Editor’s Letter

It is mid-August and at least a few of the green shoots of spring appear to have taken root. Real economic growth may well be turning back to positive, and the stock market, trying to run ahead of the news as always, has shown unusual strength: a summer rally of the sort that used to be almost expected. Still, the celebrated drop in the unemployment rate from 9.5% to 9.4%, which helped sustain the rise in the market, was accomplished only because the quarter of a million new job losses was not as large as the number of discouraged workers who dropped out of the labor force. Unemployment, a lagging economic variable, is expected to continue rising into next year. Paul Samuelson famously commented that “The stock market forecast nine of the last five recessions.” Let us hope that if the same ratio prevails on the upside, we’re currently entering one of the five that are true expansions.

This issue of the JOD begins with an article exploring the empirical observation that financial asset returns are more correlated with one another on the downside than on the upside, while the multivariate returns processes that are most widely used in theoretical pricing models, like the normal or the Student-t, have symmetrical tail-dependence for positive and negative returns. Correlation is therefore underpredicted in the left tail, which means measures of portfolio risk, like Value at Risk (VaR) and Expected Shortfall (ES), tend to be too low. Tsafack looks at U.S. and Canadian stock and bond market returns and considers using the symmetrical distributions for returns on individual assets, with an asymmetric Gumbel copula to combine them into portfolio returns. The analysis demonstrates that restricting tail-dependence to be symmetrical does lead to VaR and ES measures that are too low for extreme risk levels. Interestingly, the 5th percentile ends up about the same under all of the models, so estimates of 5% VaR are fairly accurate (but ES at 5% is still too low, because ES takes the more remote tail into account while VaR doesn’t).

The next article, by Wu and Chen, introduces a new approach, in the framework of the LIBOR Market Model or the Swap Market Model, for valuing interest rate derivatives that are subject to barriers, such as an up-and-out interest rate cap. The result is a closed-form valuation model that can be easily calibrated to market rates. Goltz and Lai then look at the returns from investing in straddles on the DAX index. An index straddle is a volatility play, and earlier research with the S&P index has shown that the returns are typically negative. This is interpreted as the market’s volatility risk premium—i.e., a long straddle position is a hedge against rising volatility, and the market is willing to accept negative returns to pay for that insurance. The article finds similar negative returns on DAX straddles that are rebalanced to remain delta (and beta) neutral, but shows that if these reflect expected volatility risk premia, most utility-maximizing investors would probably be shorting the position rather than going long. However, the transactions costs required to implement the strategy would likely outweigh any utility gains from it.

Wahab and Lee then present a rather remarkable procedure for constructing a lattice model for valuing derivatives based on multiple assets, each of which follows a diffusion. The returns processes are correlated across securities, and in addition, each asset can jump randomly among multiple regimes, each with a different returns process. Although getting one’s mind around the structure is a little like trying to work out all of the connections in an n-dimensional spider web, the end result is a model that can price a multi-asset derivative with extensive regime switching in a small fraction of the time that would be required for Monte Carlo simulation. The final article, by Bernard and Boyle, examines one of the most fascinating recent incidents in the financial world: the unraveling of the biggest Ponzi scheme in history, run by Bernie Madoff. Madoff claimed his incredible performance, extraordinarily high reported returns with virtually no volatility, was largely accomplished through the use of an option strategy known as a “split-strike conversion.”As this article shows, on both empirical and theoretical grounds, the assertion that following a split-strike conversion strategy could produce such returns has as much validity as Madoff ’s account statements.

By the time you are reading this, the summer will have passed (let’s hope that the summer rally has not) and we will all be settling back into our routines of work and school—and watching, breath held, to see what the fall season brings in the way of health-care reform, financial reform, regulation of derivatives, and, of course, the World Series. Best wishes to all for the new season.

TOPICS: Derivatives, statistical methods, financial crises and financial market history

Stephen Figlewski

Editor

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