Default Dependence Research Articles

Default dependence in the insurance and banking sectors: A copula approach

We employ a time-varying asymmetric copula model that combines the generalized autoregressive score model with the generalized hyperbolic skewed t copula to capture the dynamics and asymmetry of default dependence between insurers and banks. We identify the term structure of default dependence between these two sectors. The short-term and long-term dependence of default risk rise and converge during financial crises. We explore the determinants of the time-series variation in default dependence. While traditional macro variables can explain only a small portion of the variation in default dependence, we find a significant negative correlation between default dependence and global geopolitical risk.

Accounting for PD-LGD dependency: A tractable extension to the Basel ASRF framework

We extend the asymptotic single risk factor (ASRF) model used in the Basel regulations to accommodate the dependence between the probabilities of default (PD) and the losses given default (LGD) with arbitrary marginal distributions. The PD-LGD link is introduced via the single systematic risk factor and its strength is controlled via a dedicated parameter, in line with the treatment of the default dependence in the current Basel framework. We derive the explicit form of the mapping function translating unconditional LGDs into conditional ones, compute the portfolio-invariant semi-analytical formula of value-at-risk and propose a calibration method. An empirical study featuring defaulted corporate bonds confirms the validity of the calibration procedure and delivers realistic risk metrics. The proposed approach is easy to implement and is useful to design future guidelines for capital requirements, to perform sensitivity analysis or to compute implied downturn LGDs. Compared to the guidelines of the European Banking Authority, our approach delivers more conservative figures on the considered data.

On the Diversification of Fixed Income Assets

This article introduces a new approach for dealing with the diversification/concentration risk of fixed income assets. Because Government bonds, corporate bonds, and mortgage backed securities constitute a large proportion of the assets of institutional investors in most countries, it is important to be able to determine the number of lines/issuers of such assets, not only for portfolio management but also for risk management purposes. The approach that I introduce shows the dependence of the critical number of lines of fixed income assets on the main interest rate risk and credit risk drivers. Specifically, I examine the importance of volatility risk, force of mean reversion, default risk, recovery risk, and default dependence risk on the critical number of assets in a fixed income portfolio. The methodology in this paper relies on the use of the coefficient of variation for the computation of the critical number of credit-sensitive securities in a fixed income portfolio. To the best of my knowledge, this paper is the first to develop such an approach.

Measuring systemic risk and contagion in the European financial network

This paper introduces a novel framework to study default dependence and systemic risk in a financial network that evolves over time. We analyse several indicators of risk, and develop a new latent space model to assess the health of key European banks before, during and after the recent financial crises. We propose a new statistical model that permits a latent space visualisation of the financial system. This provides a clear and interpretable model-based summary of the interaction data, and it gives a new perspective on the topology structure of the network. Crucially, the methodology provides a new approach to assess and understand the systemic risk associated with a financial system, and to study how debt may spread between institutions. Our dynamic framework provides an interpretable map that illustrates the default dependencies between institutions, highlighting the possible patterns of contagion and the institutions that may pose systemic threats.

FACTOR COPULA MODEL FOR PORTFOLIO CREDIT RISK

A critical aspect in the valuation and risk management of multi-name credit derivatives is the modeling of the dependence among sources of credit risk. The dependence modeling poses difficulties in the pricing of a multi-name credit derivatives, in the estimation of the value-at-risk of a portfolio, or in the pricing of some other basket credit derivative as the description not only on the default arrival in an individual reference entity but on the default dependence among entities in the portfolio should be considered. Although the elliptical models have been widely used due to their mathematical tractability, the dependence modeling using the multi-dimensional Lévy process has shown growing interest among researchers despite its complexity. In this paper, we introduce one factor copula model for portfolio credit risk based on Normal Tempered Stable (NTS) distribution and calibrate the model through 5-year synthetic Collateralized Debt Obligation (CDO) tranche spreads under a large homogeneous portfolio approximation. The calibration results show that the one factor copula model based on NTS distribution is more flexible and provides a dependence structure fitting market CDO tranche spreads. As one of the major applications of the dependence modeling in credit risk, this model shares the advantage of the Gaussian one factor model, and all extensions and implementation methods used for it can be utilized.

Implications of Default Dependency on Portfolio Risk

We highlight important and specific characteristics of default risk and methodological implications. In a simulation contrasting independent, Gaussian and Clayton copulas, we also show that joint default probabilities might be a hidden source of risk in conventional portfolio models of default.

