Default Dependence Research Articles

Valuation of CDS counterparty risk under a reduced-form model with regime-switching shot noise default intensities

We study the counterparty risk for a credit default swap (CDS) in a regime-switching market driven by an underlying continuous-time Markov chain. We model the default dependence via some correlated Cox processes with regime-switching shot noise intensities containing common shock. Under the proposed model, the general bilateral counterparty risk pricing formula for CDS contracts with the possibility of joint defaults is presented. Based on some expressions for the conditional Laplace transform of the integrated intensity processes, semi-analytical solution for the bilateral credit valuation adjustment (CVA) is derived. When the model parameters satisfy some conditions, explicit formula for the bilateral CVA at time 0 is also given.

An analysis of simultaneous company defaults using a shot noise process

During subprime mortgage crisis, it became apparent that incumbent models had underestimated company default correlations. Complex models that attempt to incorporate default dependency are difficult to implement in practice. On the contrary, practical models, such as One-Factor Gaussian Copula model, greatly underestimated simultaneous default probabilities. In this article, we develop a model for a company asset process and based on this model, we calculate simultaneous default probabilities using option-theoretic approach. Our model focuses on one industry and includes a shot noise process in the asset model directly. The risk factor driving the shot noise process is common to all companies in the industry but the shot noise parameters are assumed to be company-specific; therefore, every company responds to this common risk factor differently. Apart from the shot noise process, the asset model includes company specific Brownian motion. Compared to commonly used geometric Brownian motion asset model in option-theoretic approach, our model predicted higher simultaneous default probabilities for Citigroup Inc. in 2008, and for all company combinations for the years of 2009 and 2010. Our model is easy to implement and can be extended to analyze any finite number of companies without greatly increasing computational difficulty.

Systemic Risk in the Chinese Financial System: Measuring and Ranking

In this article, we try to analyze the systemic risk of the Chinese financial institutions following the subprime crisis of 2007. We use a sample of seventy Chinese financial institutions during the period from January 2, 2008 to June 30, 2015. We employ the SRISK as a measure of systemic risk. This measure is used to determine financial institutions activity default and its potential to become systemic in whole financial system. The SRISK measure indicates not only individual financial institutions vulnerability but also the default dependency structure between financial institutions and the Chinese financial market returns. Also, these measures can be moderately useful for identifying systematically important financial institutions. Besides, the empirical findings indicate that the systemic risk of the Chinese financial institutions is very important. The contribution of each financial institution to the risk of the whole financial system in China is very significant. We show that the dynamic conditional correlation between financial institutions and market return is the main factor of the systemic risk in China. The results of systemic risk decomposition show that the institution which has the higher level of debt contributes positively and extremely to systemic risk.

Modeling Financial Sector Joint Tail Risk in the Euro Area

SummaryWe develop a novel high‐dimensional non‐Gaussian modeling framework to infer measures of conditional and joint default risk for numerous financial sector firms. The model is based on a dynamic generalized hyperbolic skewed‐t block equicorrelation copula with time‐varying volatility and dependence parameters that naturally accommodates asymmetries and heavy tails, as well as nonlinear and time‐varying default dependence. We apply a conditional law of large numbers in this setting to define joint and conditional risk measures that can be evaluated quickly and reliably. We apply the modeling framework to assess the joint risk from multiple defaults in the euro area during the 2008–2012 financial and sovereign debt crisis. We document unprecedented tail risks between 2011 and 2012, as well as their steep decline following subsequent policy actions. Copyright © 2016 John Wiley & Sons, Ltd.

Modeling default dependence with the mixture of calendar time and business time

Evaluating default correlation between securities in a portfolio is very important for credit derivatives pricing and risk management. Under the framework of the structural model proposed by Black and Cox, we assume that the asset values of companies are driven by Brownian motions in the worlds of the calendar time and the business time; they then could evolve continuously or by leap. We build the dynamic default correlations using the time-varying correlated Brownian motions in these processes. The sensitivity of default correlations to the key parameters is explored in the paper by numerical examples, and we apply the model to risk management as well. Because default times are unpredictable in the proposed model, the defaults might occur suddenly. Independent defaults and complete correlated defaults can be described in the model as well.

Inferring Correlations of Asset Values and Distances-to-Default from CDS Spreads: A Structural Model Approach

Using structural credit risk models to estimate default dependence requires estimates of correlations of changes in distance-to-default. We present a structural model that yields simple relations between asset value, distance-to-default, and CDS spreads, allowing the correlations to be estimated from CDS spreads. We generalize the model to include a randomly varying default boundary; in this version the distance-to-default dynamics also depend on the movement of the default boundary. The CDS spread correlations we estimate exceed equity correlations, consistent with a randomly varying default boundary. We also present evidence that variations in funding liquidity affect the correlations, consistent with recent models.

