We present a unified framework to study the effect of the correlation between interest rate volatility and counterparty default probability on the credit risk of collateralized interest rate derivatives contracts. When interest rates are volatile, counterparties are potentially more likely to default. Large moves in interest rates accompanied by counterparty default may lead to losses on interest rate derivatives, even if they are collateralized. An interest rate model with stochastic volatility and a reduced form default model, in which the default probability is correlated with interest rate volatility, are proposed and estimated from market data. We then analyze the effect of the correlation between interest rate volatility and a counterparty's default probability on the credit risk of collateralized interest rate derivatives contracts. Our results show that ignoring this correlation underestimates the credit risk, even with collateralized trades.
{"title":"The Relationship between Counterparty Default and Interest Rate Volatility and its Impact on the Credit Risk of Interest Rate Derivatives","authors":"Jiarui Yang, Tao Wu, Geoffrey R. Harris","doi":"10.21314/jcr.2015.190","DOIUrl":"https://doi.org/10.21314/jcr.2015.190","url":null,"abstract":"We present a unified framework to study the effect of the correlation between interest rate volatility and counterparty default probability on the credit risk of collateralized interest rate derivatives contracts. When interest rates are volatile, counterparties are potentially more likely to default. Large moves in interest rates accompanied by counterparty default may lead to losses on interest rate derivatives, even if they are collateralized. An interest rate model with stochastic volatility and a reduced form default model, in which the default probability is correlated with interest rate volatility, are proposed and estimated from market data. We then analyze the effect of the correlation between interest rate volatility and a counterparty's default probability on the credit risk of collateralized interest rate derivatives contracts. Our results show that ignoring this correlation underestimates the credit risk, even with collateralized trades.","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"7 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2015-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87863350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we consider the large homogeneous portfolio (LHP) approximation with a two-factor Gaussian copula and random recovery rate. In addition, we assume that the earlier the default occurs, the less the asset recovers; in other words, random recovery rate and individual default times have a positive rank correlation. Under the LHP assumption, the conditional cumulative loss of the reference portfolio is approximated by the product of loss given default and conditional default probability. In order to derive semi-analytic formulas for the loss distribution and the expected tranche loss, we use a Gaussian two-factor model and assume that the recovery rate depends on one systematic factor. In addition, we consider stochastic correlation for a better fit to credit default swap index tranches. The derived semi-analytic formula only involves integration with respect to the standard normal density and can be computed by Gauss–Hermite quadrature. Numerical tests show that the two-factor model with stochastic correlation and random recovery fits iTraxx tranche premiums better than other correlation or recovery assumptions under the Gaussian LHP framework. We also apply our model to credit risk assessment such as value-at-risk of the loss distribution.
{"title":"The Large Homogeneous Portfolio Approximation with a Two-Factor Gaussian Copula and Random Recovery Rate","authors":"G. Choe, Soon Won Kwon","doi":"10.21314/JCR.2014.181","DOIUrl":"https://doi.org/10.21314/JCR.2014.181","url":null,"abstract":"In this paper we consider the large homogeneous portfolio (LHP) approximation with a two-factor Gaussian copula and random recovery rate. In addition, we assume that the earlier the default occurs, the less the asset recovers; in other words, random recovery rate and individual default times have a positive rank correlation. Under the LHP assumption, the conditional cumulative loss of the reference portfolio is approximated by the product of loss given default and conditional default probability. In order to derive semi-analytic formulas for the loss distribution and the expected tranche loss, we use a Gaussian two-factor model and assume that the recovery rate depends on one systematic factor. In addition, we consider stochastic correlation for a better fit to credit default swap index tranches. The derived semi-analytic formula only involves integration with respect to the standard normal density and can be computed by Gauss–Hermite quadrature. Numerical tests show that the two-factor model with stochastic correlation and random recovery fits iTraxx tranche premiums better than other correlation or recovery assumptions under the Gaussian LHP framework. We also apply our model to credit risk assessment such as value-at-risk of the loss distribution.","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"72 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2014-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74303077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Johan Gunnesson, Alberto Fernández Muñoz de Morales
In this paper we present a rigorously motivated pricing equation for derivatives, including general cash collateralization schemes, which is consistent with quoted market bond prices. Traditionally, there have been differences in how instruments with similar cash flow structures have been priced if their definition falls under that of a financial derivative versus if they correspond to bonds, leading to possibilities such as funding through derivatives transactions. Furthermore, the problem has not been solved with the recent introduction of Funding Valuation Adjustments in derivatives pricing, and in some cases has even been made worse. In contrast, our proposed equation is not only consistent with fixed income assets and liabilities, but is also symmetric, implying a well-defined exit price, independent of the entity performing the valuation. Also, we provide some practical proxies, such as first-order approximations or basing calculations of CVA and DVA on bond curves, rather than Credit Default Swaps.
