Editor’s Letter

National economies around the world seem to have hit bottom and begun the long path upward, back towards acceptable levels of growth and employment. Yet risk and uncertainty of all kinds still surround us, whether from the more-or-less predictable political battling in Washington, or the mostly-less-predictable political battling surrounding the U.K. election and the bailout of Greece, or the not-at-all predictable Icelandic volcano and the major oil spill in the Gulf of Mexico. Strangely, almost none of these major risks seem to be among those that can be mitigated by derivatives. Put another way: none of these problems can be blamed on us! Volcanic ash that kept planes on the ground for a week all over Europe was not another derivatives disaster. (Whew!) So let us now turn our attention to derivatives.

We launch this issue of The Journal of Derivatives with three articles on lattice-based valuation models. The lead article, by Dai and Lyuu, presents a new structure combining binomial and trinomial regions that will be particularly useful for pricing barrier options. Most of the tree is binomial, which allows the risk-neutral probabilities to be obtained using combinatorial methods, with great gains in computational efficiency. Adding a small region of trinomial branching lets the user position the binomial portion optimally to minimize the error from nonlinearity in the option payoff.

Lattice models are especially needed for pricing American options, but one of the problems in using them is that it is essential for the middle nodes to recombine from one time step to the next. A number of common features of real world securities prevent this, notably time-varying volatility, and unfortunately, techniques proposed in the literature to handle stochastic volatility are generally cumbersome and slow. Here, Beliaeva and Nawalkha demonstrate a new method that achieves a major gain in efficiency by transforming the problem to make the returns process and the volatility process independent of each other.

The third option-pricing tree article, by Jabbour, Kramin, and Young, shows how credit risk in a structural “Merton model” frame-work can be handled within a lattice. One of the great difficulties with the structural approach is that real world corporations have complex capital structures, and multiple classes of debt create multiple default decision points at which the optimal decision with regard to one class of debt interacts with all of the others. Valuation equations can be easy to write down but extremely hard to solve computationally. Jabbour, Kramin, and Young present a lattice model that prices a full set of multiple debt classes efficiently.

Derivatives valuation models are based on arbitrage, or more precisely, the absence of profitable arbitrage opportunities. Demand and supply fluctuations in the market for options are supposed to have little or no effect on the option price, because it is assumed that if demand pressure were to push the price away from the model value, arbitrageurs would step in and push it back into line. But there is considerable evidence that price discrepancies do exist and can persist without generating an outpouring of arbitrage trading. If arbitrage is hard, costly, or risky (i.e., pretty much all the time in the real world), supply and demand imbalances may produce measurable price effects. Such effects have been found for U.S. options; Shiu, Pan, Lin, and Wu show that demand pressures affect option prices in Taiwan, as well.

In the last article, Shiu and Moles analyze the results from a survey of derivatives usage by banks in Taiwan.

Finally, our current co-editor, Sanjiv Das, and a former co-editor, Raghu Sundaram, have just published a new derivatives textbook, Derivatives: Principles and Practice, which I review in this issue. Not surprisingly, the book is excellent and I like it very much.

We don’t envy the uncertainties faced by the Greeks, or those living on the U.S. Gulf Coast who prefer ocean water without oil, or the owners of homes that are now worth less in the market than the mortgage loans that they are struggling to continue paying. Who knows what the final outcome of these high-risk situations will be? But for the rest of us, the weather is balmy; the flowers are blooming and the birds are chirping in the trees; students are graduating from schools and many have jobs lined up; the Icelandic volcano is behaving itself for the time being; even the stock market is relatively calm, if one overlooks the odd 15-minute free fall on an otherwise clear day that took the market down 10% and then right back up again. It is easy to feel that things could be worse. We hope you find yourself in the latter category, too. Or if you’re in the first category, we wish you a quick and easy transition into the second.

Stephen Figlewski

Editor

• © 2010 Pageant Media Ltd