Computing the survival probability in the Madan–Unal credit risk model: application to the CDS market

We obtain a quasi-analytical approximation of the survival probability in the credit risk model proposed in [Madan, D.B. and Unal, H., Pricing the risk of default. Rev. Deriv. Res., 1998, 2(2), 121–160]. Such a formula, which extensive numerical simulations reveal to be accurate and computationally fast, can also be employed for pricing credit default swaps (CDSs). Specifically, we derive a quasi-analytical approximate expression for CDS par spreads, and we use it to estimate the parameters of the model. The results obtained show a rather satisfactory agreement between theoretical and real market data.     

The Credit Risk and Pricing of OTC Options

In the over-the-counter (OTC) markets, the options traded are always subject to credit risk. Therefore the counterparty’s credit risk is a striking factor when pricing options, whereas it is not considered in the classic Black-Scholes models. Based on the first passage time models, this paper develops the credit risk and valuation model for the European options in the OTC markets, incorporating a practical default trigger mechanism. The default probability and the pricing formulae of the OTC options are obtained by using partial differential equation (PDE) techniques, especially Green’s function.     

Credit cycles and macro fundamentals

We use an intensity-based framework to study the relation between macroeconomic fundamentals and cycles in defaults and rating activity. Using Standard and Poor's U.S. corporate rating transition and default data over the period 1980–2005, we directly estimate the default and rating cycle from micro data. We relate this cycle to the business cycle, bank lending conditions, and financial market variables. In line with earlier studies, the macro variables appear to explain part of the default cycle. However, we strongly reject the correct dynamic specification of these models. The problem is solved by adding an unobserved dynamic component to the model, which can be interpreted as an omitted systematic credit risk factor. By accounting for this latent factor, many of the observed macro variables loose their significance. There are a few exceptions, but the economic impact of the observed macro variables for credit risk remains low. We also show that systematic credit risk factors differ over transition types, with risk factors for downgrades being noticeably different from those for upgrades. We conclude that portfolio credit risk models based only on observable systematic risk factors omit one of the strongest determinants of credit risk at the portfolio level. This has obvious consequences for current modeling and risk management practices.     

Effect of rollover risk on default risk: Evidence from bank financing

We study the effect of rollover risk on the risk of default using a comprehensive database of U.S. industrial firms during 1986–2013. Dependence on bank financing is the key driver of the impact of rollover risk on default risk. Default risk and rollover risk present a significant positive relation in firms dependent on bank financing. In contrast, rollover risk is uncorrelated with default probability in the case of firms that do not rely on bank financing. Our measure of rollover risk is the amount of long-term debt maturing in one year, weighted by total assets. In the case of a firm that depends on bank financing, an increase of one standard deviation in this measure leads to a significant increase of 3.2% in its default probability within one year. Other drivers affecting the interaction between rollover risk and default risk are whether a firm suffers from declining profitability and has poor credit. Additionally, rollover risk's impact on default probability is stronger during periods when credit market conditions are tighter.     

Can Listing Information Indicate Borrower Credit Risk in Online Peer-to-Peer Lending?

Effective assessment of borrower credit risk is the greatest challenge for peer-to-peer (P2P) lenders, especially in the Chinese market, where borrowers lack widely recognized credit scores. In this study, based on credit data from 2012 to 2015 from the website Renrendai.com, a logit model was used to assess borrower credit risk and predict the probability of default in every out-of-sample listing. The predicted probability of default was then compared with the actual default observation of default. The empirical results show that the logit model can evaluate the credit risk of P2P borrowers, and the model reduces the default rate to 9.5%, compared with the total sample default rate of 16.5%.     

Valuation of Portfolio Credit Derivatives with Default Intensities Using the Vasicek Model

We present a methodology for valuing portfolio credit derivatives under a reduced form model for which the default intensity processes of risk assets follow the one-factor Vasicek model. A closed-form solution of joint survival time distribution is obtained. The solution is applied to value credit derivatives of a credit default swap index and collateralized debt obligation. The limitation of methods using the Vasicek model is discussed. We propose that the method is valid and efficient for a portfolio with small-scale correlated risk assets, for which the acceptable size is much greater than for the traditional method. Numerical examples and parameter analysis are also presented.     

