Default Correlation Research Articles

Моделі ціноутворення кредитних деривативів

Derivatives play an important role in the processes that take place in the global economy and economic growth. They are critical for hedging risks in the banking sector, managing the interest rate in the activities of pension funds, satisfying insurance claims for insurers and other market participants, i. e. reducing uncertainty arising from fluctuations in prices, credit rates, currency fluctuations, interest rates, etc. Today, they are actively used in the world practice of all industry sectors. The aim of the article is to develop pricing models for credit derivatives, taking into account the relationship between credit derivatives (CD) and structured credit products (SCP), as well as on the basis of identifying differences in the results of credit correlation of defaults, analyzing the evolutionary and essential characteristics of the CD and SCP markets. The authors systematized and classified them; their structural characteristics are provided; the main trends characteristic of the CD and SCP markets in the context of the markets of traditional derivatives are studied; the method of their design with the help of clinical documentation is determined; the major aspects of their modeling and pricing are considered, also an own credit product is designed and the spread is calculated using the pricing model. The article considers the problem of choosing an approach for assessing and calculating the correlation of defaults, which is an integral part of the pricing models of credit derivatives. On the basis of the given methodology for designing the SCP with the help of CD and the key aspects of modeling and pricing of CD and SCP, a basket credit default swap was designed on the basis of three corporate names. The designed product meets all the basic requirements for standard basket products in terms of content. The calculations were made based on the use of two different copulas to assess the correlation of defaults. The results can be used to design and evaluate a derivative on the correlation risk of issuers.

Multi-factor default correlation model estimation: enhancement with bootstrapping

Multi-factor default correlation model estimation: enhancement with bootstrapping

A Framework for Integrating Extreme Weather Risk, Probability of Default, and Loss Given Default for Residential Mortgage Loans

This paper considers a hypothetical case in which a bank wants to build a routine climate stress test exercise on residential mortgage loans. The bank has regularly updated the probability of default (PD) and loss given default (LGD) on each residential mortgage loan under the internal-rating-based (IRB) approach of Basel II/III. Additionally, the bank estimates the stressed PD and stressed LGD associated with a predetermined extreme weather event. Using simulation techniques, this paper shows that the loss of the bank’s residential mortgage portfolio can reach a median of around 36% of the portfolio value. This remarkable loss comes from the effects of default correlation and property damage. Banks should pay more attention to such impacts of extreme weather events.

THE CORRELATION IN CORPORATE DEFAULTS: EVIDENCE FROM NON-FINANCIAL LISTED COMPANIES IN SRI LANKA

Default correlation is the extent to which one company's default causes another's default. It measures the relationship between a firm’s individual default probability and the joint default probability among firms. This study makes theoretical contributions by examining the degree of default correlation among non-financial listed firms in terms of credit quality, time horizon, systematic risk, firm size, and liquidity. The researcher selected 550 firm-year observations (240 for default and 310 for non-default) consisting of 55 non-financial listed companies in Sri Lanka from 2012 to 2021. The default firms are selected using the three criteria during the selection period: suffering from losses, having negative net worth, or suffering from negative operating cash flows for more than three consecutive years. The non-default firms are selected by a couple with the default firms based on the same industry and the highest market capitalization. Altman’s (1968) Z-score model is used to determine the credit ratings as high, medium, and low. The study follows Lucas’s (1995) proposed standard binomial approach to measure the default correlation. The study revealed that time horizon, poor credit ratings, high beta, and small size increase the default correlation in the Sri Lankan context; however, liquidity is not a good measurement for default correlation analysis in Sri Lankan context. Credit risk management could underestimate the portfolio credit risk without considering the default correlation. The dynamic nature of default correlation shows that an increment in default risk of individual credit assets engages with a disproportionate increment in portfolio credit assets.

