TIME‐CHANGED MARKOV PROCESSES IN UNIFIED CREDIT‐EQUITY MODELING

This paper develops a novel class of hybrid credit‐equity models with state‐dependent jumps, local‐stochastic volatility, and default intensity based on time changes of Markov processes with killing. We model the defaultable stock price process as a time‐changed Markov diffusion process with state‐dependent local volatility and killing rate (default intensity). When the time change is a Lévy subordinator, the stock price process exhibits jumps with state‐dependent Lévy measure. When the time change is a time integral of an activity rate process, the stock price process has local‐stochastic volatility and default intensity. When the time change process is a Lévy subordinator in turn time changed with a time integral of an activity rate process, the stock price process has state‐dependent jumps, local‐stochastic volatility, and default intensity. We develop two analytical approaches to the pricing of credit and equity derivatives in this class of models. The two approaches are based on the Laplace transform inversion and the spectral expansion approach, respectively. If the resolvent (the Laplace transform of the transition semigroup) of the Markov process and the Laplace transform of the time change are both available in closed form, the expectation operator of the time‐changed process is expressed in closed form as a single integral in the complex plane. If the payoff is square integrable, the complex integral is further reduced to a spectral expansion. To illustrate our general framework, we time change the jump‐to‐default extended constant elasticity of variance model of Carr and Linetsky (2006) and obtain a rich class of analytically tractable models with jumps, local‐stochastic volatility, and default intensity. These models can be used to jointly price equity and credit derivatives.     

A down-and-out exchange option model with jumps to evaluate firms' default probabilities in Brazil

We develop a tractable structural model to estimate a firm's default probability by modeling its asset and debt behavior. The model incorporates jump factors. For a set of Brazilian large corporations, we compare the structural model results to the default probabilities predicted by a survival analysis applied to the Central Bank debt information database. Our model outperforms other structural models. In a last step, we use a firm's sector failure probabilities to calibrate the model. This process is executed by adjusting the model jump volatility and it helps to explain the differences between debt and equity market failure probabilities.     

Assessing credit quality from the equity market: can a structural approach forecast credit ratings?

We investigate the empirical performance of default probability prediction based on Merton's (1974) structural credit risk model. More specifically, we study if distance‐to‐default is a sufficient statistic for the equity market information concerning the credit quality of the debt‐issuing firm. We show that a simple reduced form model outperforms the Merton (1974) model for both in‐sample fitting and out‐of‐sample predictability for credit ratings, and that both can be greatly improved by including the firm's equity value as an additional variable. Moreover, the empirical performance of this hybrid model is very similar to that of the simple reduced form model. As a result, we conclude that distant‐to‐default alone does not adequately capture the firm's credit quality information from the equity market. Copyright © 2007 ASAC. Published by John Wiley & Sons, Ltd.     

Survival of high tech firms: The effects of diversity of product–market portfolios, patents, and trademarks

High tech firms can mitigate potential risks by diversifying their product–market portfolios. A key research question is how such diversification influences firm survival. A firm exits the market in two ways, specifically, dissolution and acquisition. Here, we model how the diversity of a new firm's product–market portfolio influences the times to both types of exits. Specifically, we allow for interaction effects of the competitive intensity of a firm's environment and the diversity of a firm's product–market portfolio with its patents and trademarks. Using a competing risk hazard model, we estimate the effects of various covariates on the time to exit for 1435 US high tech firms.We observed that a more diverse product–market portfolio, in conjunction with a larger number of patents, hastens the time to a firm's exit by dissolution (9% decrease in survival duration), while in conjunction with a larger number of trademarks, portfolio diversity delays the time to exit by dissolution (12% increase). A more competitive firm environment results in a greater effect on the portfolio's diversity in delaying its exit by dissolution (7% increase). On the other hand, a diverse product–market portfolio, combined with either a larger number of patents or trademarks, hastens the firm's exit by acquisition (19% and 11% decrease respectively).     

