University of California at Irvine
Today, the Nobel prize in economics was awarded to Robert Engle and Clive Granger. In particular, the Royal Swedish Academy of Sciences stated that Professor Engle’s “ARCH models have become indispensable tools not only for researchers, but also for analysts on financial markets, who use them in asset pricing and in evaluating portfolio risk”. This announcement is a milestone for the risk management profession because it recognizes the pervasive influence of market risk modeling methods. Otherwise, this issue of the Journal of Risk could be a special issue on credit risk. It contains three excellent papers on credit risk, which reflect the state of the art in risk management. The fourth paper deals with market risk in what has now become one of the most active option markets in the world.
In “The Structure of Credit Risk: Spread Volatility and Rating Transitions”, Kiesel, Perraudin and Taylor examine the distribution of bond portfolios under different credit risk value-at-risk (VAR) models. The current state of the art includes models considering defaults only, or transitions in credit rating (such as CreditMetrics). This, however, ignores the effect of movements in credit spreads. The paper models credit spreads with a meanreverting component, which allows extrapolation of one-day changes to an annual horizon. Spread risk is found to increase VAR, particularly for high-credit portfolios.
The second paper, by Jarrow, van Deventer and Wang, “A Robust Test of Merton’s Structural Model for Credit Risk”, provides an innovative test of structural models for credit risk. Their approach focuses on the correlation between changes in the price of equity and bond for the same company. The Merton class of models predicts that the direction of changes should be identical, as both bond and equity values are driven by the same fundamental, which is the firm value. The paper reports that the observed fraction of movements in the same direction is around 55%, much lower than the 100% predicted by the Merton model, which is interpreted as a rejection of the structural class of models.
In “Dependent Defaults in Models of Portfolio Credit Risk”, Frey and McNeil give an overview of methods to estimate joint dependences in portfolio models for credit risk. The issue is important because the tails of the distribution determine the amount of economic capital to set aside against credit risk. It is well known that the shape of the distribution is affected by correlations. Conventional models assume joint multivariate normal distributions, which imply low clustering of large default events. Such models may understate the possibility of large losses, however. The paper reviews the use of copulas to model non-linear dependencies, and shows that the Bernoulli mixture model provides a general framework for industry models. The authors also compare different methods to calibrate the model.
Finally, the paper by Kim and Kim, “On the Usefulness of Implied Risk-Neutral Distributions – Evidence from the Korean KOSPI 200 Index Options Market”, analyzes the Korean index option markets. The authors compare various models for forecasting and hedging options: the two-lognormal mixture model (TLM), a simple Black–Scholes (BS) model, and an ad-hoc, smile-based Black–Scholes model (AHBS). Performance is measured by in-sample fit, forecasts over one day and one week, and delta-hedges over one day and one week. The two-lognormal model shows the best in-sample fit and out-of-sample forecasts. For hedging, however, it is inferior to the Black–Scholes model or its smileadjusted version. Thus, the best model for pricing may not be the best model for hedging purposes.
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.
On the usefulness of implied risk-neutral distributions – evidence from the Korean KOSPI 200 Index options market