The master thesis deals with the advanced methods for estimating credit risk parameters from market prices: probability of default (PD) and loss given default (LGD). Precise evaluation of these parameters is important not only for banks to calculate their regulatory capital but also for investors to price risky bonds and credit derivatives. We provide forward looking reduced-form analytical method for calculation of PD and LGD of corporate defaultable bonds based on their quoted market prices, prices of equivalent risk-free bonds and quoted credit default swap spreads of the issuer of these bonds. This is reversed to most of the studies on credit risk modeling, as aim is not to price instruments based on estimated credit risk parameters, but to calculate these parameters based on the available market prices. Furthermore, compared to other studies, the LGD parameter is assumed to be endogenous and we provide the method for its simultaneous calculation with the probability of default. Finally, using developed methods, we estimate implied PD and LGD for five European banks assuming that the risk is priced correctly by other investors and the markets are efficient. JEL Classification: C02, C63, G13, G33 Keywords: credit risk, loss given default, probability of default, credit default swap Author's...

The Basel Accord regulates risk and capital requirements to ensure that a bank holds capital proportional to the exposed risk of its lending practices. Basel II allows banks to develop their own empirical models based on historical data for probability of default (PD), loss given default (LGD) and exposure at default (EAD). Brazil was among the first emerging market countries to release a timetable for the implementation of the Basel II Accord and aimed to apply it uniformly to all Brazilian financial institutions from 2005 to 2011. Within this context, the necessity arises of conducting research that could assist the financial institutions in improving the accuracy of their models. This thesis has three objectives. The first is to develop a macro-economic model to predict the behaviour of the aggregate delinquency in Brazilian consumer loans. The model consists in testing co-integrating relationships and then estimating a short run error correction model. The results based on monthly data from 2000 to 2012 show that the delinquency rate is particularly sensitive to shocks on GDP and to the variation of workers' income. The analysis then shifts to micro or account level to model the behaviour of borrowers and certain novel types of information that can be used for prediction. Second, customers fail to make loan repayments for a number of reasons, ranging from simple forgetfulness to deliberate attempts. For this reason, the second objective is to investigate the reasons for default and to explore ways of incorporating these variables into Recovery Rate (RR = 1 - LGD) models, since the standard approach overlooks real reasons for default and uses proxies for them such as marital status and length of employment. Customers who failed to repay their loans were interviewed in order to discover the causes for this failure. In addition, the interviews included questions aimed to measure the customer's personality traits and their financial knowledge in relation to the reasons for default. The empirical results show that the variables proposed in this study, namely, reason for missing payment, financial knowledge and risk taken, improve the prediction of the recovery rate. Thirdly, it is known that recovery depends on the debt collection process and on the different options or actions that collection departments can take. Yet there is practically no literature exploring the impact of the lender's collection actions on RR/LGD. This work fills this gap by investigating the role of different collection actions at the loan-level for a retail credit product, and by estimating LGD models using Panel Data regressions.

Loss given default (LGD) modelling has become increasingly important for banks as they are required to comply with the Basel Accords for their internal computations of economic capital. Banks and financial institutions are encouraged to develop separate models for different types of products. In this thesis we apply and improve several new algorithms including support vector machine (SVM) techniques and mixed effects models to predict LGD for both corporate bonds and retail loans. SVM techniques are known to be powerful for classification problems and have been successfully applied to credit scoring and rating business. We improve the support vector regression models by modifying the SVR model to account for heterogeneity of bond seniorities to increase the predictive accuracy of LGD. We find the proposed improved versions of support vector regression techniques outperform other methods significantly at the aggregated level, and the support vector regression methods demonstrate significantly better predictive abilities compared with the other statistical models at the segmented level. To further investigate the impacts of unobservable firm heterogeneity on modelling recovery rates of corporate bonds a mixed effects model is considered, and we find that an obligor-varying linear factor model presents significant improvements in explaining the variations of recovery rates with a remarkably high intra-class correlation being observed. Our study emphasizes that the inclusion of an obligor-varying random effect term has effectively explained the unobservable firm level information shared by instruments of the same issuer. At last we incorporate the SVM techniques into a two-stage modelling framework to predict recovery rates of credit cards. The two-stage model with a support vector machine classifier is found to be advantageous on an out-of-time sample compared with other methods, suggesting that an SVM model is preferred to a logistic regression at the classification stage. We suggest that the choice of regression models is less influential in prediction of recovery rates than the choice of classification methods in the first step of two-stage models based on the empirical evidence. The risk weighted assets of financial institutions are determined by the estimates of LGD together with PD and EAD. A robust and accurate LGD model impacts banks when making business decisions including setting credit risk strategies and pricing credit products. The regulatory capital determined by the expected and unexpected losses is also important to the financial market stability which should be carefully examined by the regulators. In summary this research highlights the importance of LGD models and provides a new perspective for practitioners and regulators to manage credit risk quantitatively.