{"title":"A Bond Consistent Derivative Fair Value","authors":"Johan Gunnesson, Alberto Fernández Muñoz de Morales","doi":"10.2139/ssrn.2457786","DOIUrl":"https://doi.org/10.2139/ssrn.2457786","url":null,"abstract":"In this paper we present a rigorously motivated pricing equation for derivatives, including general cash collateralization schemes, which is consistent with quoted market bond prices. Traditionally, there have been differences in how instruments with similar cash flow structures have been priced if their definition falls under that of a financial derivative versus if they correspond to bonds, leading to possibilities such as funding through derivatives transactions. Furthermore, the problem has not been solved with the recent introduction of Funding Valuation Adjustments in derivatives pricing, and in some cases has even been made worse. In contrast, our proposed equation is not only consistent with fixed income assets and liabilities, but is also symmetric, implying a well-defined exit price, independent of the entity performing the valuation. Also, we provide some practical proxies, such as first-order approximations or basing calculations of CVA and DVA on bond curves, rather than Credit Default Swaps.","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"86 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2014-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82505257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A framework which consistently and fully integrates market, credit and country transfer risks of a general portfolio of financial assets in a multi-period setup is developed. An appropriate definition of exposure, loss-given-defaults and loss-given-transfer-events provides a unified treatment of these three risk types. Implementable algorithms are presented as well as a comparison with the industry standards and best practices. The framework discussed is generic and does not explicitly depend on the choice of the scenario generator. Generic and macroeconomical stress tests is directly obtained by selecting the paths for which the relevant risk factors are constrained by a priori given bounds.
{"title":"A Framework for Market, Credit and Transfer Risk Aggregation and Stress Testing","authors":"Simone Farinelli","doi":"10.2139/ssrn.2060855","DOIUrl":"https://doi.org/10.2139/ssrn.2060855","url":null,"abstract":"A framework which consistently and fully integrates market, credit and country transfer risks of a general portfolio of financial assets in a multi-period setup is developed. An appropriate definition of exposure, loss-given-defaults and loss-given-transfer-events provides a unified treatment of these three risk types. Implementable algorithms are presented as well as a comparison with the industry standards and best practices. The framework discussed is generic and does not explicitly depend on the choice of the scenario generator. Generic and macroeconomical stress tests is directly obtained by selecting the paths for which the relevant risk factors are constrained by a priori given bounds.","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"74 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2014-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80490794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mathieu Boudreault, Geneviève Gauthier, Tommy Thomassin
{"title":"Recovery rate risk and credit spreads in a hybrid credit risk model","authors":"Mathieu Boudreault, Geneviève Gauthier, Tommy Thomassin","doi":"10.21314/JCR.2013.164","DOIUrl":"https://doi.org/10.21314/JCR.2013.164","url":null,"abstract":"","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"32 1","pages":"3-39"},"PeriodicalIF":0.3,"publicationDate":"2013-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77417566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A clusterized copula-based probability distribution of a counting variable for high-dimensional problems","authors":"E. Bernardi, S. Romagnoli","doi":"10.21314/JCR.2013.160","DOIUrl":"https://doi.org/10.21314/JCR.2013.160","url":null,"abstract":"","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"163 1","pages":"3-26"},"PeriodicalIF":0.3,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79086216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Applying the zero-adjusted inverse Gaussian model to predict probability of default and exposure at default for a credit card portfolio","authors":"Rafael Rodrigues Troiani","doi":"10.21314/JCR.2013.161","DOIUrl":"https://doi.org/10.21314/JCR.2013.161","url":null,"abstract":"","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"52 1","pages":"68-81"},"PeriodicalIF":0.3,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78052578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we derive an explicit solution for the expected loss of a collateralized loan, focusing on the negative correlation between default intensity and collateral value. Three requirements for the default intensity and the collateral value are imposed. First, the default event can happen at any time until loan maturity according to an exogenous stochastic process of default intensity. Second, default intensity and collateral value are negatively correlated. Third, the default intensity and collateral value are non-negative. To develop an explicit solution, we propose a square-root process for default intensity and an affine diffusion process for collateral value. Given these settings, we derive an explicit solution for the integrand of the expected recovery value within an extended affine model. From the derived solution, we find the expected recovery value is given by a Stieltjes integral with a measure-changed survival probability.