Emerging Market Default Risk Charge Model

In a default event, several obligors simultaneously experience financial difficulty in servicing their debt to the point where the entire market can experience a sudden yet significant jump to a credit default. To help protect lenders against a jump-to-default event, regulators require banks to hold capital equivalent to the default risk charge as a buffer against the losses they may incur. The Basel regulatory committee has articulated and set default risk modelling guidelines to improve comparability amongst banks and enable a consistent bank-wide default risk charge estimation. Emerging markets are unique because they usually have illiquid markets and sparse data. Thus, implementing an emerging market default risk model and, at the same time, complying with the regulatory guidelines can be non-trivial. This research presents a framework for modelling the default risk charge in emerging markets in line with the regulatory requirements. The default correlation model inputs are derived and empirically calibrated using emerging market data. The paper ends with some considerations that regulators, supervisors, and banks can use to get financial institutions to adopt an emerging markets default risk charge model.

IRB Asset and Default Correlation: Rationale for the Macroprudential Mark-Ups to the IRB Risk-Weights

IRB Asset and Default Correlation: Rationale for the Macroprudential Mark-Ups to the IRB Risk-Weights

A contagion process with self-exciting jumps in credit risk applications

The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a significant role in allocating capital for solvency purposes. In this article, we derive a closed-form expression for the default probability of a single firm and probability of the total number of defaults by time $t$ in a homogeneous portfolio. We use a contagion process to model the arrival of credit events causing the default and develop a framework that allows firms to have resistance against default unlike the standard intensity-based models. We assume the point process driving the credit events is composed of a systematic and an idiosyncratic component, whose intensities are independently specified by a mean-reverting affine jump-diffusion process with self-exciting jumps. The proposed framework is competent of capturing the feedback effect. We further demonstrate how the proposed framework can be used to price synthetic collateralized debt obligation (CDO). Finally, we present the sensitivity analysis to demonstrate the effect of different parameters governing the contagion effect on the spread of tranches and the expected loss of the CDO.

IRB PD model accuracy validation in the presence of default correlation: a twin confidence interval approach

The BIS indicated in July 2020 an unprecedented rise in default risk correlation as a result of pandemics-induced credit risks’ accumulation. A third of the world banking assets credit risk measurement depends on the Basel internal-ratings-based (IRB) models. To ensure financial stability, we wish IRB models to be accurate in default probability (PD) forecasting. There naturally arises a question of which model may be deemed accurate if the data demonstrates the presence of the default correlation. The existing prudential IRB validation guidelines suggest a confidence interval of up to 100 percentage points’ length for such a case. Such an interval is useless as any model and any PD forecast seem accurate. The novelty of this paper is the justification for the use of twin confidence intervals to validate PD model accuracy. Those intervals more concentrate around the two extremes (default and its absence), the higher the default correlation is.

Effects of disruption risk on a supply chain with a risk-averse retailer

<p style='text-indent:20px;'>This paper studies a supply chain consisting of two unreliable suppliers and a retailer, where the two suppliers' default risks are correlated. We use a mean-variance function to characterize the retailer's risk aversion. In the case of exogenous wholesale prices, we find that the retailer's risk aversion has a non-monotonic effect on its total ordering quantity. We also show that when the suppliers' default correlation increases, the retailer's total ordering quantity is non-increasing. In the case of endogenous wholesale prices, we find that the profits of the suppliers and the retailer are non-monotonic in retailer's risk aversion level or suppliers' default correlation. As risk aversion level increases, the retailer becomes less sensitive to wholesale prices. Finally, the numerical results indicate that when the suppliers' delivery rates are different, the supplier with a low delivery rate can benefit from the retailer's risk aversion under certain conditions.</p>

Credit portfolio optimization: A multi-objective genetic algorithm approach

The algorithm for optimization of a credit portfolio has not been fully demonstrated. This paper fills the gap in the literature by presenting a general approach for optimizing a credit portfolio by minimizing the default risk of the entire portfolio. Default risk is measured with quadratic weighting and a matrix containing information about the default intensity of two stocks and the correlation in default between them. The default correlation and the default intensity are represented with a novel bivariate intensity model. A multi-objective genetic algorithm is introduced to optimize a credit portfolio with the purpose of overcoming limitations in the analytical method and improving the efficiency of optimization. The algorithm can be applied to a portfolio's credit risk management, which is particularly crucial for investors and regulars in emerging markets.