Em busca da adequação aos requisitos apresentados pelo Acordo de Basiléia, as instituições financeiras estão despendendo esforços para o desenvolvimento de mensurações e processos. Neste contexto se insere o desenvolvimento de modelos quantitativos para às organizações que pretendem se candidatar à abordagem avançada. O problema de pesquisa propõe mensurar o parâmetro de perda de crédito, ou loss given default, em situações em que não existam eventos de inadimplência observados. A literatura a respeito indica a utilização de modelos estruturais para estes cenários: o modelo proposto por Merton (1974) ou suas derivações são largamente empregados na determinação da probabilidade de perdas (probability of default - em inglês) e perdas de credito (loss given default - em inglês). Nesta metodologia a solução é encontrada de maneira implícita, por meio de preços de títulos e ações. Este trabalho aplica o modelo de Merton e verifica implicações deste uso para o calculo da perda de credito, neutra ao risco e implícita, em empresas listadas na Bolsa de Valores de São Paulo (Bovespa). O público foi selecionado no período de dezembro de 2006 a junho de 2013 e, informações como preço e quantidade de ações e valor da dívida contábil foram coletadas. Os principais resultados encontrados, de modo similar a de outros autores, mostram que: (i) a perda de crédito é maior em momentos de instabilidade financeira, como observado em 2008, época em que os preços dos ativos possuíram alta volatilidade, (ii) o maturity, ou duration, utilizado possui grande peso nos valores de perda de crédito: maturity maior, recuperação menor e (iii) quanto maior o peso da dívida contábil no valor da empresa, menor a volatilidade da própria. / In an effort to comply with the Basel Agreement requirements, financial institutions have engaged in developing their own measures and processes. Within that context, quantitative models are being developed for organizations seeking an advanced approach. The research-related problem aims to estimate the credit loss parameter, loss given default, in situations where events of default are not observed. Literature in that respect indicates the utilization of structural models in such scenarios: the model proposed by Merton (1974) or its derivations are widely employed in determining the probability of default and loss given default. In this methodology the solution is found in an implied manner through the price of bonds and equities. This work applies the Merton model and verifies the implications of its use in calculating loss given default, risk neutral and implicit, in companies listed on the São Paulo Stock Exchange (Bovespa). The target populations in the period from December 2006 to June 2013 and such data as stock price, number of outstanding shares and debt book value have been collected. The main results found, in a manner very similar to other authors, demonstrate that: (i) the loss given default is greater at moments of financial instability, as observed in 2008, a time at which asset prices showed high volatility, (ii) the maturity, or duration, has a great influence on loss given default: higher the maturity, lower the recovery, and as well (iii) higher the book´s value debt weight on firm value, the lower is the firm´s value volatility.