On the Diversification of Fixed Income Assets

This article introduces a new approach for dealing with the diversification/concentration risk of fixed income assets. Because Government bonds, corporate bonds, and mortgage securities constitute most of the assets of insurance companies in most countries, it is important to be able to determine the number of lines/issuers of such assets, not only for portfolio management, but also for risk management purposes. The approach that we introduce allows us to show the dependence of the critical number of lines of fixed income assets on the main interest rate risk and credit risk drivers. Specifically, we examine the importance of volatility risk, force of mean reversion, default risk, recovery risk, and default dependence risk on the critical number of fixed income assets in which an insurance business should invest.

Financial derivatives and default dependence: a time-varying copula approach

ABSTRACT The fast development of financial derivatives links financial institutions more closely. In this paper, we investigate the joint default dependence among financial institutions and its association with the recent development of financial derivatives. Two interesting findings emerge. First, time-varying default risk dependencies of financial institutions are found during our sample period. Second, the fast growth of derivatives markets contributes to the rising correlated default risk among financial institutions and further leads to an increase in systemic risk. We show that the default correlation spike coincides with the boom in the US credit derivatives market.

The Impact of Default Dependency and Collateralization on Asset Pricing and Credit Risk Modeling

This article presents a comprehensive framework for valuing financial instruments subject to credit risk and collateralization. In particular, we focus on the impact of default dependence on asset pricing, as correlated default risk is one of the most pervasive threats to financial markets. Some well-known risky valuation models in the markets can be viewed as special cases of this framework. We introduce the concept of comvariance (or comrelation) into the area of credit risk modeling to capture the default relationship among three or more parties. Accounting for default correlations and comrelations becomes important, especially during the credit crisis. Moreover, we find that collateralization works well for financial instruments subject to bilateral credit risk, but fails for ones subject to multilateral credit risk.

Spatial Dependence in Subprime Mortgage Defaults

We analyze the spatial default dependence between pairs of nonconforming securitized mortgages, originated in Los Angeles between 2000 and 2011 and clustered by zip code. Our approach allows us to estimate the range and shape of the spatial dependence function, which relates zip-code center-to-center distance between mortgages to the dependence parameter of a number of different copulas. We find significant evidence for the presence of spatial dependence, which decays to zero within 40km and can be well characterized by a squared exponential function, a special case of the Matern spatial correlation function.

Pricing Financial Derivatives Subject to Multilateral Credit Risk and Collateralization

This article presents a new model for valuing financial contracts subject to credit risk and collateralization. Examples include the valuation of a credit default swap (CDS) contract that is affected by the trilateral credit risk of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.

Dual-frailty default intensity model: estimations and an application

In this paper, a new default intensity model with dual frailties is proposed and an empirical evidence is provided to confirm the model’s adequacy. In addition to the conventional explanatory variables, Duffie et al. introduces a time frailty and Chava et al. considers an industrial frailty to model the conditional default dependence. However, from an empirical study on Taiwan’s public listed firms, Lin and Chen points out that the time frailty can only catch the default dependence along the time but not among the industries. On the other hand, the industrial frailty can only capture the default dependence from the industrial correlation but not from the time dependence. Hence, the default intensity model with time and industrial frailties is recommended. This paper introduces a dual frailty model to incorporate time and industrial frailties. Using the empirical data of Taiwan’s public listed firms from January of 1995 to January of 2015, the dual frailty model is estimated and the Fisher’s dispersion tests are conducted for bins from time and from industries. Our empirical findings indicate that the dual frailty model captures not only the time dependence of default clustering but also the industrial correlations. Therefore, our dual frailty model outperforms the intensity model with time frailty of Duffie et al. and the industrial frailty of Chava et al.

Intersectoral default contagion: A multivariate Poisson autoregression analysis

This paper analyzes credit rating default dependencies in a multisectoral framework. Using Mergent's FISD database, we study the default series in the U.S. over the last two decades, disaggregating defaults by industry-sector group. During this period, two main waves of default occurred: the implosion of the “dot-com” bubble and the global financial crisis. We estimate a Multivariate Autoregressive Conditional Poisson model according to the biweekly number of defaults that occurred in different sectors of the economy from 1996 to 2015. We discuss the contagion effect between sectors in two ways: the degree of transmission of the probability of default from one sector to another, i.e., the “infectivity” of the sector, and the degree of contagion of one sector from another, i.e., the “vulnerability” of the sector. Our results show differences between the sectors' relations during the first and second part of our sample. We add some exogenous variables to the analysis and evaluate their contribution to the goodness of fit.

