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This paper is concerned with a procedure for financial time series clustering, aimed at creating groups of time series characterized by similar behavior with regard to extreme events. The core of our proposal is a double clustering procedure: the former is based on the lower tail dependence of all the possible pairs of time series, the latter on the upper tail dependence. Tail dependence coefficients are estimated with copula functions. The final goal is to exploit the two clustering solutions in an algorithm designed to create a portfolio that maximizes the probability of joint positive extreme returns while minimizing the risk of joint negative extreme returns. In financial crisis scenarios, such a portfolio is expected to outperform portfolios generated by the traditional methods. We describe the results of a simulation study and, finally, we apply the procedure to a dataset composed of the 50 assets included in the EUROSTOXX index.

Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating worst Value-at-Risk for portfolios with arbitrary marginal loss distributions are given. In particular, a novel Adaptive Rearrangement Algorithm is introduced and investigated. These algorithms are implemented using the R package qrmtools and may be of interest in any context in which it is required to find columnwise permutations of a matrix such that the minimal (maximal) row sum is maximized (minimized).

We introduce a functional factor model to investigate the dependence of cumulative return curves of individual assets on the market and other factors. We propose a new statistical test to determine whether the dependence in two sample periods are equal. The statistical properties of the test are established by asymptotic theory and simulations. We apply this test to study the impact of the recent financial crisis and trends in oil price on individual stock and sector ETFs. Our analysis reveals the significance of the daily oil futures curves and their different impact on individual stocks and sector ETFs. It also shows that the functional approach has an information content different from that obtained from scalar factor models for point-to-point returns.

This paper proposes a rating methodology that is based on a non-linear classification method, a support vector machine, and a non-parametric isotonic regression for mapping rating scores into probabilities of default. We also propose a four data set model validation and training procedure that is more appropriate for credit rating data commonly characterised with cyclicality and panel features. Tests on representative data covering fifteen years of quarterly accounts and default events for 10,000 US listed companies confirm superiority of non-linear PD estimation. Our methodology demonstrates the ability to identify companies of diverse credit quality from Aaa to Caa–C.

Financial product prices often depend on unknown parameters. Their estimation introduces the risk that a better informed counterparty may strategically pick mispriced products. Understanding estimation risk, and how to properly price it, is essential. We discuss how total estimation risk can be minimized by selecting a probability model of appropriate complexity. We show that conditional estimation risk can be measured only if the probability model predictions have little bias. We illustrate how a premium for conditional estimation risk may be determined when one counterparty is better informed than the other, but a market collapse is to be avoided, using a simple example from pricing regime credit scoring. We empirically examine the approach on a panel data set from a German credit bureau, where we also study dynamic dependencies such as prior rating migrations and defaults.