Default Probabilities

Recently insolvent municipalities have declared bankruptcy when they are unable to meet their bond debt or pay their outstanding liability obligations.  This analysis looks at the fiscal health of Texas municipalities who have issued debt in the past two years to identify those suffering financial stress that would possibly result in the municipality seeking bankruptcy to resolve its fiscal issues.   This investigation analyzes the State of Texas and local municipalities’ fiscal health using the revised Altman Z-Score with the government’s annual financial report data.  Additional analysis relating the Z-score to entities’ bond rating is reported.  These findings provide an effective mechanism for investors and interested citizens to evaluate and identify distressed governmental entities with a possible bankruptcy risk

We develop a simple robust link between equity out-of-the-money American put options and a pure credit insurance contract on the same reference company. Assuming that the stock price stays above a barrier B > 0 before default but drops and remains below a lower barrier A < B after default, we show that the spread between two co-terminal American put options struck within the default corridor [A, B] scaled by their strike difference replicates a standardized credit insurance contract that pays one dollar at default whenever the company defaults prior to the option expiry and zero otherwise. Given the presence of the default corridor, this simple replicating strategy is robust to the details of pre-and post-default stock price dynamics, interest rate movements, and default risk fluctuations. We use quotes on American puts to infer the value of the credit insurance contract and compare it to that estimated from the credit default swap spreads. Collecting data on several companies, we identify strong co-movements between the credit insurance values inferred from the two markets. We also find that deviations between the two estimates cannot be fully explained by common variables used for explaining American put values, such as the underlying stock price and stock return volatility, but the cross-market deviations can predict future movements in American puts.

Long-term ratings of companies are obtained from public data plus some additional nondisclosed information. A model based on data from firms’ public accounts is proposed to directly obtain these ratings, showing fairly close similitude with published results from Credit Rating Agencies. The rating models used to assess the creditworthiness of a firm may involve some possible conflicts of interest, as companies pay for most of the rating process and are, thus, clients of the rating firms. Such loss of faith among investors and criticism toward the rating agencies were especially severe during the financial crisis in 2008. To overcome this issue, several alternatives are addressed; in particular, the focus is on elaborating a rating model for Moody’s long-term companies’ ratings for industrial and retailing firms that could be useful as an external check of published rates. Statistical and artificial intelligence methods are used to obtain direct prediction of awarded rates in these s...

The aim of this paper is to define a model which allows traders to assess the value of equity and credit derivatives in a unified framework. We propose closed-form formulas which traders could use to evaluate equity, equity options and credit default swaps (CDSs) in a consistent way. The model can also be used to solve the inverse problem, that is to extract credit-risk sensitive information from market quotes of equity/credit derivatives. In particular, we wish to estimate the firm's leverage, as it is perceived by traders. This goal is achieved within a model à la Leland (1994), where stockholders have a perpetual American option to default. After making the case for modeling debt in terms of a single perpetual-bond equivalent issue, we define leverage, show the stochastic nature of equity volatility and derive the term structures of default probabilities and credit spreads by making use of the first-passage time distribution function. Then, we give new formulas for call and put options written on stockholders' equity. The formulas, which depend on the leverage parameter L and make use of the univariate normal distribution function, are consistent with the volatility skew observed in the equity options market and converge to the Black-Scholes-Merton (BSM) equations for L → 1. All the Greeks are simple functions of the standard corresponding letters of the BSM model. The paper concludes with an application of the model to the case of Lehman Brothers and General Motors.

The aim of this paper is to define a model which allows traders to assess the value of equity and credit derivatives in a unified framework. We propose closed-form formulas which traders could use to evaluate equity, equity options and credit default swaps (CDSs) in a consistent way. The model can also be used to solve the inverse problem, that is to extract credit-risk sensitive information from market quotes of equity/credit derivatives. In particular, we wish to estimate the firm's leverage, as it is perceived by traders. This goal is achieved within a model à la Leland (1994), where stockholders have a perpetual American option to default. After making the case for modeling debt in terms of a single perpetual-bond equivalent issue, we define leverage, show the stochastic nature of equity volatility and derive the term structures of default probabilities and credit spreads by making use of the first-passage time distribution function. Then, we give new formulas for call and put options written on stockholders' equity. The formulas, which depend on the leverage parameter L and make use of the univariate normal distribution function, are consistent with the volatility skew observed in the equity options market and converge to the Black-Scholes-Merton (BSM) equations for L → 1. All the Greeks are simple functions of the standard corresponding letters of the BSM model. The paper concludes with an application of the model to the case of Lehman Brothers and General Motors.

Abstract: This paper discusses two of the primary motivating influences on the recentdevelopment/revisions of credit scoring models, ie, the important implications ofBasel 2 s proposed capital requirements on credit assets and the enormous amountsand rates ...

The risk neutral credit migration process captures quantitative information which is relevant to the pricing theory and risk management of credit derivatives. In this article, we derive implied migration rates by means of a recently introduced credit barrier model which is calibrated on the basis of aggregate information such as credit migration rates and credit spread curves. The model is characterized by an underlying stochastic process that represents credit quality and default events are associated to barrier crossings. The stochastic process has state dependent volatility and jumps which are estimated by using empirical migration and default rates. A risk-neutralizing drift and forward liquidity spreads are estimated to consistently match the average spread curves corresponding to all the various ratings. The implied migration rates obtained with our credit barrier model are then compared with those obtained via the Jarrow-Lando-Turnbull model by the Kijima-Komoribayashi model in a detailed example.

The risk-neutral credit migration process captures quantitative information which is relevant to the pricing theory and risk management of credit derivatives. In this article, we derive implied migration rates by means of a recently introduced credit barrier model which is calibrated ...