Editor’s Letter

As I sit down to write the Editor’s Letter for this issue, two huge sources of uncertainty are in the process of being resolved. It is Election Day in the United States. The seemingly unending barrage of negative political advertising during the long campaign has produced an electorate that is in sharp disagreement about nearly everything, except that we will all be extremely glad when the election is over.

Tomorrow we will know who has earned the job of trying to handle the many challenges facing the United States and the world. I actually do not expect much new from the newly elected Congress. We already can predict with confidence that whoever is elected President will face a Congress, half of whose members oppose everything he wants to do and who believe that the voters have sent them to Washington for just that purpose. While this situation may be normal in countries with parliamentary systems of government, it has only recently become a feature of U.S. politics and has been a major cause of the gridlock of the last few years.

The second and more immediate uncertainty concerns the aftermath of Hurricane Sandy that arrived in the New York area more than a week ago. Like millions of my neighbors, your loyal and long-suffering Editor has had no electricity, heat, light, Inter-net, e-mail, etc., in his home since then, and is wondering when it will come back, and how much longer he can stand to wait. After eight days of “living off the grid,” I must say that it is a lot less uplifting than I might have hoped.

While waiting for the arrival of new data, let us take a look at this issue of the JOD.

Our first article examines the role of hedge funds in the 2008 financial crisis. With so much misbehavior, or at least insufficient attention to risk management, on the part of so many different market participants, it is no surprise that fingers have also been pointed toward hedge funds as a source of systemic risk. But, is this accusation grounded in fact? Brown’s, Green’s, and Hand’s analysis suggests that it isn’t. Hedge funds did not show unusual profits during that period, in particular, not among funds following trading strategies that should have profited from a market downturn. Nor does it appear that hedge funds were forced into “fire-sale” liquidations by large customer redemptions or excessive leverage. In short, hedge funds appear to have lost money in the crisis just like the rest of us, and with their typical lock-in provisions, they may have had less difficulty with redemptions than other types of financial firms did.

The subject of the second article also stems from the 2008 crisis. Spiegeleer and Schoutens examine contingent convertibles (CoCos), a new type of security that automatically provides the issuer with more capital following a credit-related triggering event, when it is needed most and is the hardest to obtain in the equity market. A CoCo is like a callable convertible bond in which conversion to stock is forced upon the exercise of the call. The key difference between the two is that exercise is automatic for the CoCo when a specified trigger event occurs, rather than a decision made by the issuer. The CoCo can be thought of as a kind of credit derivative and valued within that theoretical framework, or alternatively, as more like a convertible bond for which exercise is contingent on the behavior of the stock price. The authors don’t have to take a stand on this conceptual issue, because they provide valuation methods in both frameworks.

Samuelson published a theoretical paper in 1965 on the relationship of the volatility of futures prices to volatility in the cash market. One feature of his model is that futures become more volatile as expiration approaches. This behavior has come to be called the Samuelson Hypothesis, and it has been the object of quite a lot of research over the years, much of it done within a different modeling framework from Samuelson’s. In our third article, Brooks points out that the Samuelson Hypothesis implies that prices for more distant futures expirations should be less volatile than for nearby contracts, and he develops a methodology for testing that proposition. His results show that some futures exhibit the pattern and some don’t, and the difference depends on whether pricing in the market obeys the cost-of-carry model.

The last two articles present new techniques for pricing path-dependent derivatives. Real world volatility is stochastically time varying, not constant as Black and Scholes assumed, and this causes trouble for lattice-based pricing models because the branches no longer recombine. Costabile, Massabó, and Russo develop a “forward shooting grid” approach in which, rather than the stock price, the volatility is the primary variable, and a representative set of stock prices is carried along as auxiliary variables. This produces a very efficient pricing tree that avoids some of the technical problems that arise in alternative lattice designs. Finally, Popovic and Goldsman consider the problem of pricing arithmetic Asian options, whose payoffs are path dependent with unknown probability distributions. They show how to construct closed-form payoff densities by doing the Monte Carlo simulation to generate a set of future stock price paths and then fitting a Gram–Charlier approximation to the resulting histogram of option payoffs.

Well! Two days later, the two major uncertainties have been resolved! Electricity finally came back just in time for me to watch the election returns on television and to see the nation keep Obama in the driver’s seat as President for another four years.

The voters have spoken. So with this great uncertainty removed, the stock market is sure to rally and volatility will plummet as we turn our eyes to the future with confidence, and… Oh no! Look out for that fiscal cliff dead ahead!

TOPICS: Derivatives, volatility measures, statistical methods

Stephen Figlewski

Editor

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