University of California at Irvine
This issue of The Journal of Risk reflects current developments in financial risk management. It contains three papers dealing with different aspects of credit risk and a practical paper on market risk measurement.
In “Sequential Defaults and Incomplete Information”, Giesecke and Goldberg extend structural models for credit risk. The paper analyzes portfolio effects for a first-passage credit model where investors have incomplete information about the value of the firm and the default barrier. Merton-type models assume that both variables are perfectly observed, which implies that defaults are predictable, for instance, when the value of the firm is just above the barrier. In practice, defaults are not perfectly predictable and we observe significant short-term spreads that reflect this fact. This problem can be solved with incomplete information. The paper provides results for multiple credits that take into account default correlations due to market-wide events and counterparty relations.
The second paper by Muromachi, “A Conditional Independence Approach for Portfolio Risk Evaluation”, constructs risk measures for credit portfolios. The conditional independence approach assumes that some latent variables drive the conditional distribution of values but that, given these latent variables, defaults are independent. This leads to a hybrid method to construct the portfolio distribution, using first Monte Carlo simulations for the latent variables, and, second, analytical saddlepoint approximations for the portfolio distribution. Combined with importance sampling, this approach considerably reduces the computational time for constructing the portfolio distribution. The paper also provides approximate formulas for the measurement of the risk contribution to VAR and CVAR.
The next paper, “Unconstrained Fitting of Implied Volatility Surfaces Using a Mixture of Normals”, by Rebonato and Cardoso, presents a smoothing method to estimate the volatility surface from the market prices of options. Obtaining reliable smile surfaces is important for risk management purposes, which deal with potential changes in option prices. The method fits a mixture of normal distributions that fits the risk-neutral conditions and the observed skew. The authors show that this approach provides a very good and flexible fit to volatility surfaces.
Finally, the paper by Focardi and Fabozzi, “A Percolation Approach to Modeling Credit Loss Distribution under Contagion”, examines contagion effects for modeling credit loss distributions. The approach uses concepts from statistical physics, most notably percolation theory, to demonstrate how default for one company could spread to other companies. These cascading defaults could explain why credit loss distributions have fat tails.
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.