Journal of Risk

Stan Uryasev

University of Florida

The current economic crisis has clearly highlighted the paramount importance of capital requirements for financial institutions to help them cover the risks they take. The aggregation of different risk types into a single figure is quite challenging and lacks a universal standard. Assessing the dependence between different risk types is at the core of their aggregation. In the first paper of this issue, Böcker and Hillebrand propose an approach that combines a classical factor model for credit risk with a linear factor model with another risk type, such as market risk, to derive a correlation-based aggregate risk value, with numerical and analytical illustrations on sample portfolios.

In the face of uncertainty, the opportunity to benefit from favorable market developments while being assured of a minimum payout is always attractive. In recent years, financial products presenting such features have grown substantially, particularly in the area of unit-linked life insurance. As the form of the guarantee varies among these financial innovations, their relative market-based performance is of great interest. In their paper, Gatzert and Schmeiser compare pricing and performance of mutual funds with look-back and interest rate guarantees for portfolios invested in stock, bonds, real estate and money markets. A main challenge in the comparison stems from the differences in maturity, underlying and payment. Their results suggest that fund volatility significantly increases the price of the look-back guarantee in comparison to the interest-rate guarantee.

For the third paper in this issue, Ghorbel and Trabelsi propose a method combining univariate times-series, extreme value theory and copula fitting to estimate the values-at-risk of correlated portfolios, which were particularly salient through recent financial events. Their empirical results support the notion that conditional extreme-value copula methods provide a better representation of the dependence structure of multivariate data and produce the most accurate estimates of risk.

In the fourth and last paper of this issue, Joshi conducts an extensive study to compare the convergence of binomial trees to price American puts under various parameterizations and implementations. The classical convergence of such schemes leads to an infinite number of possible combinations as the only requirements are made on the asymptotic mean and variance. Given the practical limitation to a finite number of steps, it is shown that the most effective implementations typically rely on truncation and Richardson extrapolation, while the best tree structures require third-order matching or a proposed new tree using a time-dependent drift with extrapolation and truncation.