University of Florida
The American subprime crisis and the large single-trader-generated loss at Société Générale have dominated the financial news in early 2008. Overall, both issues have been clearly cast in risk management terms. However, it is still unclear whether they point to exclusive limitations of mathematical models, available riskmitigation instruments or failures of operational procedures. Certainly, though, these crises have highlighted an even greater need for solutions and enforcement of risk management in all its different aspects.
Some views may impute the subprime problems to adjustable interest rates. Interestingly, in the first paper in this issue, authored by Lindset, a new type of instantaneous caps and floors is proposed. They could prove particularly useful insurance instruments to protect the mortgage payment ability of homebuyers who chose floating interest rates. The main impediment to the pricing of these interestrate derivatives is in their inherent high dimensionality,which is addressed through approximations that are shown to be accurate.
Although its origins go back to the pioneering days of mean-variance optimization, the Sharpe ratio has been used to evaluate a variety of risk management strategies. In their paper, Leung and Wong focus on the statistical estimation of this parameter, particularly in the multi-dimensional case. Specifically, they propose a statistic to test the hypothesis of equality of multiple Sharpe ratios, developing its properties and asymptotic distribution.
Another statistical issue at the center of risk management is that of the estimation of value-at-risk (VaR). In his paper, Tolikas compares different VaR estimates based on various assumptions. In particular, his study indicates that VaR estimates based on extreme value theory under the generalized extreme value, generalized Pareto or generalized logistic distribution are critically better than those currently in use. In addition, generalized logistic estimates are relatively better than those based on the generalized extreme value distribution assumption. In his paper, Caporin investigates the effect of long memory conditional volatility on VaR estimates and also assesses more generally the impact of misspecified models on risk management performance. This study shows that, when the latter is measured through the Basel-based backtesting approach, loss function evaluations may favor simpler models.
Finally, Fábián and Veszprémi consider portfolio optimization when conditional value-at-risk (CVaR) is used instead of the traditional variance. They develop a numerical scheme for a model that captures dynamic CVaR constraints to reflect a decision-maker's preference over time. In particular, they present an application to mid-term constraints in an asset liability management problem.
Note. The last paper was presented at the International Conference on Financial Engineering at the University of Florida in March 2006 and has been available on the Journal website since Fall 2007.
Algorithms for handling CVaR constraints in dynamic stochastic programming models with applications to finance