Controlling Risk in Accounts Receivable Management

In granting trade credit, the credit manager must weigh the expected profit from a sale against the risk of customer default. A common procedure is to sell on credit only to those customers whose risk of default is below some critical level. This procedure does not effectively control a firm's ratio of bad debt to sales. In this paper, formulas are derived for the variance of this ratio under various assumptions regarding the number and size distribution of customers. Knowledge of this variance enables the credit manager to more accurately control his credit losses.     

Empirical credit cycles and capital buffer formation

We model 1927–1997 US business failure rates using an unobserved components time series model. Clear evidence is found of cyclical behavior in default rates. We also detect significant longer term movements in default rates and default correlations. In a multi-year backtest experiment we show that accommodation of default rate dynamics has important consequences for credit risk capitalization requirements. Static or myopic variants of credit portfolio models miss significant periods of credit risk accumulation. Empirically congruent dynamic models by contrast provide more timely warning signals of credit risk build-up. In this way they may mitigate some of the pro-cyclicality concerns.     

Stochastic reserve changes and expansion of bank credit: The case of additional risks

In this paper we examine the effects of introducing additional risks to the Orr-Mellon-Cooper model on the asymptotic behavior of bank credit expansion, and derive monetary policy implications therefrom. Our model of additional risks corrects a loss of generality existing in the Orr-Mellon-Cooper model. It shows that the local solution for optimal credit expansion is the global solution, regardless of the parameters of the reserve loss functions, when the default risk is introduced. The analysis further points out necessary conditions to determine the direction of credit changes caused by a monetary injection under uncertainty.     

Optimal Portfolios with Credit Default Swaps

Using a continuous-time, stochastic, and dynamic framework, this study derives a closed-form solution for the optimal investment problem for an agent with hyperbolic absolute risk aversion preferences for maximising the expected utility of his or her final wealth. The agent invests in a frictionless, complete market in which a riskless asset, a (defaultable) bond, and a credit default swap written on the bond are listed. The model is calibrated to market data of six European countries and assesses the behaviour of an investor exposed to different levels of sovereign risk. A numerical analysis shows that it is optimal to issue credit default swaps in a larger quantity than that of bonds, which are optimally purchased. This speculative strategy is more aggressive in countries characterised by higher sovereign risk. This result is confirmed when the investor is endowed with a different level of risk aversion. Finally, we solve a static version of the optimisation problem and show that the speculative/hedging strategy is definitely different with respect to the dynamic one.     

The term structure of credit spreads with jump risk

Default risk analysis is important for valuing corporate bonds, swaps, and credit derivatives and plays a critical role in managing the credit risk of bank loan portfolios. This paper offers a theory to explain the observed empirical regularities on default probabilities, recovery rates, and credit spreads. It incorporates jump risk into the default process. With the jump risk, a firm can default instantaneously because of a sudden drop in its value. As a result, a credit model with the jump risk is able to match the size of credit spreads on corporate bonds and can generate various shapes of yield spread curves and marginal default rate curves, including upward-sloping, downward-sloping, flat, and hump-shaped, even if the firm is currently in a good financial standing. The model also links recovery rates to the firm value at default so that the variation in recovery rates is endogenously generated and the correlation between recovery rates and credit ratings before default reported in Altman [J. Finance 44 (1989) 909] can be justified.     

Credit risk spillovers and cash holdings

This paper examines how credit risk spillovers affect corporate financial flexibility. We construct separate empirical proxies to disentangle the two channels of credit risk spillovers—credit risk contagion (CRC), where one firm's default increases the distress likelihood of another; and product market rivalry (PMR), where the same default strengthens the position of a competitor. We show that firms facing greater CRC have weaker subsequent operating performance and must contend with less favorable bank loan terms. Meanwhile, they accumulate more cash by issuing equity, selling assets, and reducing investment and payout. In contrast, PMR generally has opposite, albeit weaker, effects. Our findings suggest that credit risk spillovers, especially CRC, play an important role in corporate liquidity management.     