Sometimes more, sometimes less: Prudence and the diversification of risky insurance coverage

We analyze the optimal coverage level for an unreliable insurance contract if a utility-maximizing policyholder can transfer the intrinsic nonperformance risk to several co-insurers. Our discussion starts with an insurance demand model under default risk and the introduction of a multiple risk-sharing instrument called co-insurance policy. Subsequently, we examine the interrelation between the recovery rate and the optimal coverage level, the utility of the policyholder, and the optimal coverage level in the limit. We then consider the monotonicity of the optimal coverage level for a changing number of co-insurers and an increasing default correlation. Our proposed criteria indicate that the policyholders’ preferences for more or less coverage are primarily determined by their degree of prudence. We conclude that more prudent policyholders are more likely to accept the costs for any risk management measure intended to provide a hedge against default rik in insurance contracts.

Parameter estimation of default portfolios using the Merton model and phase transition

We discuss the parameter estimation of the probability of default (PD), the correlation between the obligors, and a phase transition. In our previous work, we studied the problem using a beta-binomial distribution. A non-equilibrium phase transition with an order parameter occurs when the temporal correlation decays by a power law. In this study, we adopt the Merton model, which uses an asset correlation as the default correlation, and find that a phase transition occurs when the temporal correlation decays by the power law. When the power index is less than one, the PD estimator converges slowly. Thus, it is difficult to estimate the PD with limited historical data. Conversely, when the power index is greater than one, the convergence speed is inversely proportional to the number of samples. We investigate the empirical default data history of several rating agencies. The estimated power index is in the slow-convergence range when we use long history data. This suggests that the PD can have a long memory and that it is difficult to estimate parameters due to slow convergence.

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.

Modeling Portfolio Credit Risk Taking into Account the Default Correlations Using a Copula Approach: Implementation to an Italian Loan Portfolio

This work aims to illustrate an advanced quantitative methodology for measuring the credit risk of a loan portfolio allowing for diversification effects. Also, this methodology can allocate the credit capital coherently to each counterparty in the portfolio. The analytical approach used for estimating the portfolio credit risk is a binomial type based on a Monte Carlo Simulation. This method takes into account the default correlations among the credit counterparties in the portfolio by following a copula approach and utilizing the asset return correlations of the obligors, as estimated by rigorous statistical methods. Moreover, this model considers the recovery rates as stochastic and dependent on each other and on the time until defaults. The methodology utilized for coherently allocating credit capital in the portfolio estimates the marginal contributions of each obligor to the overall risk of the loan portfolio in terms of Expected Shortfall (ES), a risk measure more coherent and conservative than the traditional measure of Value-at-Risk (VaR). Finally, this advanced analytical structure is implemented to a hypothetical, but typical, loan portfolio of an Italian commercial bank operating across the overall national country. The national loan portfolio is composed of 17 sub-portfolios, or geographic clusters of credit exposures to 10,500 non-financial firms (or corporates) belonging to each geo-cluster or sub-portfolio. The outcomes, in terms of correlations, portfolio risk measures and capital allocations obtained from this advanced analytical framework, are compared with the results found by implementing the Internal Rating Based (IRB) approach of Basel II and III. Our chief conclusion is that the IRB model is unable to capture the real credit risk of loan portfolios because it does not take into account the actual dependence structure among the default events, and between the recovery rates and the default events. We underline that the adoption of this regulatory model can produce a dangerous underestimation of the portfolio credit risk, especially when the economic uncertainty and the volatility of the financial markets increase.

How correlation risk in basket credit derivatives might be priced and managed?

Abstract In this paper, we construct quantitative models in which the dependence structure of the firms’ default times is incorporated. Such models serve as the underlying frameworks in our proposed approach to price and hedge basket credit derivatives. Through the Gaussian copula-based method, we model the default correlation risk and develop valuation formulas for credit derivatives. Using single-name derivatives in a hedging strategy for basket credit derivatives, the utility of the delta and delta-gamma hedging techniques are examined. This enables the management of risk attributed to the changes in correlation without the need for a large number of hedging instruments. Our research contributions provide insights on how dependent risks in basket credit derivatives could be dealt with effectively.

