University of California at Irvine
This issue of the Journal of Risk illustrates the breadth of topics that fall under the general heading of market risk management. This includes value-at-risk (VAR) decomposition, distribution forecasts, diversification across space and time, and a smile-consistent option pricing model.
The first paper, “Decomposing Portfolio Value-at-Risk: a General Analysis”, by W. G. Hallerbach, provides a much-needed analysis of VAR tools, including marginal VAR, component VAR (CVAR), and incremental VAR. The author generalizes the standard results under normality to an elliptical world. In addition, the paper shows how to compute these statistics in a simulation setting. CVAR is computed from the group of observations around the cutoff VAR observation, with some adjustment. This method provides simple but accurate CVAR measures from simulations.
The second paper, by E. Eberlein, J. Kallsen and J. Kristen, “Risk Management Based on Stochastic Volatility”, compares the performance of various distributional models for volatility. The authors proceed in two steps. First, volatility is modeled as a time-varying component, including GARCH-type and implied volatility models. Second, after scaling by the conditional volatility, they examine the distribution of the residuals using the hyperbolic distribution, which has fatter tails than the normal. The authors report that both time-varying volatility and fat-tail distributions are important for the modeling of financial asset returns.
Next, in “Space-Time Diversification: Which Dimension is Better?”, M. A. Milevsky compares the diversification properties of portfolios diversified across assets (space) and across time. We know that portfolio risk generally decreases as the number of assets in the portfolio decreases. Likewise, the annualized volatility of a portfolio return generally decreases as the horizon lengthens. The paper describes the trade-off between number of assets and time period, using the probability of underperforming the risk-free asset as a benchmark for comparisons. This yields interesting insights. For instance, with typical parameter values, increasing the number of assets from one to ten decreases risk as much as holding one asset only over a ten-year horizon.
Finally, the paper by F. Antonuccio and M. Proebsting, “A Risk-Neutral Approach to Option Pricing with Jumps and Diffusion”, presents an option pricing framework that incorporates jumps in the underlying price process. This allows calibration to the observed pattern of volatility smiles. The additional model parameters can be interpreted as higher moments, skewness and kurtosis, of the spot process. This approach captures the correct smile dynamics in a model-consistent way, which is useful for consistent pricing and hedging of options.
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.