University of California at Irvine
This issue of the Journal of Risk further advances the state of knowledge in risk management, with a number of significant papers.
The first paper, “Coherent allocation of risk capital”, by Denault, discusses methods to allocate diversification benefits to risk capital. Traditional RAROC measures are based on VAR, or stand-alone risk measures that fail to account for diversification across business units. This is because the firm’s total VAR is less than the sum of business VARs. The allocation problem consists of apportioning this diversification advantage to units in a fair manner. Using results from game theory, the paper shows how to allocate capital using a concept similar to that of component VAR.
Next is “Valuing American options in the presence of user-defined smiles: scenario analysis, model stress and lower-bound pricing applications”, by Jäckel and Rebonato. The authors examine the valuation of American options as a function of an exogenously assigned future implied volatility surface evolution. They provide a computational method where the user requires the dynamics of the underlying to reflect not only today’s smile surface, but also a user-defined evolution over time. This is an interesting and practical generalization of option pricing methods.
The third paper, “Dynamic hedging with a deterministic local volatility function model”, by Coleman et al. compares the dynamic hedging performance of various volatility models. The authors show that using the implied volatility method can lead to significant hedging errors, even though the method is able to calibrate current option prices effectively. The paper proposes a deterministic local volatility function approach, which leads to lower hedging error.
Finally, the paper by Bhansali and Wise, “Forecasting portfolio risk in normal and stressed markets”, extends previous work by Rebonato and Jäckel (Journal of Risk, Volume 2 / Number 2, Winter 1999/2000) on adjustments to the co-variance matrix. Such adjustments can be quite useful for considering changing correlations during stress test periods, but it must be ensured that the final covariance matrix is positive definite. The authors propose a method to mix covariance matrix forecasts and the usual estimates in a way that generates an “acceptable” covariance matrix.
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. Please see “Guidelines for Authors” for further details.
Valuing American options in the presence of user-defined smiles and time-dependent volatility: scenario analysis, model stress and lower-bound pricing applications