Em busca da adequação aos requisitos apresentados pelo Acordo de Basiléia, as instituições financeiras estão despendendo esforços para o desenvolvimento de mensurações e processos. Neste contexto se insere o desenvolvimento de modelos quantitativos para às organizações que pretendem se candidatar à abordagem avançada. O problema de pesquisa propõe mensurar o parâmetro de perda de crédito, ou loss given default, em situações em que não existam eventos de inadimplência observados. A literatura a respeito indica a utilização de modelos estruturais para estes cenários: o modelo proposto por Merton (1974) ou suas derivações são largamente empregados na determinação da probabilidade de perdas (probability of default - em inglês) e perdas de credito (loss given default - em inglês). Nesta metodologia a solução é encontrada de maneira implícita, por meio de preços de títulos e ações. Este trabalho aplica o modelo de Merton e verifica implicações deste uso para o calculo da perda de credito, neutra ao risco e implícita, em empresas listadas na Bolsa de Valores de São Paulo (Bovespa). O público foi selecionado no período de dezembro de 2006 a junho de 2013 e, informações como preço e quantidade de ações e valor da dívida contábil foram coletadas. Os principais resultados encontrados, de modo similar a de outros autores, mostram que: (i) a perda de crédito é maior em momentos de instabilidade financeira, como observado em 2008, época em que os preços dos ativos possuíram alta volatilidade, (ii) o maturity, ou duration, utilizado possui grande peso nos valores de perda de crédito: maturity maior, recuperação menor e (iii) quanto maior o peso da dívida contábil no valor da empresa, menor a volatilidade da própria. / In an effort to comply with the Basel Agreement requirements, financial institutions have engaged in developing their own measures and processes. Within that context, quantitative models are being developed for organizations seeking an advanced approach. The research-related problem aims to estimate the credit loss parameter, loss given default, in situations where events of default are not observed. Literature in that respect indicates the utilization of structural models in such scenarios: the model proposed by Merton (1974) or its derivations are widely employed in determining the probability of default and loss given default. In this methodology the solution is found in an implied manner through the price of bonds and equities. This work applies the Merton model and verifies the implications of its use in calculating loss given default, risk neutral and implicit, in companies listed on the São Paulo Stock Exchange (Bovespa). The target populations in the period from December 2006 to June 2013 and such data as stock price, number of outstanding shares and debt book value have been collected. The main results found, in a manner very similar to other authors, demonstrate that: (i) the loss given default is greater at moments of financial instability, as observed in 2008, a time at which asset prices showed high volatility, (ii) the maturity, or duration, has a great influence on loss given default: higher the maturity, lower the recovery, and as well (iii) higher the book´s value debt weight on firm value, the lower is the firm´s value volatility.

In Sweden, all banks must report their regulatory capital in their reports to the market and their models for calculating this capital must be approved by the financial authority, Finansinspektionen. The regulatory capital is the capital that a bank has to hold as a security for credit risk and this capital should serve as a buffer if they would loose unexpected amounts of money in their lending business. Loss-Given-Default (LGD) is one of the main drivers of the regulatory capital and the minimum required capital is highly sensitive to the reported LGD. Workout LGD is based on the discounted future cash flows obtained from defaulted customers. The main issue with workout LGD is the incomplete workouts, which in turn results in two problems for banks when they calculate their workout LGD. A bank either has to wait for the workout period to end, in which some cases take several years, or to exclude or make rough assumptions about those incomplete workouts in their calculations. In this study the idea from Survival analysis (SA) methods has been used to solve these problems. The mostly used SA model, the Cox proportional hazards model (Cox model), has been applied to investigate the effect of covariates on the length of survival for a monetary unit. The considered covariates are Country of booking, Secured/Unsecured, Collateral code, Loan-To-Value, Industry code, Exposure-At- Default and Multi-collateral. The data sample was first split into 80 % training sample and 20 % test sample. The applied Cox model was based on the training sample and then validated with the test sample through interpretation of the Kaplan-Meier survival curves for risk groups created from the prognostic index (PI). The results show that the model correctly rank the expected LGD for new customers but is not always able to distinguish the difference between risk groups. With the results presented in the study, Nordea can get an expected LGD for newly defaulted customers, given the customers’ information on the considered covariates in this study. They can also get a clear picture of what factors that drive a low respectively high LGD. / I Sverige måste alla banker rapportera sitt lagstadgade kapital i deras rapporter till marknaden och modellerna för att beräkna detta kapital måste vara godkända av den finansiella myndigheten, Finansinspektionen. Det lagstadgade kapitalet är det kapital som en bank måste hålla som en säkerhet för kreditrisk och den agerar som en buffert om banken skulle förlora oväntade summor pengar i deras utlåningsverksamhet. Loss- Given-Default (LGD) är en av de främsta faktorerna i det lagstadgade kapitalet och kravet på det minimala kapitalet är mycket känsligt för det rapporterade LGD. Workout LGD är baserat på diskonteringen av framtida kassaflöden från kunder som gått i default. Det huvudsakliga problemet med workout LGD är ofullständiga workouts, vilket i sin tur resulterar i två problem för banker när de ska beräkna workout LGD. Banken måste antingen vänta på att workout-perioden ska ta slut, vilket i vissa fall kan ta upp till flera år, eller så får banken exkludera eller göra grova antaganden om dessa ofullständiga workouts i sina beräkningar. I den här studien har idén från Survival analysis (SA) metoder använts för att lösa dessa problem. Den mest använda SA modellen, Cox proportional hazards model (Cox model), har applicerats för att undersöka effekten av kovariat på livslängden hos en monetär enhet. De undersökta kovariaten var Land, Säkrat/Osäkrat, Kollateral-kod, Loan-To-Value, Industri-kod Exposure-At-Default och Multipla-kollateral. Dataurvalet uppdelades först i 80 % träningsurval och 20 % testurval. Den applicerade Cox modellen baserades på träningsurvalet och validerades på testurvalet genom tolkning av Kaplan-Meier överlevnadskurvor för riskgrupperna skapade från prognosindexet (PI). Med de presenterade resultaten kan Nordea beräkna ett förväntat LGD för nya kunder i default, givet informationen i den här studiens undersökta kovariat. Nordea kan också få en klar bild över vilka faktorer som driver ett lågt respektive högt LGD.