INCORPORATING RISK AND AMBIGUITY AVERSION INTO A HYBRID MODEL OF DEFAULT

It is well known that purely structural models of default cannot explain short‐term credit spreads, while purely intensity‐based models lead to completely unpredictable default events. Here we introduce a hybrid model of default, in which a firm enters a “distressed” state once its nontradable credit worthiness index hits a critical level. The distressed firm then defaults upon the next arrival of a Poisson process. To value defaultable bonds and credit default swaps (CDSs), we introduce the concept of robust indifference pricing. This paradigm incorporates both risk aversion and model uncertainty. In robust indifference pricing, the optimization problem is modified to include optimizing over a set of candidate measures, in addition to optimizing over trading strategies, subject to a measure dependent penalty. Using our model and valuation framework, we derive analytical solutions for bond yields and CDS spreads, and find that while ambiguity aversion plays a similar role to risk aversion, it also has distinct effects. In particular, ambiguity aversion allows for significant short‐term spreads.     

Implications of marketing capability and research and development intensity on firm default risk

Marketing capability and research and development intensity are firm resources used to increase firm performance and reduce investor risk. This study aims to link marketing capability and research and development intensity, and their interaction to firm default risk. This study is the first to examine marketing capability and research and development intensity regarding their influences on firm default vulnerability and to demonstrate how marketing capability may strengthen research and development intensities’ power on risk reduction. The results reveal a U-shaped relationship between research and development intensity and firm default risk, while marketing capability’s impact is unidirectional. Further, marketing capability strongly moderates the relationship between research and development intensity and firm default risk. For low marketing capability firms, the U-shaped pattern is more significant. For high marketing capability firms, the pattern is not salient and the risk reduction power of research and development intensity is stronger. This research provides useful implications for marketing theories, as well as business practice.     

On the simultaneity of real and financial policies

This study investigates the interdependencies between a firm's real and financial decisions. One cause of this interdependence is, as with several previous studies, the real costs associated with bankruptcy. A classical multiperiod model is developed which allows for the endogeneity of debt issues, interest rates, the probability of firm default, and dividends. The modeling suggests an explanation for dividend determination which differs from traditional views. The resulting explanation is that funds are always channelled into the most profitable use. Thus, the model generates an optimal quantity of dividends which cannot be altered without decreasing the expected return to equity.     

PRICING EQUITY DERIVATIVES SUBJECT TO BANKRUPTCY

We solve in closed form a parsimonious extension of the Black–Scholes–Merton model with bankruptcy where the hazard rate of bankruptcy is a negative power of the stock price. Combining a scale change and a measure change, the model dynamics is reduced to a linear stochastic differential equation whose solution is a diffusion process that plays a central role in the pricing of Asian options. The solution is in the form of a spectral expansion associated with the diffusion infinitesimal generator. The latter is closely related to the Schrödinger operator with Morse potential. Pricing formulas for both corporate bonds and stock options are obtained in closed form. Term credit spreads on corporate bonds and implied volatility skews of stock options are closely linked in this model, with parameters of the hazard rate specification controlling both the shape of the term structure of credit spreads and the slope of the implied volatility skew. Our analytical formulas are easy to implement and should prove useful to researchers and practitioners in corporate debt and equity derivatives markets.     

Distress and default contagion in financial networks

We develop a new model for solvency contagion that can be used to quantify systemic risk in stress tests of financial networks. In contrast to many existing models, it allows for the spread of contagion already before the point of default and hence can account for contagion due to distress and mark‐to‐market losses. We derive general ordering results for outcome measures of stress tests that enable us to compare different contagion mechanisms. We use these results to study the sensitivity of the new contagion mechanism with respect to its model parameters and to compare it to existing models in the literature. When applying the new model to data from the European Banking Authority, we find that the risk from distress contagion is strongly dependent on the anticipated recovery rate. For low recovery rates, the high additional losses caused by bankruptcy dominate the overall stress test results. For high recovery rates, however, we observe a strong sensitivity of the stress test outcomes with respect to the model parameters determining the magnitude of distress contagion.     

Monotonicities in a Markov Chain Model for Valuing Corporate Bonds Subject to Credit Risk

In recent years, it has become common to use a Markov chain model to describe the dynamics of a firm's credit rating as an indicator of the likelihood of default. Such a model can be used not only for describing the dynamics but also for valuing risky discount bonds. The aim of this paper is to explain how the Markov chain model leads to the known empirical findings such that prior rating changes carry predictive power for the direction of future rating changes and a firm with low (high, respectively) credit rating is more likely to be upgraded (downgraded) conditional on survival as the time horizon lengthens. The model will also explain practically plausible statements such as that bond prices as well as credit risk spreads would be ordered according to their credit qualities. Stochastic monotonicities of absorbing Markov chains play a prominent role in these issues.     

