Jumps in intensity models: investigating the performance of Ornstein-Uhlenbeck processes in credit risk modeling

This work presents intensity-based credit risk models where the default intensity of the point process is modeled by an Ornstein-Uhlenbeck type process completely driven by jumps. Under this model we compute the default probability over time by linking it to the characteristic function of the integrated intensity process. In case of the Gamma and the Inverse Gaussian Ornstein-Uhlenbeck processes this leads to a closed-form expression for the default probability and to a straightforward estimate of credit default swaps prices. The model is calibrated to a series of real-market term structures and then used to price a digital default put option. Results are compared with the well known cases of Poisson and CIR dynamics. Possible extensions of the model to the multivariate setting are finally discussed.     

Premia for correlated default risk

Using data on corporate default experience in the U.S. and market rates of CDX index and tranche swaps of various maturities, we estimate reduced-form models of correlated default timing in the CDX High Yield and Investment Grade portfolios under actual and risk-neutral probabilities. The striking contrast between the estimated processes followed by the actual and risk-neutral arrival intensities of defaults, and between the parameters governing the actual and risk-neutral dynamics of the risk-neutral intensities, indicates the presence of substantial default risk premia in CDX swap market rates. The effects of risk premia on swap rates covary strongly across maturities, and depend on general stock market volatility and several measures of credit spreads. Large moves in the effects of these premia on swap rates have natural interpretations in terms of economic and financial market developments during the sample period, April 2004 to October 2007. Our results suggest that a large portion of the movements in CDX swap market rates observed during the sample period may be caused by changing attitudes toward correlated default risk rather than changes in the economic factors affecting the actual risk of clustered defaults, which ultimately governs swap payoffs.     

Spillover effects in oil-related CDS markets during and after the sub-prime crisis

This paper investigates the return and volatility spillover effects across oil-related credit default swaps (CDSs), the oil market, and financial market risks for the US during and after the subprime crises. The empirical analysis is based on monthly return and realized volatility data from February 2004 to April 2020. We estimate both static and dynamic generalized dynamic spillover measures based on vector autoregressive (VAR) models. Our full sample empirical findings show that the oil market is the primary source of risk transmission for all the oil-related credit default swaps, while the bond market is the highest source of risk transmission to the stock market and vice versa. We also provide evidence that the regulated monopoly US utility sector has the least role in volatility transmission. Furthermore, the bailout program conducted by the US Treasury and Federal Reserve helped stabilize the US financial market through the purchase of toxic assets after the subprime financial crisis. We find strong evidence that the federal funds rate hike cycles lessen total risk transmission throughout the US bond market. Finally, our findings assert that oil price shocks have a significant effect on the oil-related CDSs in some sub-periods via the demand and supply transmission channels.     

A revised version of the Cathcart & El-Jahel model and its application to CDS market

Decisions in Economics and Finance - The paper considers the pricing of credit default swaps (CDSs) using a revised version of the credit risk model proposed in Cathcart and El-Jahel (2003)....     

Comparisons of linear regression and survival analysis using single and mixture distributions approaches in modelling LGD

Estimating the recovery rate and recovery amount has become important in consumer credit due to the new Basel Accord regulation and the increase in the number of defaulters as a result of the recession. We compare linear regression and survival analysis models for modelling recovery rates and recovery amounts, in order to predict the loss given default (LGD) for unsecured consumer loans or credit cards. We also look at the advantages and disadvantages of using single and mixture distribution models for estimating these quantities.     

UNCOVERING THE COMMON RISK‐FREE RATE IN THE EUROPEAN MONETARY UNION

We introduce longitudinal factor analysis (LFA) to extract the common risk‐free (CRF) rate from a sample of sovereign bonds of countries in a monetary union. Since LFA exploits the typically very large longitudinal dimension of bond data, it performs better than traditional factor analysis methods that rely on the much smaller cross‐sectional dimension. European sovereign bond yields for the period 2006–2011 are decomposed into a CRF rate, a default risk premium and a liquidity risk premium. Our empirical findings suggest that investors chase both credit quality and liquidity, and that they price double default risk on credit default swaps. Copyright © 2013 John Wiley & Sons, Ltd.     

A mixture model for credit card exposure at default using the GAMLSS framework

The Basel II and III Accords propose estimating the credit conversion factor (CCF) to model exposure at default (EAD) for credit cards and other forms of revolving credit. Alternatively, recent work has suggested it may be beneficial to predict the EAD directly, i.e.modelling the balance as a function of a series of risk drivers. In this paper, we propose a novel approach combining two ideas proposed in the literature and test its effectiveness using a large dataset of credit card defaults not previously used in the EAD literature. We predict EAD by fitting a regression model using the generalised additive model for location, scale, and shape (GAMLSS) framework. We conjecture that the EAD level and risk drivers of its mean and dispersion parameters could substantially differ between the debtors who hit the credit limit (i.e.“maxed out” their cards) prior to default and those who did not, and thus implement a mixture model conditioning on these two respective scenarios. In addition to identifying the most significant explanatory variables for each model component, our analysis suggests that predictive accuracy is improved, both by using GAMLSS (and its ability to incorporate non-linear effects) as well as by introducing the mixture component.     