Wrong Way Risk Done Right

We present an arbitrage-free valuation framework for the counterparty exposure of credit derivatives portfolios based on a Clayton dynamical default dependency approach. The method is able to capture consistently the effects of credit spread volatility and credit correlations. By introducing fast semi-analytical approximations of the conditional survival probabilities we demonstrate how the proposed approach can be used to handle large size portfolios of CDS under financially realistic models of default intensities.

Portfolio Diversification in Concentrated Bond and Loan Portfolios

I develop an algorithm to approximate the loss rate distribution for fixed income portfolios with obligor concentrations. The approximation requires no advanced mathematics or statistics, only the summation of large exposures and the evaluation of binomial probabilities. The approximation is model-independent and can be used after removing default dependence using any risk modeling approach. It is especially useful for capital calculations given its inherent accuracy in the upper tail of the cumulative portfolio loss rate distribution. The approximation provides a simple way to calculate the capital needed when a marginal credit is added to a concentrated portfolio.

Modeling Financial Sector Joint Tail Risk in the Euro Area

We develop a novel high-dimensional non-Gaussian modeling framework to infer measures of conditional and joint default risk for many financial sector firms. The model is based on a dynamic Generalized Hyperbolic Skewed-t block-equicorrelation copula with time-varying volatility and dependence parameters that naturally accommodates asymmetries, heavy tails, as well as non-linear and time-varying default dependence. We apply a conditional law of large numbers in this setting to define joint and conditional risk measures that can be evaluated quickly and reliably. We apply the modeling framework to assess the joint risk from multiple defaults in the euro area during the 2008–2012 financial and sovereign debt crisis. We document unprecedented tail risks during 2011–2012, as well as their steep decline after subsequent policy actions.

CVA calculation for CDS under a contagion model with regime-switching intensities

This paper considers the bilateral credit valuation adjustment (CVA) of a credit default swap (CDS) under a contagion model with regime-switching intensities, where the interest rate, the recovery, and the default intensities of the investor, the protection seller and the reference entity are all driven by a continuous-time homogenous Markov chain describing the macro-economy. By using the idea of “change of measure” and some formulas for the Laplace transforms of the cumulated intensities, we obtain the formula for the bilateral CVA of a CDS contract in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations. Based on the results, we perform some numerical experiments to examine how the regime-switching and the default dependence affect the bilateral CVA.

Counterparty risk for CDS: Default clustering effects

We derive a closed-form expression for the bilateral credit valuation adjustment of a credit default swap in presence of simultaneous defaults. We develop our analysis under a default intensity model specified by a class of three-dimensional subordinators, allowing for default dependence through common risk factors. We performance a suitable decomposition of the bilateral price into debit and credit valuation adjustment components. Those components do not have a symmetric impact on the price because of the joint event occurrences. Our analysis indicates that simultaneous defaults have material impact on the size and directionality of the adjustments. Our findings suggest policymakers to consider default clustering when designing counterparty valuation procedures, especially during periods of financial distress.

Counterparty Risk: A Review

This review provides formal definitions of the terms credit value adjustment (CVA) and debt value adjustment (DVA). Estimating these quantities requires modeling the probabilities of default and the loss given default, recognizing the dependence structure among all these inputs. In practice, marginal distributions are used and a copula function assumed. Although it has long been known that different copula functions can produce very different price estimates, keeping marginal distributions constant, there is little empirical evidence about the appropriate form of function to use for modeling default dependence. This review discusses the use of collateral for risk mitigation and its effects on CVA. Regulators have argued that standardized contracts should be cleared through central counterparties (CCPs). However, there are arguments against CCPs.

Bilateral counterparty risk valuation for credit default swap in a contagion model using Markov chain

The computation of the bilateral counterparty valuation adjustment for a credit default swap (CDS) contract is in effect the modeling of the default dependence among the investor, the protection seller, and the reference entity. We present a contagion model, where defaults of three parties are all driven by a common continuous-time Markov chain describing the macroeconomic conditions. We give the explicit formula for the bilateral credit valuation adjustment (CVA) of CDS and examine the effect of the regime switching on the CVA.