{"title":"Analytical Solution for Expected Loss of a Collateralized Loan: A Square-root Intensity Process Negatively Correlated with Collateral Value","authors":"Satoshi Yamashita, Toshinao Yoshiba","doi":"10.21314/JCR.2013.162","DOIUrl":"https://doi.org/10.21314/JCR.2013.162","url":null,"abstract":"In this study, we derive an explicit solution for the expected loss of a collateralized loan, focusing on the negative correlation between default intensity and collateral value. Three requirements for the default intensity and the collateral value are imposed. First, the default event can happen at any time until loan maturity according to an exogenous stochastic process of default intensity. Second, default intensity and collateral value are negatively correlated. Third, the default intensity and collateral value are non-negative. To develop an explicit solution, we propose a square-root process for default intensity and an affine diffusion process for collateral value. Given these settings, we derive an explicit solution for the integrand of the expected recovery value within an extended affine model. From the derived solution, we find the expected recovery value is given by a Stieltjes integral with a measure-changed survival probability.","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"64 6 1","pages":"27-44"},"PeriodicalIF":0.3,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89849703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present the results of a business solution on how to measure credit and counterparty risk with the main focus on OTC derivatives. Moreover, we use this approach to include the measurement of liquidity risk exposure. We explain how we measure the exposure for each counterparty with netting arrangements and collaterals. Further we introduce the concept of PFE (potential future exposure) and explain why we opted for a parametric approach. We then develop the concepts of credit loss and default probability as a result of a Poisson process. Further we use the concept of unexpected loss in order to derive the economic capital as the difference between the unexpected loss and the credit loss. Finally we show how this approach can be applied as a refinement of liquidity risk measurement by considering collateral requirements, so as to enhance the monitoring of liquidity congruence between funds' asset and liability, especially under stressed market conditions.
{"title":"A Parametric Approach to Counterparty and Credit Risk","authors":"G. Orlando, Maximilian Härtel","doi":"10.2139/ssrn.2344682","DOIUrl":"https://doi.org/10.2139/ssrn.2344682","url":null,"abstract":"In this paper, we present the results of a business solution on how to measure credit and counterparty risk with the main focus on OTC derivatives. Moreover, we use this approach to include the measurement of liquidity risk exposure. We explain how we measure the exposure for each counterparty with netting arrangements and collaterals. Further we introduce the concept of PFE (potential future exposure) and explain why we opted for a parametric approach. We then develop the concepts of credit loss and default probability as a result of a Poisson process. Further we use the concept of unexpected loss in order to derive the economic capital as the difference between the unexpected loss and the credit loss. Finally we show how this approach can be applied as a refinement of liquidity risk measurement by considering collateral requirements, so as to enhance the monitoring of liquidity congruence between funds' asset and liability, especially under stressed market conditions.","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"144 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2013-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78581086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
B. Grün, Paul Hofmarcher, K. Hornik, C. Leitner, Stefan Pichler
This paper introduces a model framework for dynamic credit rating processes. Our framework aggregates ordinal rating information stemming from a variety of rating sources. The dynamic of the consensus rating captures systematic as well as idiosyncratic changes. In addition, our framework allows to validate the different rating sources by analyzing the mean/variance structure of the rating errors. In an empirical study for the iTraxx Europe companies rated by the big three external rating agencies we use Bayesian techniques to estimate the consensus ratings for these companies. The advantages are illustrated by comparing our dynamic rating model to a benchmark model. (author´s abstract)
{"title":"Deriving Consensus Ratings of the Big Three Rating Agencies","authors":"B. Grün, Paul Hofmarcher, K. Hornik, C. Leitner, Stefan Pichler","doi":"10.21314/JCR.2013.156","DOIUrl":"https://doi.org/10.21314/JCR.2013.156","url":null,"abstract":"This paper introduces a model framework for dynamic credit rating processes. Our framework aggregates ordinal rating information stemming from a variety of rating sources. The dynamic of the consensus rating captures systematic as well as idiosyncratic changes. In addition, our framework allows to validate the different rating sources by analyzing the mean/variance structure of the rating errors. In an empirical study for the iTraxx Europe companies rated by the big three external rating agencies we use Bayesian techniques to estimate the consensus ratings for these companies. The advantages are illustrated by comparing our dynamic rating model to a benchmark model. (author´s abstract)","PeriodicalId":44244,"journal":{"name":"Journal of Credit Risk","volume":"68 1","pages":"75-98"},"PeriodicalIF":0.3,"publicationDate":"2013-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86727140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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