A note on the calculation of default probabilities in “Structural credit risk modeling with Hawkes jump–diffusion processes”

Ma and Xu (2016) proposed a Hawkes jump–diffusion model for the firm’s value to describe the unexpectedness of default and default clustering in the framework of Merton’s structural default. However, the authors resorted to Monte-Carlo simulations for the calculation of the default probability and the default correlation, as no other solution method was available in the literature. In this note, we present a closed-form solution for the probability of default and the default correlation using the characteristic function. Our new solution can substantially improve the computational efficiency for the problem.

From equity to default correlation with taxes

For fixed income investment, the preponderant risk is the clustering of defaults in the portfolio. Accurate prediction of such clustering depends on the knowledge of default correlation. We develop models with exogenous debt and endogenous debt to predict default correlations from equity correlations based on a self-consistent structural framework. We also examine how taxes affect the prediction of default correlations based on the two models. The empirical analysis shows that the corporate taxes tend to decrease default correlations, while personal taxes could increase or decrease default correlations. Our default correlation model with exogenous debt does a better job of predicting default correlations for high quality bonds, while the one with endogenous debt predicts more accurately for lower rated bonds. Our studies not only theoretically improve the modeling of default correlation in the structural setting but also shed new light on various aspects of default correlations and thereby help financial practitioners price credit derivatives more accurately and formulate more effective strategies to manage default risk of credit portfolios.

Corporate governance and correlation in corporate defaults

AbstractResearch Question/IssueThis study examines the effect of weak corporate governance in terms of concentrated ownership, low board effectiveness, low financial transparency and higher shareholder rights on default correlation when firms have different credit qualities.Research Findings/InsightsUsing historical default data in the United States from 2000 to 2015, we find that the degree of default correlation increases disproportionately for firms with concentrated ownership, low board effectiveness, low financial transparency and disclosures, and higher shareholder rights. More importantly, the effect of weak corporate governance on default correlation is high during a financial crisis.Theoretical/Academic ImplicationsThis is one of the first studies testing the impact of corporate governance on the correlation in corporate defaults. It indicates new avenues of research for both corporate governance and credit risk management in relation to why joint default probabilities vary among firms.Practitioner/Policy ImplicationsOur results imply that good corporate governance is essential for credit risk management because poor corporate governance may increase individual default risk and create the domino effect of credit defaults. Practitioners and policy makers should enhance control over poor governance practices to reduce the probabilities of default. Moreover, the impact of corporate governance on correlation in corporate defaults is more pronounced in financial crises and warrants consideration from policy makers to take steps toward cushioning its effects.

Liability-driven investments of life insurers under investment credit risk

In this paper, we present a model of liability-driven investments for life insurers by assuming that equity portfolios can be wiped out by catastrophic default risk of the firms whose stock the life insurer holds. A model of trinomial defaultable asset trees is used and it is calibrated to market data, while a stochastic programming model is set up to solve for the optimal asset allocation strategy of the life insurer to ensure maximization of assets while keeping solvency at a specific confidence level. We find relatively invariant allocations with changes to default correlation, while we find that previous models without taking credit risk explicitly into account require very high volatility parameters to reproduce allocations similar to those of the model with credit risk.

Valuation of collateralized debt obligations: An equilibrium model

In this paper, we present a new equilibrium model for pricing collateralized debt obligations (CDOs). The model is grounded on option pricing theory and features a random jump size to account for default correlation across reference entities. This feature is important for pricing CDOs during times of market turmoil. Simulation results show that jump size volatility, capturing uncertainty about the size of simultaneous corporate defaults, is a key parameter in pricing CDOs. The effect of jump size volatility on CDO spreads is substantial and depends on the relative position of the mean jump size to loss-coverage limits.