Using an extensive cross-section of US corporate CDS this paper offers an economic understanding of implied loss given default (LGD) and jumps in default risk. We formulate and underpin empirical stylized facts about CDS spreads, which are then reproduced in our affine intensity-based jump-diffusion model. Implied LGD is well identified, with obligors possessing substantial tangible assets expected to recover more. Sudden increases in the default risk of investment-grade obligors are higher relative to speculative grade. The probability of structural migration to default is low for investment-grade and heavily regulated obligors because investors fear distress rather through rare but devastating events. (authors' abstract)

As instituições financeiras que pretendem utilizar a IRB (Internal Ratings Based) avançada precisam desenvolver métodos para estimar a componente de risco LGD (Loss Given Default). Desde a década de 1950 são apresentadas propostas para modelagem da PD (Probability of default), em contrapartida, a previsão da LGD somente recebeu maior atenção após a publicação do Acordo Basileia II. A LGD possui ainda uma literatura pequena, se comparada a PD, e não há um método eficiente em termos de acurácia e interpretação como é a regressão logística para a PD. Modelos de regressão para LGD desempenham um papel fundamental na gestão de risco das instituições financeiras. Devido sua importância este trabalho propõe uma metodologia para quantificar a componente de risco LGD. Considerando as características relatadas sobre a distribuição da LGD e na forma flexível que a distribuição beta pode assumir, propomos uma metodologia de estimação da LGD por meio do modelo de regressão beta bimodal inflacionado em zero. Desenvolvemos a distribuição beta bimodal inflacionada em zero, apresentamos algumas propriedades, incluindo momentos, definimos estimadores via máxima verossimilhança e construímos o modelo de regressão para este modelo probabilístico, apresentamos intervalos de confiança assintóticos e teste de hipóteses para este modelo, bem como critérios para seleção de modelos, realizamos um estudo de simulação para avaliar o desempenho dos estimadores de máxima verossimilhança para os parâmetros da distribuição beta bimodal inflacionada em zero. Para comparação com nossa proposta selecionamos os modelos de regressão beta e regressão beta inflacionada, que são abordagens mais usuais, e o algoritmo SVR , devido a significativa superioridade relatada em outros trabalhos. / Financial institutions willing to use the advanced Internal Ratings Based (IRB) need to develop methods to estimate the LGD (Loss Given Default) risk component. Proposals for PD (Probability of default) modeling have been presented since the 1950s, in contrast, LGDs forecast has received more attention only after the publication of the Basel II Accord. LGD also has a small literature, compared to PD, and there is no efficient method in terms of accuracy and interpretation such as logistic regression for PD. Regression models for LGD play a key role in the risk management of financial institutions, due to their importance this work proposes a methodology to quantify the LGD risk component. Considering the characteristics reported on the distribution of LGD and in the flexible form that the beta distribution may assume, we propose a methodology for estimation of LGD using the zero inflated bimodal beta regression model. We developed the zero inflated bimodal beta distribution, presented some properties, including moments, defined estimators via maximum likelihood and constructed the regression model for this probabilistic model, presented asymptotic confidence intervals and hypothesis test for this model, as well as selection criteria of models, we performed a simulation study to evaluate the performance of the maximum likelihood estimators for the parameters of the zero inflated bimodal beta distribution. For comparison with our proposal we selected the beta regression models and inflated beta regression, which are more usual approaches, and the SVR algorithm, due to the significant superiority reported in other studies.

