Wilmott� Wilmott magazine

editor’s letter

The problem is that large

institutional players now find their ability to execute at volume is hugely hampered,

hence the predi-lection for greater and greater speed and the continuing fragmentation of

liquidity that we are witnessing

An Affair to Remember

Just over a year ago everyone held their breath as the markets went into an unprecedented freefall before regaining 60 percent of its losses at the end of the day. The Flash Crash of May 2010 was many things to many people, but we discern it as being a harbinger of things to come. Appropriate then

to examine what got us there. If anything, the proliferation of market technology and the shifting sands of market practice are a direct result of market regulation – the issue of the era. In this issue’s cover story we discuss the development of regulatory practice in defining what the market is and whom it is for with Larry Tabb, CEO of Tabb Group.

Market regulation has, over the past 30 years, aimed at promot-ing the markets to small investors and has evolved market structures that exist to protect them. However, the problem is that large insti-tutional players now find their ability to execute at volume is hugely hampered, hence the predilection for greater and greater speed and the continuing fragmentation of liquidity that we are witnessing. The Flash Crash represents a defining moment in this progression. As part of this examination, Gunduz Caginalp, Mark DeSantis and David Swigon of the University of Pittsburgh Mathematics Department examine recent record breaking market moves and ask if flash crashes caused by instabilities arising from rapid trading?

Satyajit Das returns to the subject of the central counter party (CCP) in the second part of his article “Tranquilizer Solutions Part 2: CCP Risk Taming.” The CCP is designed to reduce and help manage credit risk in derivative transactions. It also simplifies and reduces the complex chains of risk that link market participants in derivative mar-kets. What is in question, though, is the assumptions about the CCP’s ability to itself manage risk.

Rachel Ziemba looks at the challenge global economies face in pricing in two wildly different but substantially impactful events: the earthquake in Japan and the Arab Spring. The focus now is on how institutions across the global economy benefit or detract from resil-ience and recovery.

As is his wont, Aaron Brown takes it upon himself to make us face down the happy assumptions we blithely apply to our comfortable worldviews. In the world of quant, the idea that standard deviation is risk is not just viewed as heretical but bordering on the moronic. But can we learn anything useful from examining this unpopular view. Unfortunately, the quant community does not have its own Jerry Fodor, but fortunately for us Brown has managed to unearth a certain Professor Wandom Rocker, who is prepared to step up to the plate.

Colin Magee returns with his series on the application of quant strategies on betting exchanges. Having drawn similarities between online betting markets and financial markets, Magee points out that what enables the application of quantitative finance methods to betting markets is the availability of a reliable and comprehensive Application Programming Interface (API) for those markets. This means that market data can be programmatically accessed, manipu-lated, and analyzed; strategies formulated and back tested; and, critically, transactions on the exchange can be automated. Magee has developed an open source R package for enabling the same advan-

tages available to quants in finance for betting markets using the Betfair Sports Exchange API.

Mike Staunton takes us back to the very beginning (well, one of the beginnings) by invoking the Dutch Tulip frenzy before focusing on a paper by Dominique Bang, which gives an exact series represen-tation of the call payoff in terms of trigonometric functions and, in practical terms, promises an excellent approximation to the Black–Scholes value with fewer than a score of terms. Staunton illustrates his periodic decomposition of the quasi-call payoff (his formula from theorem 3.1) for the Black–Scholes case.

In “The Alternating Direction Explicit (ADE) Method for One-Factor Problems” Guillaume Pealat and Daniel J. Duffy apply the ADE method to a number of partial differential equations in option pricing using one factor models (Black–Scholes, Local Volatility, Uncertain Volatility). The authors discuss the stability, accuracy, and performance of ADE for a generic one-factor partial differential equation. Particularly important is how they transform a problem on an unbounded domain to one on a bounded domain, thus avoiding complex mathematical techniques to find the optimal truncated boundary and the determination of the cor-responding numerical boundary conditions. The authors also examine a number of applications.

In “A Market Model of Interest Rates with Dynamic Basis Spreads in the Presence of Collateral and Multiple Currencies” Masaaki Fujii, Yasufumi Shimada, and Akihiko Takahashi argue that the textbook-style application of a market model of interest rates has now become inappropriate for financial firms; It cannot even reflect the exposures to these basis spreads in pricing, to say nothing of proper delta and vega (or kappa) hedges against their movements. The authors present a new framework of the market model to address all these issues.

In “Rare Events Analysis for High-Frequency Equity Data” Dragos Bozdog, Ionut Florescu, Khaldoun Khashanah, and Jim Wang present a methodology to detect rare events which are defined as large price movement relative to the volume traded. The authors analyze the behavior of equity after the detection of these rare events. Methods are provided to calibrate trading rules based on the detection of these events and the authors exemplify for a particular trading rule. The methodology is applied to tick data for thousands of equities over a period of five days. In order to draw comprehensive conclusions, equi-ties are grouped into classes, and probabilities of price recovery are calculated after these rare events and for each class. The methodol-ogy developed is based on non-parametric statistics and makes no assumption about the distribution of the random variables in the study.

Enjoy!

Dan Tudball

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