Controlling Default Contagion Through Small-World Networks Analysis

In our increasingly connected business environment, an enterprise’s financial downturn can spread to its economic associates, a phenomenon defined as default contagion. In academic research, the default contagion is usually measured by the default dependence degree. This paper utilizes the Copula metric method to capture the default dependence degree, and studies the default dependence degree of listed companies in China through quantitative analysis. Related properties of default dependence of the listed companies are then explored through a simulation method. Results find that the default dependence degrees of listed companies in China present the remarkable characteristics of a small-world network, which are a high cluster and a short path. This indicates that once the core company defaults, the adverse effect will quickly spread to other companies through the network diffusion effect of the financial market. Hence, this study can provide some theoretical basis for the design of a mechanism to prevent and control large-scale default events.

Pricing Financial Derivatives Subject to Multilateral Credit Risk and Collateralization

This article presents a new model for valuing financial contracts subject to credit risk and collateralization. Examples include the valuation of a credit default swap (CDS) contract that is affected by the trilateral credit risk of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.

The Valuation of Credit Default Swap with Counterparty Risk and Collateralization

This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.

Modelling Credit Risk in the Jump Threshold Framework

ABSTRACTThe jump threshold framework for credit risk modelling developed by Garreau and Kercheval enjoys the advantages of both structural- and reduced-form models. In their article, the focus is on multidimensional default dependence, under the assumptions that stock prices follow an exponential Lévy process (i.i.d. log returns) and that interest rates and stock volatility are constant. Explicit formulas for default time distributions and basket credit default swap (CDS) prices are obtained when the default threshold is deterministic, but only in terms of expectations when the default threshold is stochastic. In this article, we restrict attention to the one-dimensional, single-name case in order to obtain explicit closed-form solutions for the default time distribution when the default threshold, interest rate and volatility are all stochastic. When the interest rate and volatility processes are affine diffusions and the stochastic default threshold is properly chosen, we provide explicit formulas for the default time distribution, prices of defaultable bonds and CDS premia. The main idea is to make use of the Duffie–Pan–Singleton method of evaluating expectations of exponential integrals of affine diffusions.

Modelling default dependence in automotive supply networks using vine-copula

This paper presents an intuitive model for default dependencies in supply networks and its application in firms’ capital management. Modern supply chain networks are characterised by horizontal ties between firms within a particular industry or group, which are sequentially arranged based on vertical ties between firms in different layers. The recognition and accounting of these simultaneous interdependencies is crucial for a more advanced understanding of complex inter-organisational relations. Using the state-of-the art vine-copulae, we model these multidimensional interdependencies in the automotive industry, and capture the default tail dependency between alliance partners. Further, we apply our model to determine the optimal economic capital, such that companies can absorb unexpected losses from defaults in supply chain, while avoiding over-capitalisation. Our findings should spur managers to analyse their supplier networks with respect to default dependencies and to take this phenomenon into consideration when making sourcing decisions.

Pricing Credit Default Swap Subject to Counterparty Risk and Collateralization

This article presents a new model for valuing a credit default swap (CDS) contract that is affected by multiple credit risks of the buyer, seller and reference entity. We show that default dependency has a significant impact on asset pricing. In fact, correlated default risk is one of the most pervasive threats in financial markets. We also show that a fully collateralized CDS is not equivalent to a risk-free one. In other words, full collateralization cannot eliminate counterparty risk completely in the CDS market.

RISE AND FALL OF SYNTHETIC CDO MARKET: LESSONS LEARNED

This paper uses a unique data set of more than 1000 synthetic Collateralized Debt Obligations (CDOs) deals to describe typical structures, their pricing and performance with the aim of identifying the factors behind the spectacular collapse of this important segment of structured credit market in late 2008. The data suggests that mark-to-market losses on many synthetic CDO tranches were much more significant than in case of simpler, lower-rated products despite the former experiencing little or no impairment of the notional. The losses were driven instead by the concentration of relatively limited number of defaults in a short period of time, suggesting that pre-crisis pricing must have seriously underestimated such risk of default clustering. In view of the post-crisis pick-up in synthetic CDO issuance, the paper attempts to heed this lesson and offer a simple factor model of default correlation in the spirit of Marshall–Olkin that is naturally suited to capturing the temporal dimension of default dependencies that have been crucial for synthetic CDOs investors. The model allows building a rich dependence structure capable of consistently fitting standardized iTraxx and CDX index tranches, which makes it ideal for pricing bespoke CDOs.