Editor’s Letter

Wait! Can those be green shoots of financial recovery hiding among the springtime flowers? It does seem possible, and the U.S. stock market certainly seems to think so. The most recent jobs report for the United States showed job growth accelerated to the highest rate in two years during April 2014, and unemployment fell to 6.3%, the lowest since before the 2008 crisis. The Fed has decided it is safe to begin “tapering” its monthly bond purchases. In the eurozone, GDP growth appears to be resuming, with small but steady increases in recent months, and Ireland and Portugal have both celebrated their ability to exit from the bailout program this year.

Yet despite the green shoots, it is not hard to find evidence that the aftermath of the 2008 financial crisis is still with us and may well have done lasting damage that will not go away even when recovery is more complete. What we are seeing might be called “financial climate change,” or maybe economic “global cooling.” In the United States, many of the new jobs are in low-paying, low-skill occupations, not the kind of middle-class jobs that were lost during the downturn, while a significant portion of the sharp drop in the unemployment rate is due to discouraged workers leaving the labor force. U.S. labor force participation is lower today than it has been in decades. Eurozone economies may be recovering, but unemployment still averages 11.8% across the region, with much higher rates in some countries (Greece: 26.7%, Spain: 25.3%), and about half of the unemployed have been out of work for more than a year. Youth unemployment is much worse than the average everywhere—15.8% in the United States, 22.8% in the Eurozone as a whole, and more than 50% in Greece and Spain. Compounding the problem for the long-term unemployed is that job skills tend to erode over time. Moreover, the very fact that they are unemployed seems to make it harder to find a new job, because employers tend to view them as “damaged goods.” Older workers who lose jobs are frequently forced into involuntary retirement, while young workers who can’t get their first job lose out on important opportunities to develop skills and advancement.

Against this at best weakly positive news, stock markets have been doing exceedingly well, and volatilities have been low. How bad can things be? Well, it depends on whether you own a lot of stock or not. From an unexpected quarter has come Thomas Piketty’s new book Capital in the Twenty-First Century, which argues that the concentration of wealth that has been developing over recent decades and appears to have accelerated sharply during the current recovery will lead to reduced output and growth over the long run, with little realistic hope that the process can be reversed.

So how green are those shoots? And what is the chance that they will continue to grow and eventually flower in the long run? Fortunately, being an academic researcher and not a policymaker, I can raise uncomfortable questions like these and then quickly retreat to the Ivory Tower without offering any answers. So, on to this issue of The Journal of Derivatives!

Our first article, by Chen, Wang, and Wu, presents a valuable new variant on the popular LIBOR market model. The LMM has become the workhorse of practical interest rate derivative valuation. It simplifies the now-standard modeling of short-term interest rates as diffusion processes by modeling the rate explicitly only on repricing dates, where it is constrained to be lognormal. A problem with this powerful but flexible model, however, is that the individual densities are not sufficiently fat-tailed to match the empirical data and do not generate the volatility smiles observed in the market. These features make it hard to price barrier contracts properly, because the rate must be near the barrier in order to hit it within a short period of time, even though a policy change typically produces an instantaneous jump of 25 basis points or more. In this article, the authors add up-and-down exponential jumps to the short-rate process and still obtain closed-form valuation equations for the four standard kinds of barrier contracts.

The next article considers the problem of valuing the trading restriction on a restricted stock. Being prohibited from selling when the investor wants to eliminate the possibility of trading at an advantageous price that may turn up in the market before the restriction period is over. Earlier work in the literature developed a formula for a loose upper bound on the value of the constraint, but it really applies only to an investor with perfect foresight of the best possible price to trade at. Ghaidarov models the problem using a kind of forward-starting put, which produces much tighter, and more plausible, bounds on the appropriate discount for a restricted stock relative to its unrestricted twin.

The next two closely related articles, authored by Chen, Chen, and Huang; and Chiu, Lee, and Wang, examine trading in the Taiwan stock index futures market. The exchange records data on each trade that include the type of trader who initiated the transaction. In general, domestic and foreign institutions, proprietary futures trading firms, and market makers all make money, while individual traders lose to everyone. Deeper exploration examines the choice and profitability of different types of orders and the information content of the various groups’ put/call ratios.

In the next article, Marabel Romo develops a new pricing model for quantos, and the related combination contracts, based on a continuous-time multivariate Wishart process. This process is particularly useful because it permits stochastic evolution of both volatilities and correlations. The final article, by Lo, Palmer, and Yu, presents a new attack on Asian options. The problem with Asian options is always that while the underlying asset price may follow a logarithmic diffusion, averaging those prices over time produces a different distribution of unknown type for the option payoff. Several approaches in the literature proceed by estimating the moments of this distribution and fitting them to a standard density, such as lognormal. The authors propose using a shifted reciprocal gamma distribution for this purpose and show that it performs very well in a horse race against the alternatives.

Well, May is here. So, whether or not there are any true green shoots in the economy, we do have beautiful weather, spring flowers, graduations, and weddings to celebrate. So, I shall try to stop obsessing about the state of the economy, for a while anyway, and offer my heartiest congratulations to all graduates, newlyweds, parents, and friends. And indeed, best wishes to everyone in this excellent season. Have a great summer!

Stephen Figlewski

Editor

• © 2014 Pageant Media Ltd