信息不完全的信用风险定价模型及其在我国的应用

基于信息不完全的信用风险定价模型与传统的结构化模型和约化模型的最大区别在于它将信息不完全这一前提引入了以信息完全为前提的结构化模型,同时它又考虑了约化模型中强度的优点,引入短期信用风险的度量,成为当前最切合现实的信用风险定价模型。本文认为,应用基于信息不完全的信用风险定价模型来测度信用风险,将具有十分重要的现实意义。     

The effect of systematic risk factors on counterparty default and credit risk of interest rate swaps

This research investigates the effect of specific systematic risk factors on credit risk pricing and capital allocation of interest rate swaps. Because of the stochastic nature of uncertain future cash flows and interest rates, practitioners typically employ the Black-Scholes option pricing model in combination with a simulation analysis to establish capital requirements and estimate the shadow price of an interest rate swap. However, this practice of pricing swap risk excludes systematic risk factors that affect the risk shadow price, thereby underestimating the capital allocation required for financial institutions. This research demonstrates the effect of risk mispricing when simulation models ignore systematic risk factors such as model risk, convexity risk, and parameter risk on the pricing of interest rate swaps.     

Credit Default Swaps: Risk Hedge or Financial Weapon of Mass Destruction?

Credit default swaps (CDSs) are contracts between buyers and sellers of protection against default. They are a form of debt insurance, or more precisely derivatives contracts that investors buy to either insure against or profit from a default. In this way CDS contracts act as a form of debt insurance in that they provide a means of protection against credit risk. In the aftermath of the global financial crisis, the CDS earned the reputation of a ‘financial weapon of mass destruction’. Why? Is this charge justified? This paper shows that the reality is more complex: CDSs carry benefit as well as costs, and the risks associated with them can be mitigated through prudent supervision.     

Credit default swaps and sovereign debt markets

This study investigates the link between the price discovery dynamics in sovereign credit default swaps (CDS) and bond markets and the degree of financial integration of emerging markets. Using CDS and sovereign bond spreads, the price discovery mechanism was tested using a vector error correction model. Financial integration is measured using news-based methods. We find that sovereign CDS and bond markets are co-integrated. In five out of seven sovereigns (71%), the bond market leads in price discovery by adjusting to new information regarding credit risk before CDS. In 29% of times, CDS markets are the source of price discovery. We also find a positive correlation of 0.67 between the degree of financial integration and the bond market information share. The evidence suggests that changes in sovereign credit risk and bond yields are significantly influenced by common external (global) factors, while country-specific factors play an insignificant role.     

Do interest rate options contain information about excess returns?

There is strong empirical evidence that long-term interest rates contain a time-varying risk premium. Options may contain valuable information about this risk premium because their prices are sensitive to the underlying interest rates. We use the joint time series of swap rates and interest rate option prices to estimate dynamic term structure models. The risk premiums that we estimate using option prices are better able to predict excess returns for long-term swaps over short-term swaps. Moreover, in contrast to the previous literature, the most successful models for predicting excess returns have risk factors with stochastic volatility. We also show that the stochastic volatility models we estimate using option prices match the failure of the expectations hypothesis.     

Asymmetric determinants of corporate bond credit spreads in China: Evidence from a nonlinear ARDL model

This study utilizes the nonlinear ARDL (NARDL) model proposed by Shin, Yu, and Greenwood-Nimmo (2014) to quantify the potentially asymmetric transmission of positive and negative changes in each of the possible determinants of industry-level corporate bond credit spreads in China. The determinants we consider include the corresponding industry stock price, China’s stock market volatility, the level and slope of the yield curve (i.e., the interest rate), the industrial production growth rate, and the inflation rate. The empirical results suggest substantial asymmetric effects of these determinants on credit spreads, with the positive changes in the determinants showing larger impacts than the negative changes for most industries we consider. Moreover, the corresponding industry stock prices, the interest rate, and the industrial production growth rate negatively drive the industry credit spreads for many industries. In turn, China’s stock market volatility and the inflation rate positively affect the credit spreads at each industry level. These findings may be helpful to investors, bond issuers and policymakers in understanding the dynamics of credit risks and corporate bond rates at the industry level.     