Pricing credit default swaps with bilateral counterparty risk in a reduced form model with Markov regime switching

This paper provides an intensity-based model with Markov regime switching. We assume that the default intensities depend on the economic state described by a Markov chain and that default dependence comes from common shock. We derive some closed-form expressions for the joint distribution of the default times and a pricing formula of credit default swap (CDS) with bilateral counterparty risk. We use two different approaches to obtain the closed pricing formula. We perform some numerical experiments to examine how the default intensities and the regime switching affect the CDS spread.

Banking systemic vulnerabilities: A tail-risk dynamic CIMDO approach

This study proposes a novel framework which combines marginal probabilities of default estimated from a structural credit risk model with the consistent information multivariate density optimization (CIMDO) methodology and the generalized dynamic factor model (GDFM) supplemented by a dynamic t-copula. The framework models banks’ default dependence explicitly and captures the time-varying non-linearities and feedback effects typical of financial markets. It measures banking systemic credit risk in the three forms categorized by the European Central Bank: (1) credit risk common to all banks; (2) credit risk in the banking system conditional on distress on a specific bank or combinations of banks; and (3) the buildup of banking system vulnerabilities over time which may unravel disorderly. In addition, the estimates of the common components of the banking sector short-term and conditional forward default measures contain early warning features, and the identification of their drivers is useful for macroprudential policy. Finally, the framework produces robust out-of-sample forecasts of the banking systemic credit risk measures. This paper advances the agenda of making macroprudential policy operational.

A Markov Chain Copula Model for Credit Default Swaps with Bilateral Counterparty Risk

Reduced-form credit risk models are widely used in pricing and hedging credit derivatives. Generating default dependency is the key element in any such model. In this article, we use Markov copulae approach to model the dependence structure of defaults between the three obligors, one is the reference entity, another is the protection seller, the other is the protection buyer(the investor), so we can consider the bilateral counterparty risk of credit default swaps(CDS). In this Markov chain copula model, we obtain the explicit formulas of the CDS premium rates C 1(T) (with unilateral counterparty risk) and C 2(T) (with bilateral counterparty risk). And then we perform some numerical experiments to analyze the difference of the fair spreads between the unilateral case and the bilateral case.

A multifactor bottom-up model for pricing credit derivatives

In this note we continue the study of the stress event model, a simple and intuitive dynamic model for credit risky portfolios, proposed by Duffie and Singleton (1999). The model is a bottom-up version of the multi-factor portfolio credit model proposed by Longstaff and Rajan (2008). By a novel identification of independence conditions, we are able to decompose the loss distribution into a series expansion which not only provides a clear picture of the characteristics of the loss distribution but also suggests a fast and accurate approximation for it. Our approach has three important features: (i) it is able to match the standard CDS index tranche prices and the underlying CDS spreads, (ii) the computational speed of the loss distribution is very fast, comparable to that of the Gaussian copula, (iii) the computational cost for additional factors is mild, allowing for more flexibility for calibrations and opening the possibility of studying multi-factor default dependence of a portfolio via a bottom-up approach. We demonstrate the tractability and efficiency of our approach by calibrating it to investment grade CDS index tranches.

Measuring Credit Risk in a Large Banking System: Econometric Modeling and Empirics

We develop a novel high-dimensional non-Gaussian modeling framework to infer conditional and joint risk measures for many financial sector firms. The model is based on a dynamic Generalized Hyperbolic Skewed-t block-equicorrelation copula with time-varying volatility and dependence parameters that naturally accommodates asymmetries, heavy tails, as well as non-linear and time-varying default dependence. We demonstrate how to apply a conditional law of large numbers in this setting to define risk measures that can be evaluated quickly and reliably. We apply the modeling framework to assess the joint risk from multiple financial firm defaults in the euro area during the 2008-2012 financial and sovereign debt crisis. We document unprecedented tail risks during 2011-12, as well as their steep decline after subsequent policy actions.

Bilateral Exposures and Systemic Solvency Risk

By introducing a structure of the balance sheets of the banks, which takes into account their bilateral exposures in terms of stocks or lendings, we get a structural model for default analysis. This model allows distinguishing the exogenous and endogenous default dependence. We prove the existence and uniqueness of the liquidation equilibrium, we study the consequences of exogenous shocks on the banking system and we measure contagion phenomena. This approach is illustrated by an application to the French banking system

Bilateral exposures and systemic solvency risk

Abstract By introducing a structure of the balance sheets of the banks, which takes into account their bilateral exposures in terms of stocks or lendings, we get a structural model for default analysis. This model allows us to distinguish the exogenous and endogenous default dependence. We prove the existence and uniqueness of the liquidation equilibrium, we study the consequences of exogenous shocks on the banking system and we measure contagion phenomena. This approach is illustrated by an application to the French banking system.