Dynamic prediction of hedge fund survival in crisis-prone financial markets

This study focuses on dynamic changes in survival probabilities over the lifetimes of hedge funds. To model such probabilities, a mixed Cox proportional hazards (CPH) model-specifically, a survival/hazard model with time-varying covariates and fixed covariates- is employed. Resulting dynamic survival probabilities show that the mixed CPH model provides significantly higher accuracy in predicting hedge fund failure than other models in the literature, including fixed covariate CPH models and discrete logit models. Our results are useful to investors and regulators of hedge funds in crisis-prone financial markets.     

Mortgage Termination: An Empirical Hazard Model with a Stochastic Term Structure

Pricing for mortgage and mortgage-backed securities is complicated due to the stochastic and interdependent nature of prepayment and default risks. This paper presents a unified economic model of the contingent claims and competing risks of mortgage termination by prepayment and default. I adopt a proportional hazard framework to analyze these competing and interdependent risks in a model with time-varying covariates. The paper incorporates a stochastic interest rate model into the hazard function for prepayment. The empirical results reported in the paper provide new evidence about the ruthlessness of default and prepayment behavior and the sensitivity of these decisions to demographic as well as financial phenomena. The results also illustrate that evaluating the interest rate contingent claims with a stochastic term structure has effects on predicting not only the mortgage prepayment behavior but also the mortgage default behavior.     

Forecasting forward defaults: a simple hazard model with competing risks

A forward default prediction method based on the discrete-time competing risk hazard model (DCRHM) is proposed. The proposed model is developed from the discrete-time hazard model (DHM) by replacing the binary response data in DHM with the multinomial response data, and thus allowing the firms exiting public markets for different causes to have different effects on forward default prediction. We show that DCRHM is a reliable and efficient model for forward default prediction through maximum likelihood analysis. We use actual panel data-sets to illustrate the proposed methodology. Using an expanding rolling window approach, our empirical results statistically confirm that DCRHM has better and more robust out-of-sample performance than DHM, in the sense of yielding more accurate predicted number of forward defaults. Thus, DCRHM is a useful alternative for studying forward default losses on portfolios.     

An Estimation Model for the Term Structure of Yield Spread

An estimation model for term structure of yield spread has become an extremely important subject to evaluate securities with default risk. By Duffie and Singleton model, yield spread was explained by two factors, namely collection rate and default probability. An estimation of the collection rate is given from historical earnings data, but estimation of default probability is known to be a remaining problem.There are some approaches to express default probability. One of them is to describe it through hazard process, and the other is to represent it by risk neutral transition probability matrix of credit-rating class. Some models that use Gaussian type hazard process or Vasicek type hazard process have already constructed.An advantage of evaluation using a rating transition probability matrix is that it is easy to obtain an image of movement of the credit-rating class. We do not need to show the calculation basis of the threshold or an assumption for distribution of prospective yield spread. But the model that uses the risk neutral transition probability matrix has not established yet, because of the computational difficulty required to estimate large number of the parameters.At first, for the purposes of this article, we will estimate the term structure of credit spreads results from the possibility of future defaults. It is assumed that credit risk is specified as a discrete-state Markov chain. And we construct a model which can be used to estimate the baseline transition matrix of the credit-rating class, risk-adjusting factors, industrial drift factors, corporate drift factors and recovery ratio, from yield spreads for individual bond. This enables us to compute the implied term structure from market data. We are capable of computing the implied term structure from market date by this process. Next, we will provide a valuation model for the term structure of yield spread.     

Risk aversion and the yield of corporate debt

This paper develops a model to estimate the implied default probability of corporate bonds. The model explicitly considers the risk averse behavior of investors to provide a more precise framework for estimating the implied default probability. A Kalman filter method is used to estimate time-varying risk premium associated with the investor's risk aversion. The results of nonlinear regressions indicate that previous risk-neutrality models consistently overestimate the implied default rates of corporate bonds. The results also suggest that investors may have been adequately compensated for investment in risky bonds.     

Predicting bankruptcy using the discrete-time semiparametric hazard model

The usual bankruptcy prediction models are based on single-period data from firms. These models ignore the fact that the characteristics of firms change through time, and thus they may suffer from a loss of predictive power. In recent years, a discrete-time parametric hazard model has been proposed for bankruptcy prediction using panel data from firms. This model has been demonstrated by many examples to be more powerful than the traditional models. In this paper, we propose an extension of this approach allowing for a more flexible choice of hazard function. The new method does not require the assumption of a parametric model for the hazard function. In addition, it also provides a tool for checking the adequacy of the parametric model, if necessary. We use real panel datasets to illustrate the proposed method. The empirical results confirm that the new model compares favorably with the well-known discrete-time parametric hazard model.     

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.     

