Extreme value statistics provides a practical, flexible, mathematically elegant framework in which to develop financial risk management tools that are consistent with empirical data. In this introductory survey, we discuss some of the basic tools including power law distributions, the peaks over...

We propose a multi-firm first-passage credit model in which investors have incomplete information. In this model, investors observe neither a firm's value nor its default barrier. The model accounts for the short term risk inherent in default events, the market-wide impact of defaults on...

We give an empirical assessment of I^2, a structural credit model based on incomplete information. In this model, investors cannot observe a firm's default barrier. As a consequence, I^2 exhibits both the economic appeal of a structural model and the tractable pricing formulae and empirical...

Credit contagion refers to the propagation of economic distress from one firm to another. This article proposes a reduced-form model for these contagion phenomena, assuming they are due to the local interaction of firms in a business partner network. We study aggregate credit losses on large...

In a traditional structural model of default it is implicitly assumed that the information used to calibrate and run the model is publicly available. In reality, model inputs and parameters are unobservable. In this article we analyze the role of information in structural models, which we...

Credit risk is the distribution of financial losses due to unexpected changes in the credit quality of a counterparty in a financial agreement. We review the structural, reduced form and incomplete information approaches to estimating joint default probabilities and prices of credit sensitive...

A thorough understanding of the joint default behavior of credit-risky securities is essential for credit risk measurement as well as the valuation of multi-name credit derivatives and Collateralized Debt Obligations. In this paper we study a simple and tractable intensity-based model for...

The Modigliani-Miller theorem describes conditions under which the value of a firm is independent of its leverage ratio. It is one of the cornerstones of finance. A history of this result along with a modern perspective on its derivation is given in Rubinstein (2003). We extend this history by...

We model aggregate credit losses on large portfolios of financial positions contracted with firms subject to both cyclical default correlation and direct default contagion processes. Cyclical correlation is due to the dependence of firms on common economic factors. Credit contagion phenomena are...

The recent accounting scandals at Enron, WorldCom, and Tyco were related to the (intentional) non-disclosure of a part of the firm's liabilities. We provide a structural model of correlated multi-firm default, in which public bond investors are uncertain about the liability-dependent barrier at...