基于KMV模型的中国短期融资券信用风险评级研究

针对短期融资券主体信用评级未能完全准确地反映出短期融资券信用风险的问题,本文引入信用风险计量的KMV模型,运用Matlab软件计算出短期融资券的违约距离,按照违约距离的大小通过聚类分析将样本划分为六组。在此基础上,以信用利差表示投资者对短期融资券信用风险的认可,将各组信用利差与其违约距离对应起来,对各组的信用利差进行方差分析,结果显示各组之间的差异非常显著,表明分组状况比较理想,按违约距离判断短期融资券的信用风险是合适的,实现了对短期融资券的信用风险评级。     

Incorporating the dynamics of leverage into default prediction

A firm’s current leverage ratio is one of the core characteristics of credit quality used in statistical default prediction models. Based on the capital structure literature, which shows that leverage is mean-reverting to a target leverage, we forecast future leverage ratios and include them in the set of default risk drivers. An out-of-sample analysis of default predictions from a hazard model reveals that the discriminative power increases substantially when leverage forecasts are included. We further document that credit ratings contain information beyond the one contained in standard variables but that this information is unrelated to forecasts of leverage ratios.     

Implied Default Probability and Credit Derivatives

Recently many kinds of credit derivatives are traded in the market. The default probability implied in the market becomes important to price some credit derivatives. Also it is useful for managing the credit risk because it includes the market information. In this paper we show how to calculate the implied default probability in the default swap market or the defaultable bond market.This paper is developed from author’s master thesis (Matsumoto, 2000), Graduate School of Systems Management, the University of Tsukuba.     

Interaction of credit and liquidity risks: Modelling and valuation

In this paper we discuss the interaction of default risk and liquidity risk on pricing financial contracts. We show that two risks are almost indistinguishable if the underlying contract has non-negative values; however, if it can take both positive and negative values then these two risks demand different risk premiums depending on their loss rates and distributions. We discuss a structural default model and a discrete time default model with exponentially distributed liquidity shocks. We show that short-term yield spreads are dominated by liquidity risk rather than credit risk. We suggest a two-stage procedure to calibrate the model with one scalar optimization problem and one linear programming problem.     

News sentiment and sovereign credit risk

We explore the impact of media content on sovereign credit risk. Our measure of media tone is extracted from the Thomson Reuters News Analytics database. As a proxy for sovereign credit risk we consider credit default swap (CDS) spreads, which are decomposed into their risk premium and default risk components. We find that media tone explains and predicts CDS returns and is a mixture of noise and information. Its effect on risk premium induces a temporary change in investors’ appetite for credit risk exposure, whereas its impact on the default component leads to reassessments of the fundamentals of sovereign economies.     

Credit Derivatives and the Default Risk of Large Complex Financial Institutions

This paper proposes and implements a multivariate model of the coevolution of the first and second moments of two broad credit default swap indices and the equity prices of sixteen large complex financial institutions. We use this empirical model to build a bank default risk model, in the vein of the classic Merton-type, which utilises a multi-equation framework to model forward-looking measures of market and credit risk using the credit default swap (CDS) index market as a measure of the conditions of the global credit environment. In the first step, we estimate the dynamic correlations and volatilities describing the evolution of the CDS indices and the banks’ equity prices and then impute the implied assets and their volatilities conditional on the evolution and volatility of equity. In the second step, we show that there is a substantial ‘asset shortfall’ and that substantial capital injections and/or asset insurance are required to restore the stability of our sample institutions to an acceptable level following large shocks to the aggregate level of credit risk in financial markets.     

Default correlation: An empirical investigation of a subprime lender

In recent years, subprime lending has grown substantially as an important sector of the credit markets. This paper is concerned with the risk management of subprime loan portfolios and the importance of default correlation in measuring that risk. Using a large portfolio of residential subprime loans from an anonymous subprime lender, we show that default correlation is substantial for this lender. In particular, the significance of default correlation increases as the internal credit rating declines. Our results suggest that lenders and regulators would be well served investing in the understanding of default correlation in subprime portfolios.     

Credit Derivatives in an Affine Framework

An efficient method for valuing credit derivatives based on three entities is developed in an affine framework. This includes interdependence of market and credit risk, joint credit migration and counterparty default risk of three firms. As an application we provide closed form expressions for the joint distribution of default times, default correlations, and default swap spreads in the presence of counterparty default risk. Vienna Institute of Finance is funded by WWTF (Vienna Science and Technology Fund).