Made available in DSpace on 2016-03-15T19:25:38Z (GMT). No. of bitstreams: 1 Gustavo de Magalhaes Rezende.pdf: 1393519 bytes, checksum: 29eb5b0b0c12d95da19bb067fc0df68c (MD5) Previous issue date: 2011-08-08 / Fundo Mackenzie de Pesquisa / Basel II Accord will allow banks in Brazil to calculate their capital requirements using internal ratings based on the advanced IRB (Internal Rating-Based) approach, depending on their credit risk exposure. The main modeling components that must be estimated are the probability of default (PD), loss given default (LGD) and exposure at default (EAD). The aim of this dissertation is to estimate the parameter LGD using different models found in the literature in order to compare the obtained results. For that, the credit portfolios within this study will be simulated via Monte Carlo simulation, due to the difficulty in getting real losses data. / O acordo de Basileia II no Brasil vai permitir que os bancos utilizem modelos internos, na abordagem IRB avançada (Internal Rating-Based), que sirvam de base para o cálculo dos requisitos mínimos de capital em função do nível de exposição ao risco de crédito. Dentre os principais componentes estimados estão a probabilidade de default (PD probability of default), a perda dado o default (LGD loss given default) e a exposição no default (EAD exposure at default). Esta dissertação tem como objetivo realizar estimativas de LGD utilizando alguns modelos descritos na literatura e comparando os resultados obtidos. Para tanto, os portfólios de crédito do estudo serão simulados através de técnicas de Monte Carlo, dada a escassez de dados de perdas reais.

As instituições financeiras que pretendem utilizar a IRB (Internal Ratings Based) avançada precisam desenvolver métodos para estimar a componente de risco LGD (Loss Given Default). Desde a década de 1950 são apresentadas propostas para modelagem da PD (Probability of default), em contrapartida, a previsão da LGD somente recebeu maior atenção após a publicação do Acordo Basileia II. A LGD possui ainda uma literatura pequena, se comparada a PD, e não há um método eficiente em termos de acurácia e interpretação como é a regressão logística para a PD. Modelos de regressão para LGD desempenham um papel fundamental na gestão de risco das instituições financeiras. Devido sua importância este trabalho propõe uma metodologia para quantificar a componente de risco LGD. Considerando as características relatadas sobre a distribuição da LGD e na forma flexível que a distribuição beta pode assumir, propomos uma metodologia de estimação da LGD por meio do modelo de regressão beta bimodal inflacionado em zero. Desenvolvemos a distribuição beta bimodal inflacionada em zero, apresentamos algumas propriedades, incluindo momentos, definimos estimadores via máxima verossimilhança e construímos o modelo de regressão para este modelo probabilístico, apresentamos intervalos de confiança assintóticos e teste de hipóteses para este modelo, bem como critérios para seleção de modelos, realizamos um estudo de simulação para avaliar o desempenho dos estimadores de máxima verossimilhança para os parâmetros da distribuição beta bimodal inflacionada em zero. Para comparação com nossa proposta selecionamos os modelos de regressão beta e regressão beta inflacionada, que são abordagens mais usuais, e o algoritmo SVR , devido a significativa superioridade relatada em outros trabalhos. / Financial institutions willing to use the advanced Internal Ratings Based (IRB) need to develop methods to estimate the LGD (Loss Given Default) risk component. Proposals for PD (Probability of default) modeling have been presented since the 1950s, in contrast, LGDs forecast has received more attention only after the publication of the Basel II Accord. LGD also has a small literature, compared to PD, and there is no efficient method in terms of accuracy and interpretation such as logistic regression for PD. Regression models for LGD play a key role in the risk management of financial institutions, due to their importance this work proposes a methodology to quantify the LGD risk component. Considering the characteristics reported on the distribution of LGD and in the flexible form that the beta distribution may assume, we propose a methodology for estimation of LGD using the zero inflated bimodal beta regression model. We developed the zero inflated bimodal beta distribution, presented some properties, including moments, defined estimators via maximum likelihood and constructed the regression model for this probabilistic model, presented asymptotic confidence intervals and hypothesis test for this model, as well as selection criteria of models, we performed a simulation study to evaluate the performance of the maximum likelihood estimators for the parameters of the zero inflated bimodal beta distribution. For comparison with our proposal we selected the beta regression models and inflated beta regression, which are more usual approaches, and the SVR algorithm, due to the significant superiority reported in other studies.