On the Prediction of Corporate Financial Distress in the Light of the Financial Crisis: Empirical Evidence from Greek Listed Firms

This paper evaluates the impact of accounting and market-driven information on the prediction of bankruptcy for Greek firms using the discrete hazard approach. The findings show that a hazard model that incorporates three accounting ratio components of Z-score and three market-driven variables is the most appropriate model for the prediction of corporate financial distress in Greece. This model outperforms a univariate model that uses the expected default frequency (EDF) derived from the Merton distance to default model, a multivariate model that is exclusively based on accounting variables, a model that combines the EDF and accounting variables, and a multivariate model that uses only market-driven variables. Classification accuracy and bankruptcy forecast tests confirm the main results. The model is also able to sustain high long-term performance when augmenting the forecast horizon from one to two and three years.     

Firm exit after distress: differentiating between bankruptcy, voluntary liquidation and M&A

This paper examines firm-level determinants of mature firm exits after economic distress. Using nested logit models and a sample of 6,118 distress-related exits in Belgium, we analyze the type of exit that distressed firms experience. We show that 41% of the firms in our sample exit through a court driven exit procedure (mainly bankruptcy), 44% are voluntarily liquidated and 14% are acquired, merged or split (hereafter M&A). Distressed firm exit follows two distinct stages. First, a firm either decides to exit voluntarily or is forced into bankruptcy, which is the least efficient exit strategy. Compared to bankruptcy, the probability of a voluntary exit increases with higher levels of cash, lower leverage, holding no secured debt and being embedded in a group. If a firm exits voluntarily, it enters a second stage and decides either to exit through voluntary liquidation or through a M&A. Conditional on not going bankrupt, the likelihood of voluntary liquidation compared to M&A increases with higher levels of cash or secured debt, with smaller size and with an absence of group relations. We contribute to the firm exit literature by jointly analyzing three exit types and showing that bankruptcy and voluntary liquidation are fundamentally different exit routes. While voluntary liquidation is an important exit route for distressed firms, most previous studies have failed to distinguish between bankruptcy and liquidation. We hence contribute to the exit literature by showing that bankruptcy, voluntary liquidation and M&A are fundamentally distinct exit routes for distressed firms, driven by different firm level characteristics and following a two-stage process.     

The geographic determinants of bankruptcy: evidence from Switzerland

This paper examines the geographic determinants of firm bankruptcy. We employ hazard rate models to study the bankruptcy risk of a firm, allowing for time-varying covariates. Based on a large sample from all geographic areas and the major sectors of the Swiss economy, we find the following main results: (1) Bankruptcy rates tend to be lower in the central municipalities of agglomerations; (2) bankruptcy rates are lower in regions with favorable business conditions (where corporate taxes and unemployment are low and public investment is high); (3) private taxes and public spending at the local level have little impact on bankruptcy rates.     

OPTIMAL INVESTMENT IN CREDIT DERIVATIVES PORTFOLIO UNDER CONTAGION RISK

We consider the optimal portfolio problem of a power investor who wishes to allocate her wealth between several credit default swaps (CDSs) and a money market account. We model contagion risk among the reference entities in the portfolio using a reduced‐form Markovian model with interacting default intensities. Using the dynamic programming principle, we establish a lattice dependence structure between the Hamilton‐Jacobi‐Bellman equations associated with the default states of the portfolio. We show existence and uniqueness of a classical solution to each equation and characterize them in terms of solutions to inhomogeneous Bernoulli type ordinary differential equations. We provide a precise characterization for the directionality of the CDS investment strategy and perform a numerical analysis to assess the impact of default contagion. We find that the increased intensity triggered by default of a very risky entity strongly impacts size and directionality of the investor strategy. Such findings outline the key role played by default contagion when investing in portfolios subject to multiple sources of default risk.     

