Welcome to Volume 9 Issue 4 of The Journal of Risk. This issue is made up of 4 technical papers: This issue contains papers that deal mostly with risk model validation from both empirical and theoretical perspectives. Peter Winker and Dietmar Maringer discuss an issue that arises when VaR is used as a risk constraint in portfolio optimization. Specifically, they show that the actual empirical VaR of an optimized bond portfolio is significantly larger than the nominal VaR constraint.
In his paper, Larry Eisenberg proposes a VaR-based capital budgeting model that, unlike the CAPM, prices total risk, not just systemic risk. As a consequence, the marginal price of risk for a manager who uses a VaR constraint is elucidated. A particular advantage of the VaR-based approach is that it can accommodate a larger universe of risky assets than CAPM, which requires a finite variance assumption.
Raymond Brummelhuis and Roger Kaufmann examine empirically and theoretically the rule of converting 1-day VaR to N-day VaR. Finally, Marc Henrard contrasts two models to price an exotic interest ratemodel. The first is a Gaussian HJM model, which leads to an explicit formula, and the second is a shifted Gaussian Libor market model, which leads to a closed-form approximation. An advantage of the latter is its potential for calibration to the skew present in the cap market.