Journal of Risk

This issue of The Journal of Risk contains papers that address parameter estimation uncertainty in two contexts: first in credit-risk modeling, and second with respect to portfolio optimization. It concludes with an analysis that highlights the importance of public reporting for insurers, as required by Solvency II.


In our first paper, “Parameter estimation, bias correction and uncertainty quantification in the Vasicek credit portfolio model”, Marius Pfeuffer, Maximilian Nagl, Matthias Fischer and Daniel Ro¨ sch derive confidence intervals for value-at-risk and expected shortfall due to default, accounting for asset correlation. They show how the latter can be estimated via a copula, establishing a direct link between inter-cohort correlation and observed default rates, thus reducing the built-in bias of plug-in estimates in a computaactionally efficient and stable manner.


Giorgio Costa and Roy H. Kwon address the notoriously challenging problem of parameter estimation for mean–variance optimization in the issue’s second paper: “A regime-switching factor model for mean–variance optimization”. The authors propose a regime-switching factor model to capture the cyclical nature of financial markets. While, traditionally, such regime-switching models have been considered in multiperiod settings, Costa and Kown avoid the resulting “curse of dimensionality” issue by adapting their model to a single period. In particular, they show that it results in a covariance matrix with lower ex post volatility, and they provide numerical illustrations of better risk-adjusted portfolio performances over long horizons.


The third paper in the issue, “A new dynamic hedging model with futures: the Kalman filter error-correction model”, is by Chien-Ho Wang, Chang-Ching Lin, Shu- Hui Lin and Hung-Yu Lai. It considers the problem of estimating the optimal hedge ratio for a portfolio involving a stock index and associated futures contracts. In their approach, the authors combine a Kalman filter state-space model with error correction in order to identify the best latent trend common to the index and its futures contracts. Through empirical data, including periods of financial distress, the authors demonstrate the superiority of their approach relative to existing alternatives.


In our fourth and final paper, “The impact of shareholders’ limited liability on risk- and value-based management”, Christian Eckert and Johanna Eckert consider the portfolio selection problem of an insurer whose objective is to maximize the returns of shareholders – who provide equity capital in addition to policyholder premiums – while minimizing the ruin probability. The authors illustrate the criticality of adequate monitoring by policyholders in the presence of limited liability for share- holders. They thus lend support to public reporting as required by the Solvency and Financial Condition Report of Solvency II, the European regulatory framework for insurers.

Farid AitSahlia
Warrington College of Business, University of Florida

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