DYNAMIC DEFAULTABLE TERM STRUCTURE MODELING BEYOND THE INTENSITY PARADIGM

The two main approaches in credit risk are the structural approach pioneered by Merton and the reduced‐form framework proposed by Jarrow and Turnbull and by Artzner and Delbaen. The goal of this paper is to provide a unified view on both approaches. This is achieved by studying reduced‐form approaches under weak assumptions. In particular, we do not assume the global existence of a default intensity and allow default at fixed or predictable times, such as coupon payment dates, with positive probability. In this generalized framework, we study dynamic term structures prone to default risk following the forward‐rate approach proposed by Heath, Jarrow, and Morton. It turns out that previously considered models lead to arbitrage possibilities when default can happen at a predictable time. A suitable generalization of the forward‐rate approach contains an additional stochastic integral with atoms at predictable times and necessary and sufficient conditions for an appropriate no‐arbitrage condition are given. For efficient implementations, we develop a new class of affine models that do not satisfy the standard assumption of stochastic continuity. The chosen approach is intimately related to the theory of enlargement of filtrations, for which we provide an example by means of filtering theory where the Azéma supermartingale contains upward and downward jumps, both at predictable and totally inaccessible stopping times.     

OPTIMAL DIVIDEND POLICY WITH MEAN-REVERTING CASH RESERVOIR

Motivated by empirical evidence and economic arguments, we assume that the cash reservoir of a financial corporation follows a mean reverting process. The firm must decide the optimal dividend strategy, which consists of the optimal times and the optimal amounts to pay as dividends. We model this as a stochastic impulse control problem, and succeed in finding an analytical solution. We also find a formula for the expected time between dividend payments. A crucial and surprising economic result of our paper is that, as the dividend tax rate decreases, it is optimal for the shareholders to receive smaller but more frequent dividend payments. This results in a reduction of the probability of default of the firm.     

Environmental Hostility and Firm Behavior—An Empirical Examination of New Technology-Based Firms on Science Parks

Firms often respond to challenging environmental conditions, such as those in high-technology environments. Thus, in a hostile environment, the intensity of competition exerts more pressure on the firm and also a greater necessity for firm behavior. This study was conducted with empirical data collected in 1999 from 134 small firms on science parks in Sweden. The discussion in this paper is focused at the firm level. Analysis of firm behavior was conducted using a multivariate approach. The content of firm-level behavior is defined in terms of the firm's overall collection of business practices and competitive tactics. The investigation of customer preferences and competitors are the manifestations of the firm's more basic strategic direction and how the firm will reach the markets. Two different types of firms were analyzed: university spin-offs (USOs) and corporate spin-offs (CSOs). The importance of the science park was included in the study as a control variable. The variable showed whether the firms had received support from a science park. This study indicated that the relations between change of marketing activities and long-term forecasting are strongest for both USOs and CSOs. The long-term forecasting, technology–importance of science park, was another key factor. This is exemplified by the two samples used in this study.     

Labor Productivity in the Efficiency-Wage Model: A Consideration of the Firm's Death Rate

It is inappropriate to equate the "representative firm" with the typical firm, particularly for economies which consist of small enterprises where a large number of jobs are created or disappear as establishments are born or die. If workers care about the job disappearance risk, their utility and effort offered will be influenced by the death rate of firms. This paper sets out an efficiency-wage model and takes the probability of the firm's closure into account. By extension, it is shown that equilibrium labor productivity is plausibly procyclical under certain circumstances, which is consistent with the stylized facts observed in many countries.     

The sources of management innovation: When firms introduce new management practices

Management innovation is the introduction of management practices new to the firm and intended to enhance firm performance. Building on the organizational reference group literature, this article shows that management innovation is a consequence of a firm's internal context and of the external search for new knowledge. Furthermore the article demonstrates a trade-off between context and search, in that there is a negative effect on management innovation associated with their joint occurrence. Finally the article shows that management innovation is positively associated with firm performance in the form of subsequent productivity growth.     

Deconstructing the notion of blame in corporate failure

Corporate failure is the subject of considerable academic debate since the 1960s. Failure in the retail sector receives less attention however. This paper addresses the notion of blame in corporate failure. Reference to A Goldberg and Sons, a failed retailer, exemplifies the discussion. Prior to bankruptcy in 1990, this firm was a successful Scottish department store and clothing retailer. The study takes a historical approach, using in-depth interviews, archival material, and other secondary data sources. Findings reveal that, despite warning signs from various key performance indicators and external reviews, the company's board failed to act appropriately. A series of bad strategic decisions contributed to the company's failure. In line with theories of blame attribution, through their (in)actions, the board's negligence played a major role in the firm's demise.