Editor's Letter

Hurtling at top speed through uncharted territory, who knows where we will end up? The last few months have revealed unexpected things about how the financial system works and shown how some issues that once seemed to be relatively minor can become much more important during times of stress. In the latter category, I would place counterparty credit risk. Under normal conditions, and even under abnormal conditions that fall short of a large-scale financial meltdown, the probability that an underlying issuer and a major financial institution selling protection on that issuer would both default at the same time was quite reasonably considered to be a very low probability event. But not today. Indeed, in September 2008, it was a sharp increase in perceived counterparty risk, which led to a huge collateral call by AIG's trading partners, that precipitated one of the first, and largest, of the government bailouts.

Along the same lines, but in the category of surprising market behavior, was the remarkably powerful effect of great uncertainty of financial firms about the financial condition of their customary counterparties, and their own financial condition as well, caused by the widespread losses in investment portfolios. These institutions cut back on lending, which forced leveraged borrowers to dump securities onto the market at fire-sale prices because they could no longer afford to carry them. This created more losses for institutions who held onto those securities and then had to mark them to “market” at the depressed prices, thus weakening their balance sheets and leading to more uncertainty and even less lending. And then the downward spiral of deleveraging spilled over into the real economy to produce the sharpest decline in economic activity in many years.

Against this unappealing backdrop, let us turn to more enjoyable topics: the articles in this issue of The Journal of Derivatives.

The Black-Scholes (BS) model introduced finance and economics to an entirely new branch of mathematics: continuous-time stochastic processes. Diffusion processes captured the continuous nature of price formation and risk exposure for stocks and other securities. Continuous-time also allows continuous trading, which dynamically completes the market so all kinds of derivatives can be priced. Yet despite the vast increase in the power and realism of the financial models that could be built, as soon as we “took the models to the data” it was clear that the BS constant volatility assumption was not an accurate description of stock price movements. The persistent volatility “smile” and then “skew” in option-implied volatilities was clear evidence that investors do not price options as if the BS assumptions are correct.

The first article in this issue explores more general returns processes with stochastic volatility and non-diffusive jumps. By comparing the risk-neutral probability density for the price of the underlying asset at option expiration, as revealed in option prices, against the real-world density, Wang is able to show that the market expects stochastic volatility and jumps in both returns and volatilities for the FTSE stock index. The second article, by Eriksson, Ghysels and Wang, is also concerned with the risk-neutral probability density, but from the perspective of obtaining a well-behaved estimate of it from options data. The density under BS assumptions is lognormal, but the pricing errors when the lognormal model is applied to the data suggest that the actual density is negatively skewed and has fat tails. The Gram-Charlier and Edgeworth expansion techniques offer one way to approximate a density with non-Gaussian 3rd and 4th moments, but the authors show that the Negative Inverse Gaussian distribution performs better over a much broader range of parameter values.

Departure from lognormality plays a major role in the third article as well, but from a different perspective. In the LIBOR Market Model, interest rates at a finite set of future dates are all assumed to be lognormal; this assumption greatly simplifies pricing interest-dependent securities. The problem for Wu and Chen is that for derivatives that depend on a simple function of those lognormal rates, such as an option that pays off based on the spread between two rates, the density for the underlying becomes intractable. Their trick is to replace the nonlognormal density with a lognormal approximation. This allows closed-form valuation equations in place of pricing options with Monte Carlo simulation, and the loss in accuracy is minimal.

Finally, mortgage-backed derivative securities have played a central role in the financial crisis, especially at the outset, and much bandwidth has been used in criticizing them and pretty much anyone involved with them. Although there are clearly important issues that need to be addressed, particularly those involving market transparency, much of the commentary misses an extremely important feature of all derivatives, and other financial instruments as well—that they are a zero-sum game. That is, there are always two sides to the contract such that if one counterparty loses a dollar, the other must necessarily gain that dollar. This principle allows us to take a high-level perspective on how the financial system works overall, without being distracted by the complex details of individual securities. In the final article of this issue, I offer an intuitive high-level explanation of how the crisis was touched off by the deflation of the bubble in the real estate sector and of what is happening in the financial system as it tries to pass through those huge losses. The argument is designed for the intelligent layman (i.e., not you sophisticated readers of the JOD, but perhaps your friends and family). The chain of reasoning arrives at the bottom line that all of the “toxic” mortgage-backed securities poisoning the big banks and financial institutions could have been entirely detoxified if the cash flows on the underlying mortgage loans were guaranteed by the government. Such a move might have completely defused the crisis, if it had been done at the beginning. Since then, financial instability has spread throughout the economy, and many sectors are now generating additional risk and uncertainty so that even “curing” the problems with mortgages would probably not be enough to end the crisis. But it would certainly help.

Well, we are all hunkered down, expecting that things are likely to get worse before they get better and hoping that we don't have to wait too long for the regime shift to occur. In the meantime, if you're an academic, you can take comfort in the fact that we typically learn more from outliers than from outcomes near the sample mean, and that we're getting many new data points from a part of the state space that we have rarely seen before. If you're a practitioner, perhaps you should think of this as a stress test, in real time. Those who survive it can at least see where the financial system's greatest weaknesses were and what parts of the system are in most need of reinforcement.

While this data-gathering exercise continues, I wish everyone good luck in surviving to the point where the new insights will become useful.

TOPICS: Options, credit risk management, statistical methods

Stephen Figlewski

Editor

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