David Lando

Term Structures of Credit Spreads with Incomplete Accounting Information

We study the implications of imperfect information for term structures of credit spreads on corporate bonds. We suppose that bond investors cannot observe the issuers assets directly, and receive instead only periodic and imperfect accounting reports. For a setting in which the assets of the firm are a geometric Brownian motion until informed equityholders optimally liquidate, we derive the conditional distribution of the assets, given accounting data and survivorship. Contrary to the perfect-information case, there exists a default-arrival intensity process. That intensity is calculated in terms of the conditional distribution of assets. Credit yield spreads are characterized in terms of accounting information. Generalizations are provided.

On Cox Processes and Credit Risky Securities

A framework is presented for modeling defaultable securities and credit derivatives which allows for dependence between market risk factors and credit risk. The framework reduces the technical issues of modeling credit risk to the same issues faced when modeling the ordinary term structure of interest rates. It is shown how to generalize a model of Jarrow, Lando and Turnbull (1997) to allow for stochastic transition intensities between rating categories and into default. This generalization can handle contracts with payments explicitly linked to ratings. It is also shown how to obtain a term structure model for all different rating categories simultaneously and how to obtain an affine-like structure. An implementation is given in a simple one factor model in which the affine structure gives closed form solutions.

Analyzing rating transitions and rating drift with continuous observations

We consider the estimation of credit rating transitions based on continuous-time observations. Through simple examples and using a large data set from Standard and Poor’s, we illustrate the difference between estimators based on discrete-time cohort methods and estimators based on continuous observations. We apply semi-parametric regression techniques to test for two types of non-Markov effects in rating transitions: Duration dependence and dependence on previous rating. We find significant nonMarkov effects, especially for the downgrade movements. 2002 Elsevier Science B.V. All rights reserved.

Credit Risk Modeling

The chapter gives a broad outline of the central themes of credit risk modeling starting with the modeling of default probabilities, ratings and recovery.We present the two main frameworks for pricing credit risky instruments and credit derivatives. The key credit derivative - the Credit Default Swap - is introduced. The premium on this contract provides a meausure of the credit spread of the reference issuer. We then provide some key empirical works looking at credit spreads thorugh CDS contracts and bonds and finish with a description of the role of correlation in credit risk modeling.

Confidence Sets for Continuous-Time Rating Transition Probabilities

This paper addresses the estimation of default probabilities and associated confidence sets with special focus on rare events. Research on rating transition data has documented a tendency for recently downgraded issuers to be at an increased risk of experiencing further downgrades compared to issuers that have held the same rating for a longer period of time. To capture this non-Markov effect we introduce a continuous-time hidden Markov chain model in which downgrades firms enter into a hidden, excited state. Using data from Moody s we estimate the parameters of the model, and conclude that both default probabilities and confidence sets are strongly influenced by the introduction of hidden excited states. 2004 Elsevier B.V. All rights reserved. JEL classification: C41; G21; G28

Correlation in Corporate Defaults: Contagion or Conditional Independence?

We revisit a test for conditional independence in intensity models of default proposed by Das, Duffie, Kapadia, and Saita (2007) (DDKS). Based on a sample of US corporate defaults, they reject the conditional independence assumption but also observe that the test is a joint test of the specification of the default intensity of individual firms and the assumption of conditional independence. We show that using a different specification of the default intensity, and using the same test as DDKS, we cannot reject the assumption of conditional independence for default histories recorded by Moody’s in the period from 1982 to 2006. We also show, that the test proposed by DDKS is not able to detect all violations of conditional independence. Specifically, the tests will not capture contagion effects which are spread through the explanatory variables (’covariates’) used as conditioning variables in the Cox regression and which determine the default intensities of individual firms. We therefore perform different tests to see if firm-specific variables, i.e quick ratios and distance-to-default, are affected by defaults. We find no influence from defaults on Quick ratios, but some influence on distance-to-default. This suggests, that violations of conditional independence do indeed arise from balance sheet effects. JEL Classification: G33, G32, C52

Robustness of Distance-to-Default

Distance-to-default (DD) is a measure of default risk derived from observed stock prices and book leverage using the structural credit risk model of Merton (1974). Despite the simplifying assumptions that underlie its derivation, DD has proven empirically to be a strong predictor of default. We use simulations to show that the empirical success of DD may well be a result of its strong robustness to model misspecifications. We consider a number of deviations from the Merton model which involve different asset value dynamics and different default triggering mechanisms. We show that, in general, DD is successful in ranking firms’ default probabilities, even if the underlying model assumptions are altered. A possibility of large jumps in asset value or stochastic volatility challenge the robustness of DD. We propose a volatility adjustment of the distance-to-default measure that significantly improves the ranking of firms with stochastic volatility, but this measure is less robust to model misspecifications than DD.

Safe-Haven CDS Premia

Credit Default Swaps can be used to lower capital requirements of dealer banks who enter into uncollateralized derivatives positions with sovereigns. We show in a model that the regulatory incentive to obtain capital relief makes CDS contracts valuable to dealer banks and empirically that, consistent with the use of CDS for regulatory purposes, there is a disconnect between changes in bond yield spreads and in CDS premiums especially for safe sovereigns. Additional empirical tests related to volumes of contracts outstanding, effects of regulatory proxies, and the corporate bond and CDS markets support that CDS contracts are used for capital relief.

Some Lessons From CDO Markets on Mathematical Models

Bad mathematical models or over reliance on mathematical models is frequently cited as one of the culprits of the financial crisis. While models surely played a role, putting such a responsibility on models is giving too much credit to the influence that models have in the larger political decisions in financial institutions and in political decision making. Decisions to run banks with extreme leverage, to systematically try to loosen up capital constraints using off-balance sheet vehicles, searching-for-yield behavior by institutional and private investors, political desires to increase house ownership even at the cost of increasing riskiness in lending — these decisions are not deeply rooted in models. When they are, one is suspicious that the model selection has often been such that the decisions were justified in the selected models.

Intensity Modeling: The Cox Process

We define the Cox process as a randomly time-changed Poisson process and outline the most important specifications and some simple properties. An example from credit risk modeling is given. Keywords: Cox process; credit risk modeling; intensity modeling; state estimation