University of California at Irvine
This issue of the Journal of Risk further advances the state of knowledge in risk management, with two papers on risk measurement and two others on options.
The first paper, “Value-at-Risk Risk Measures versus Traditional Risk Measures: an Analysis and Survey” by G. Kaplanski and Y. Kroll, compares available risk measures and discusses whether value-at-risk (VAR), or its variants, are consistent with expected utility maximization. The decision framework is evaluated in terms of stochastic dominance criteria and is compared to a series of other risk measures that have been analyzed in the literature. The paper confirms that VAR-based decision-making can be justified based on expected utility for normal distributions of returns. For general distributions, however, VAR implies a very unusual utility function, which has a discontinuity around VAR. In contrast, the utility function for expected tail-loss risk measures is much better behaved. This article gives a convincing argument for augmenting VAR measures with tail-loss measures (such as conditional VAR), or stress tests.
Next, in “Is Implied Volatility an Informationally Efficient and Effective Predictor of Future Volatility?”, L. Ederington and W. Guan extend previous work on regressions of realized volatility on implied volatility. Efficiency implies that the intercept should be zero and the slope unity. The setup attempts to minimize the effect of measurement errors, which has plagued most other studies of this topic. The authors use daily data from Standard & Poor’s 500 futures options, which is better synchronized with the underlying asset price. They also implement instrument variables, which should correct for measurement errors in option data. The authors find that implied volatilities subsume information in historical time-series models. Even so, the paper identifies a downward bias in the slope coefficient. Their conclusion is that this puzzling effect cannot be explained by measurement error.
The third paper, by A. Doffou and J. E. Hilliard, “Testing a Three-State Model in Currency Derivative Markets”, presents tests of a jump–diffusion/stochastic interest rates pricing model on Philadelphia Stock Exchange currency options. This class of models does substantially better than the simple Black model premised on a geometric Brownian motion, and even the jump–diffusion model developed by Bates. The authors show that the addition of parameters improves the in-sample fit but also out-of-sample performance. The paper also reports that stochastic interest rates do make a difference for short-dated options, contrary to what has been reported in the literature.
Finally, the paper by C. Friedman, “Conditional Value-at-Risk in the Presence of Multiple Probability Measures”, extends the concept of conditional VAR (CVAR) to a situation where the probability space is unknown. This is an important question, as traditional risk measures assume a fixed probability space, or density function. In practice, the probability measures governing stochastic processes in financial markets may not be stable. Correlation patterns are prone to break down, for example. The paper derives risk management rules that are robust under multiple probability measures. This approach allows practitioners to discover dangerous risk measures, or risk holes.
The mission of the Journal of Risk is to further our understanding of risk management. Contributions to the journal are welcome from academics, practitioners, and regulators in the field. With this in mind, authors are encouraged to submit full-length papers. (See Guidelines for Authors for further details.)