Forecasting and stress testing credit card default using dynamic models

We present discrete time survival models of borrower default for credit cards that include behavioural data about credit card holders and macroeconomic conditions across the credit card lifetime. We find that dynamic models which include these behavioural and macroeconomic variables provide statistically significant improvements in model fit, which translate into better forecasts of default at both account and portfolio levels when applied to an out-of-sample data set. By simulating extreme economic conditions, we show how these models can be used to stress test credit card portfolios.     

Joint Bayesian Analysis of Parameters and States in Nonlinear non‐Gaussian State Space Models

We propose a new methodology for designing flexible proposal densities for the joint posterior density of parameters and states in a nonlinear, non‐Gaussian state space model. We show that a highly efficient Bayesian procedure emerges when these proposal densities are used in an independent Metropolis–Hastings algorithm or in importance sampling. Our method provides a computationally more efficient alternative to several recently proposed algorithms. We present extensive simulation evidence for stochastic intensity and stochastic volatility models based on Ornstein–Uhlenbeck processes. For our empirical study, we analyse the performance of our methods for corporate default panel data and stock index returns. Copyright © 2016 John Wiley & Sons, Ltd.     

Credit risk and asymmetric information: A simplified approach

We present a simple model for risky, corporate debt. Debtholders and equityholders have incomplete information about the financial state of the debt issuing company. Information is incomplete because it is delayed for all agents, and it is asymmetrically distributed between debtholders and equityholders. We solve for the equityholders' optimal default policy and for the credit spreads required by debtholders. Delayed information accelerates the equityholders' optimal decision to default. Interestingly, this effect is small, implying only a small impact on credit spreads. Asymmetric information, however, has a major impact on credit spreads. Our model predicts high credit spreads for short-term debt, as observed empirically in credit markets.     

Forecasting short-term defaults of firms in a commercial network via Bayesian spatial and spatio-temporal methods

To protect financial institutions from unexpected credit losses, during the monitoring phase of granted loans it is of primary importance to foresee any evidence of a contagion of liquidity distress across a network of firms. This term indicates a situation of lack of solvency of a firm (e.g., a customer) that propagates to other firms (e.g, its suppliers), which could consequently face challenges in repaying their own granted loans. In this paper, we look for the evidence of contagion of liquidity distress on an Intesa Sanpaolo proprietary dataset by means of Bayesian spatial and spatio-temporal models. Our results indicate that such models can detect cases of distress not yet apparent from covariate information collected on the firms by instead borrowing information from the network, leading to improved forecasting performance on the prediction of short-term default with respect to state-of-the-art methods.     

Homogeneous semi-Markov reliability models for credit risk management*

Abstract The credit risk problem is one of the most important issues of modern financial mathematics. Fundamentally it consists in computing the default probability of a company going into debt. The problem can be studied by means of Markov transition models. The generalization of the transition models by means of homogeneous semi-Markov models is presented in this paper. The idea is to consider the credit risk problem as a reliability problem. In a semi-Markov environment it is possible to consider transition probabilities that change as a function of waiting time inside a state. The paper also shows how to apply semi-Markov reliability models in a credit risk environment. In the last section an example of the model is provided. Mathematics Subject Classification (2000): 60K15, 60K20, 90B25, 91B28 Journal of Economic Literature Classification: G21, G33     

Efficiency measurement with multiple outputs and multiple inputs

This paper discusses modeling technical and allocative inefficiencies in both cost minimizing and profit maximizing frameworks with special emphasis on multiple inputs and multiple outputs. Both primal and dual models are considered for this purpose. In the primal approach we use a separable output and input function (the constant elasticity of transformation output function and Cobb-Douglas input function). The dual models assume translog cost or profit functions. Technical inefficiency is assumed to be random in the cross-sectional models, and fixed firm-specific parameter in the panel data models. Allocative inefficiencies are always treated as input-specific parameters. We derive exact relations linking technical inefficiency and allocative inefficiencies to cost and profit when the underlying technology is represented by a flexible functional form such as the translog. It is shown that appending a one-sided homoscedastic error term to model technical inefficiency, or neglecting technical inefficiency altogether in a translog profit tunciton results in model misspecification and inconsistent parameter estimates.     

Recovering default risk from CDS spreads with a nonlinear filter

We propose a nonlinear filter to estimate the time-varying default risk from the term structure of credit default swap (CDS) spreads. Based on the numerical solution of the Fokker–Planck equation (FPE) using a meshfree interpolation method, the filter performs a joint estimation of the risk-neutral default intensity and CIR model parameters. As the FPE can account for nonlinear functions and non-Gaussian errors, the proposed framework provides outstanding flexibility and accuracy. We test the nonlinear filter on simulated spreads and apply it to daily CDS data of the Dow Jones Industrial Average component companies from 2005 to 2010 with supportive results.