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An Introduction to High-Frequency Finance

Michel M. Dacorogna, Ramazan Gençay, Ulrich A. Müller, Richard B. Olsen, Olivier V.

posted on 01 July 2002

reviewed by J. McCauley

This book, written by the Michel Dacorogna and other foreign exchange experts of the former Olsen & Associates in Zürich, is a welcome addition to the new field of econophysics. In the text one finds discussions of known empirical facts (basic stylized facts?) that constrain modelling. Scaling and correlations are discussed empirically via Hurst and multiaffine scaling exponents. A very positive aspect aspect is that extreme value theory is used to obtain fat tail exponents for logarithmic returns. In general, correlations are studied by taking absolute values of returns , which they try to characterize by multiaffine scaling exponents, (called ?drift exponents? in the text) analogous to studying velocity structure functions in soft turbulence. Now for the criticism.

The text is unpedagogical, written like a collection of review papers. Instead of taking one or two aspects and explaining them clearly for the benefit of the reader, too many authors are cited with no explanation (this does not constitute what I would regard as an ?Introduction?!). Worse, the notation is devilish, making Bouchaud and Potters seem relatively easy in comparison. The normal notation is bad but ?ccomputerese? is often used as well (examples: EMA (?)=ma(?), wt(T,k,n)(t)=ma(T,n)(t)?., ..). No one wants to read a computer program. Everyone wants to read papers written in good style. For finance theorists I strongly recommend reading and adopting the style of Fischer Black, who was clear and precise even when he was sometimes wrong (as in his belief in the ?beauty? of the neo-classical idea of ?equilibrium?). A minor point: fractional Brownian motion is not Gaussian distributed. This error comes from following texts like Hull or Feder where stochastic calculus is formulated wrong, ignoring the rules of Ito calculus. Also, it is misleading and unnecessary to label something as simple as market interactions as ?relativistic effects?. I hope for a second edition, rewritten for greenhorns like me (instead of for experts in the field), so that the book can be used by students in a course on finance. I confess that I did not review the chapters on ARCH and GARCH because I have yet to find a reason why I should bother to learn about those particular ad-hoc approximations (reflecting a personal pecularity of mine). However, I am advised by Michel that I have thereby missed reading about some of their most interesting results.

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