High-frequency Trading

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Acknowledgements

It is a pleasure to acknowledge useful comments from Prof Donald MacKenzie.

Notes

¹ MacKenzie (2014), p. 15.

² Page 2, quoted in MacKenzie (2014).

³ It is important to stress that the omerta’-inspired behaviour encountered in high-frequency trading is not found in other areas of financial modelling and research, such as derivatives pricing. This, I believe, is no accident, but it would take too long a detour to explain why these different behaviours have become established. The interested reader is referred to Rebonato (2013).

⁴ For instance, in their introductory chapter (p. xvi), the editors mention the expenditure of ‘hundreds of millions of US dollars to lay a new cable under the Atlantic Ocean’ to shave off a few milliseconds in the communication of trading order. They then rather elliptically remark: ‘[i]t is only natural to question whether such expenditures are socially optimal’.

⁵ If the market maker has to remain committed to making a two-way market in all market conditions, the attending capitalization requirements can be onerous indeed. Not so for the fair-weather market maker. As we shall see, this has profound implications for the quality of the liquidity provision, i.e. for the availability of liquidity in conditions of market distress (when most needed).

⁶ The picture I have painted bears a good resemblance to how reality worked, but should not be taken too literally. In periods of severe market dislocations, even old-fashioned market makers have been known to lose the ability to ‘pick up the phone’. It must be added, however, that, in the ‘old days’, the social and institutional memory of who the fair-weather market makers was and who could truly be relied to provide liquidity when needed remained vivid in the trading community for a long time.

⁷ ‘Large’ in this context means several multiples of the typical market size.

⁸ See, Easley, De Prado and O’Hara, p. 14 and passim. See also Chapter 5 of the book under review.

⁹ Roughly speaking, this is the (unobservable) fundamentals-linked price that would obtain absent the market impact. For a more precise discussion, see Chapter 9 in Easley, De Prado and O’Hara.

¹⁰ See MacKenzie (2014), p. 9–10 for a short but good discussion of these points.

¹¹ For a discussion of the differences between liquidity-making and liquidity-taking (a distinction that, as McKenzie (2014) points out is ‘freighted with moral significance’), see McKenzie (2014), p. 25 and passim.

¹² Easley, De Prado and O’Hara, p. 9, emphasis added.

¹³ Page xvi, Easley, De Prado and O’Hara.

¹⁴ Mackenzie (2014), p. 10.

¹⁵ Even if rarely publicized, these are rather common occurrences: the sudden fall and rise of the 10-year US Treasury over a few-hour period in late 2014 is the best example after the Flash Crash of May 2010.

¹⁶ Kirilenko et al. (2011) look in detail at the May 2010 flash crash and analyse how a large sell order generated a range of coordinated responses from a variety of diverse market participants.

¹⁷ To my knowledge, Mandelbrot (1973) was among the first to point out that when an appropriate ‘local time’ different from ‘clock time’ was used, the resulting distribution of price changes was closely approximated by a Gaussian distribution. Recent developments in the probabilistic description of price process for derivatives-pricing purposes that make use of deterministic or stochastic time changes employ a similar intuition.

¹⁸ Easley, De Prado and O’Hara, p. xvii.

¹⁹ Page 159.

²⁰ See, in particular, p. 209 and passim.

²¹ The reader is even informed that Oanda pays interest on a second-by-second basis.