Pricing defaultable bonds: a middle-way approach between structural and reduced-form models

In this paper we present a valuation model that combines features of both the structural and reduced-form approaches for modelling default risk. We maintain the cause and effect or ‘structural’ definition of default and assume that default is triggered when a state variable reaches a default boundary. However, in our model, the state variable is not interpreted as the assets of the firm, but as a latent variable signalling the credit quality of the firm. Default in our model can also occur according to a doubly stochastic hazard rate. The hazard rate is a linear function of the state variable and the interest rate. We use the Cox et al. (A theory of the term structure of interest rates. Econometrica, 1985, 53(2), 385–407) term structure model to preclude the possibility of negative probabilities of default. We also horse race the proposed valuation model against structural and reduced-form default risky bond pricing models and find that term structures of credit spreads generated using the middle-way approach are more in line with empirical observations.     

Pricing of credit default index swap tranches with one-factor heavy-tailed copula models

In this paper, we provide two one-factor heavy-tailed copula models for pricing a collateralized debt obligation and credit default index swap tranches: (1) a one-factor double t distribution with fractional degrees of freedom copula model and (2) a one-factor double mixture distribution of t and Gaussian distribution copula model. A time-varying tail-fatness parameter is introduced in each model, allowing one to change the tail-fatness of the copula function continuously. Fitting our model to comprehensive market data, we find that a model with fixed tail-fatness cannot fit market data well over time. The two models that we propose are capable of fitting market data well over time when using a proper time-varying tail-fatness parameter. Moreover, we find that the time-varying tail-fatness parameters change dramatically over a one-year period.     

Does modeling framework matter? A comparative study of structural and reduced-form models

This study provides a rigorous empirical comparison of structural and reduced-form credit risk frameworks. The literature differentiates between structural models that are based on modeling of the evolution of the balance sheet of the issuer, and reduced-form models that specify credit risk exogenously by a hazard rate process. Until now, there has been no common agreement in academia and practice on which model framework better captures credit risk. As major difference we focus on the discriminative modeling of the default time. In contrast to the previous literature, we calibrate both approaches to the same data set, apply comparable estimation techniques, and assess the out-of-sample prediction quality on the same time series of credit default swap prices. As our empirical implementations of both approaches rely on the same market information we are able to judge whether empirically the model structure itself makes an important difference. Interestingly, our study shows that the models’ prediction power are quite close on average indicating that for pricing purposes the modeling type does not greatly matter compared to the input data used. Still, the reduced-form approach outperforms the structural for investment-grade names and longer maturities. In contrast the structural approach performs better for shorter maturities and sub-investment grade names.     

Predicting unlisted SMEs' default: Incorporating market information on accounting-based models for improved accuracy

The risk associated with lending to small businesses has become more important since regulations started obliging banks to use separate procedures in assessing SMEs' credit worthiness. However, current accounting-based models for SMEs do not account for the impact of market information on default prediction. We fill this gap in the literature by introducing a hybrid default prediction model for unlisted SMEs that uses market information of listed SMEs (comparable approach) alongside existing accounting information of unlisted SMEs. Our results suggest that the accuracy of this default prediction modelling approach in the hold-out sample, during the period of the financial crisis 2007-09 and for the entire sample-period, improves considerably. We conclude that the proposed hybrid model is a good replacement for existing standard accounting-based methods on SMEs' default prediction.     

A Prepayment Model for the Japanese Mortgage Loan Market: Prepayment-Type-Specific Parametric Model Approach

This paper proposes a framework for construction of a prepayment model suitedto the Japanese mortgage loan market and assesses the validity of thisframework based on an empirical analysis using data from Japan. In thisframework, a model is constructed for each of three prepayment types, namely,`full prepayment', `partial prepayment', and `subrogation', using a parametricproportional hazards model, which was also employed by Schwartz and Torous(1989). Combining these three types of models allows one to take into accountthe effects of partial prepayments, which are frequently used in the Japanesemortgage market, and to simultaneously construct a model for both prepaymentand default. Time-dependent (path-dependent) covariates are introduced intothe model, which are estimated by the maximum likelihood method based on thefull likelihood that takes into account the time-dependence of the covariates.Results of the empirical analysis indicate that the hazard functions differsubstantially depending on the prepayment type. In addition, results indicatethat the fit of the model can be improved by the distinction of prepaymenttypes and the introduction of the market interest rates as path-dependentcovariates.     

A new mixture cure model under competing risks to score online consumer loans

In credit scoring, survival analysis models have been widely applied to answer the question as to whether and when an applicant would default. In this paper, we propose a novel mixture cure proportional hazards model under competing risks. Most existing mixture cure models either do not consider competing risks or generally assume that a subpopulation of subjects is immune to any risk from all the competing risks. Compared with existing models, the proposed model is more flexible since it assumes that a subpopulation of subjects is immune to a subset of risks instead of being immune to all the risks. To estimate model parameters, we derive the likelihood function of the proposed model, based on which an expectation maximization estimation algorithm is developed. A simulation algorithm is designed to simulate time-to-event observations from the proposed model, and simulation studies are conducted to verify the proposed methodology. A real world example of credit scoring for online customer loans based on the proposed model is demonstrated.     

