University of Florida
As this winter issue went to press, the effects of the American sub-prime mortgage market crisis were still being evaluated. One aspect that emerged in the related discussions is that of the pre-eminence of (good and bad) mathematical models. It is clearly within the mandate of The Journal of Risk to seek and encourage the development of risk models that are increasingly realistic and more comprehensive. In particular, this issue contains papers that address both internal (within a firm) and external (market-based) aspects of risk assessment.
Marumo and Wolff consider the application of Hermite and Laguerre polynomials to approximate the distributions of financial returns. A known advantage of expansionmethods is that they only require the moments of the distribution up to a specified order. Using market data, the authors show that these expansionmethods can be particularly useful in addressing the problem of risk measurement for long time horizons.
In his article, Shepard offers an approach to integrate factor models for different markets in a manner that ensures both local and global consistency. In addition, his method manages the proper balance between detail and parsimony in order to avoid problems related to spurious correlations.
How do managers of nonfinancial firms manage risk? Brown and Khokher point out the relatively small and variable use of derivatives and posit a model that highlights the endogenous predominance of risk management. This framework may partly explain, for example, the increasing tendency for firms to sell put options and buy call options on their own shares.
Returns based on high frequency data tend to show fatter tails and more peaked distributions. This departure from normality has risk implications as extreme movements are more likely than predicted under the normality assumption. In his paper, Gurrola compares alternative distributions to better estimate related quantile-based risk measures. His empirical evidence shows that SU curves are competitive when compared with normal mixtures and student distributions.
Lim addresses the American-style feature of dynamic fund protection options, such as those in equity-indexed annuities that offer protection against downside risk while participating in good returns when compared against a possibly stochastic benchmark. In the context of a bivariate geometric Brownian motion, he makes use of a change of numeraire and scaling properties to arrive at an efficient numerical solution of the American option valuation.
In their paper, Fatone et al develop a series expansion approach to price continuously monitored barrier options, where the underlying process is modeled according to the Black-Scholes assumptions with time-dependent parameters. The authors provide explicit expressions for the first three terms of the series, which they show are sufficient for accuracy through numerical evidence.
Note. The last two papers were presented at the International Conference on Financial Engineering at the University of Florida in March 2006 and have been available on the Journal website since Fall 2007.
Capturing fat-tail risk in exchange rate returns using SU curves: a comparison with the normal mixture and skewed Student distributions
A perturbative formula to price barrier options with time-dependent parameters in the Black and Scholes world