New problems, old solutions

A quiet revolution is taking place in the equity market. Away from the reverberationsof the burst technology bubble, and the continuing debate over retail equityderivatives products, quants are discovering how to reapply old techniques tonew problems, and are making money doing it.

Some call it algorithmic trading. Others use the term statistical arbitrage.An obsolete expression is technical trading. Perhaps the most generic and usefulterm is quantitative trading: using the full panoply of mathematical financeand statistics to trade cash markets, whether on a proprietary or client-executionbasis. A growing number of derivatives cognoscenti are now moving into the field.

Neil Chriss epitomises the trend among practitioners. Formerly known to Riskreaders for his work on tree models and volatility swaps, Chriss made an earlystep in this new direction in 1999. With his academic collaborator Robert Almgren,he published a little-noticed article in these pages analysing the liquidationof a stock portfolio as a trade-off between market impact and price uncertainty,represented by a characteristic time parameter.

Since then, the market has caught up with Chriss and Almgren. Programme tradingaccounts for an ever-growing percentage of stock exchange volume, and principalbids – undertakings to liquidate a given portfolio at an agreed discountto fair value – are an important part of this. Such bids, which involvea commitment of trading capital, are often priced aggressively, but since manyrisk managers see the cash equity markets as reassuringly liquid, the pricingis not closely scrutinised.

In this month’s first Cutting Edge article, Chriss and Almgren developthe ideas of their 1999 paper to show how principal bid programme trades canbe priced and evaluated as part of a trading business. By annualising the priceimpacts and variances of such trades, they construct an information ratio measurethat can be used to set hurdles below which bids at a given discount should notbe accepted.

We note that Chriss and Almgren’s results should apply not only to equitymarkets, and not only to the liquidation of long positions. What would be thecharacteristic liquidation time for Warren Buffett’s derivatives portfolio,for instance? We hope this article will encourage more submissions on similarsubjects.

The second and third Cutting Edge articles this month focus on credit derivatives.The much-discussed pricing of basket products and synthetic CDO tranches resemblesthe evolution of options markets in the past, albeit with more polarisation,since investors are invariably protection sellers. The Gaussian copula approachfirst introduced by Li has played a similar role to the Black-Scholes formula,and is likely to remain a benchmark due to its tractability.

However, unlike the Black-Scholes formula, the Gaussian copula does not generateprices analytically: Monte Carlo must be used. That makes calculation of Greeksdifficult. Moreover, the appearance of implied correlation and skew effects inthis rapidly developing market has prompted a move towards more sophisticatedcopula models that calibrate better, at the cost of even more onerous Monte Carlo.

These issues are behind the article by Jon Gregory and Jean-Paul Laurent. Incredit portfolio risk management, analytical conditional dependence frameworkssuch as CreditRisk+ have proved highly popular. Here, Gregory and Laurent applythe idea to the valuation of default baskets and synthetic CDO tranches, matchingMonte Carlo results for pricing and showing significant improvement in the calculationof deltas.

Meanwhile, for single-name credit derivatives, research continues into underlyingdefault processes, in particular for fair-valuation applications. To the well-establishedtraditions of structural or firm-value models and reduced-form models, a thirdtype has gained a foothold. Credit barrier models were invented to get rounda fundamental deficiency of structural models: the problem of determining distanceto default given publicly available accounting information. Enron was a casein point.

Credit barrier models do not provide a solution to fraudulent accounting, butthey do allow distance to default to be treated as a risk-neutral measure thatcan be calibrated to observed credit spread curves and used to price credit defaultswaps. In our final Cutting Edge article this month, Claudio Albanese, GiuseppeCampolieti, Oliver Chen and Andrei Zavidonov construct an analytic credit barriermodel driven by credit ratings, constrained to fit the term structure of creditspreads.

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