Default Clustering Risks in Commercial Mortgage-Backed Securities

This paper proposes an intensity-based pricing model with default dependence structure for CMBS bonds. Three features are incorporated into the proposed model. First, default is a Poisson jump process defined by a function of mortgage rating information. Second, property risks are modeled using a high dimensional Brownian motion process that captures both systematic risk and idiosyncratic risk in property value. Third, default dependence structure is built into the extended model. Based on a set of input parameters, we simulate various pricing effects on a hypothetical CMBS using the proposed model structure. The results of the base-line intensity model show that yield spreads on CMBS bonds increase in the recovery rate, but decreases in the hazard rate. Security structured with smaller subordination tranche exposes CMBS bonds to higher default risks. The model predicts that default clustering increases required yield spreads of CMBS bonds. At a 70% recovery rate and a 3% default hazard rate, yield spreads of Junior bonds are expected to increase by 169 basis points when counterparty risks increase by 50%. The results highlight the importance of clustering risks associated with counterparty default when valuing CMBS bonds.     

Credit rating dynamics in the presence of unknown structural breaks

In many credit risk and pricing applications, credit transition matrix is modeled by a constant transition probability or generator matrix for Markov processes. Based on empirical evidence, we model rating transition processes as piecewise homogeneous Markov chains with unobserved structural breaks. The proposed model provides explicit formulas for the posterior distribution of the time-varying rating transition generator matrices, the probability of structural break at each period and prediction of transition matrices in the presence of possible structural breaks. Estimating the model by credit rating history, we show that the structural break in rating transitions can be captured by the proposed model. We also show that structural breaks in rating dynamics are different for different industries. We then compare the prediction performance of the proposed and time-homogeneous Markov chain models.     

Measuring systemic risk: A factor-augmented correlated default approach

In this paper, we extend existing correlated default models for measuring systemic risk by proposing a model that incorporates an observable common factor that features conditional heteroscedasticity. The addition of the common factor helps to effectively capture realistic time-varying characteristics in individual asset return volatility as well as return correlations. We apply the model for large US financial institutions. The common factor proves its importance in explaining asset return dynamics and measuring systemic risk. We also apply the model in the context of systemic risk contribution analysis and show its applicability.     

Distressed debt prices and recovery rate estimation

This paper has two purposes. First, it uses distressed debt prices to estimate recovery rates at default. In this regard, estimates are obtained for three recovery rate models: recovery of face value, recovery of Treasury, and recovery of market value. We show that identifying the “economic” default date, as distinct from the recorded default date, is crucial to obtaining unbiased estimates. The economic default date is defined to be the first date when the market prices the firm’s debt as if it has defaulted. An implication is that the standard industry practice of using 30-day post default prices to compute recovery rate yields biased estimates. Second, we construct and estimate a distressed debt pricing model. We use this model to implicitly estimate the parameters of the embedded recovery rate process and to price distressed debt. Our distressed debt pricing model fits market prices well, with an average pricing error of less than one basis point.      

Correlation in corporate defaults: Contagion or conditional independence?

We revisit a method used by Das et al. (2007) (DDKS) who jointly test and reject a specification of firm default intensities and the doubly stochastic assumption in intensity models of default. The method relies on a time change result for counting processes. With an almost identical set of default histories recorded by Moody’s in the period from 1982 to 2006, but using a different specification of the default intensity, we cannot reject the tests based on time change used in DDKS. We then note that the method proposed by DDKS is mainly a misspecification test in that it has very limited power in detecting violations of the doubly stochastic assumption. For example, it will not detect contagion which spreads through the explanatory variables “covariates” that determine the default intensities of individual firms. Therefore, we perform a different test using a Hawkes process alternative to see if firm-specific variables are affected by occurrences of defaults, but find no evidence of default contagion.     

A Markov-switching generalized additive model for compound Poisson processes,with applications to operational loss models

This paper is concerned with modelling the behaviour of random sums over time. Such models are particularly useful to describe the dynamics of operational losses, and to correctly estimate tail-related risk indicators. However, time-varying dependence structures make it a difficult task. To tackle these issues, we formulate a new Markov-switching generalized additive compound process combining Poisson and generalized Pareto distributions. This flexible model takes into account two important features: on the one hand, we allow all parameters of the compound loss distribution to depend on economic covariates in a flexible way. On the other hand, we allow this dependence to vary over time, via a hidden state process. A simulation study indicates that, even in the case of a short time series, this model is easily and well estimated with a standard maximum likelihood procedure. Relying on this approach, we analyse a novel data-set of 819 losses resulting from frauds at the Italian bank UniCredit. We show that our model improves the estimation of the total loss distribution over time, compared to standard alternatives. In particular, this model provides estimations of the 99.9% quantile that are never exceeded by the historical total losses, a feature particularly desirable for banking regulators.     

Default prediction with dynamic sectoral and macroeconomic frailties

This paper extends the macroeconomic frailty model to include sectoral frailty factors that capture default correlations among firms in a similar business. We estimate sectoral and macroeconomic frailty factors and their effects on default intensity using the data for Japanese firms from 1992 to 2010. We find strong evidence for the presence of sectoral frailty factors even after accounting for the effects of observable covariates and macroeconomic frailty on default intensity. The model with sectoral frailties performs better than that without. Results show that accounting for the sources of unobserved sectoral default risk covariations improves the accuracy of default probability estimation.