Quantitative risk management relies on a constellation of tools that are used to analyze portfolio risk. We develop the standard toolkit, which includes betas, risk budgets and correlations, in a general, coherent, mnemonic framework centered around marginal risk contributions. We apply these...

We present a generalization of the two sample t-test for the equality of means to the case where the sample values have unequal weights. This is a natural situation in financial risk modelling where some samples are considered more reliable than others in predicting a common mean. We describe...

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 describe a class of quantitative credit risk models that take account of the unavoidable gaps in investors' information. These incomplete information models are structural/reduced form hybrids. They combine the best features of both traditional approaches while avoiding many of their shortcomings

A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among...

We examine the efficacy of the I-squared incomplete information credit model in a broad context that is relevant to fund and asset managers.Using a rigorous statistical analysis, we show that I-squared is a powerful forecaster of the following events:- Rating agency downgrades- Investment grade...

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...

Given a collection of single-market covariance matrix forecasts for different markets, we describe how to embed them into a global forecast of total risk.We do this by starting with any global covariance matrix forecast that contains information about cross-market correlations, and revising it...

Recent high-profile defaults of investment grade bond issuers have demonstrated the weakness of conventional ratings in rapidly changing circumstances. We propose a simple method to derive market-based ratings from spread data, and show that classifying bonds using such ratings provides a more...