA1c value from registry data. We performed CFAs in R using the Lavaan package to evaluate three models: 1) a one-factor structure, 2) a two-factor structure reflecting items higher and lower in risk (item level of risk assessed by surveying diabetes health care providers), and 3) another two-factor structure reflecting items that associate with higher HbA1c (>9%) and lower HbA1c (<9%). Results: The DSRI measure contains 31 items; however, one item was removed from CFA analyses due to a nonsignificant factor loading value. The one-factor CFA model demonstrated poor fit χ2(399, n=224) =1714.94, p<0.001, RMSEA=0.12, CFI=0.52, TLI=0.49, as did the two-factor structure differentiating between higher and lower HbA1c χ2(399, n=224) =1121.02, p<0.001, RMSEA=0.090, CFI=0.72, TLI=0.69. The two-factor CFA reflecting higher and lower risk items model demonstrated improved fit χ2(399, n=224) =896.19, p<0.001, RMSEA=0.085, CFI=0.77, TLI=0.75. Conclusions: The DSRI is a valuable self-report measure that providers may use to screen for high-risk behaviors not routinely assessed in T1D clinical care. The results suggest that the high-risk vs. low-risk two-factor model is slightly better fitting than the one-factor model; however, additional factor structures should be assessed to identify a more robust structural model. Disclosure A.Monzon: None. J.Pierce: None. R.M.Wasserman: None. Funding The Leona M. and Harry B. Helmsley Charitable Trust (2016PG-T1D053); National Institutes of Diabetes and Digestive and Kidney Diseases (1K12DK097696)

The interconnectedness of financial institutions affects instability and credit crises. To quantify systemic risk we introduce here the PD model, a dynamic model that combines credit risk techniques with a contagion mechanism on the network of exposures among banks. A potential loss distribution is obtained through a multi-period Monte Carlo simulation that considers the probability of default (PD) of the banks and their tendency of defaulting in the same time interval. A contagion process increases the PD of banks exposed toward distressed counterparties. The systemic risk is measured by statistics of the loss distribution, while the contribution of each node is quantified by the new measures PDRank and PDImpact. We illustrate how the model works on the network of the European Global Systemically Important Banks. For a certain range of the banks’ capital and of their assets volatility, our results reveal the emergence of a strong contagion regime where lower default correlation between banks corresponds to higher losses. This is the opposite of the diversification benefits postulated by standard credit risk models used by banks and regulators who could therefore underestimate the capital needed to overcome a period of crisis, thereby contributing to the financial system instability.