Superkurtosis

• Published date: 01 December 2023
• Author: STAVROS DEGIANNAKIS,GEORGE FILIS,GRIGORIOS SIOUROUNIS,LORENZO TRAPANI
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/jmcb.12988

DOI: 10.1111/jmcb.12988

STAVROS DEGIANNAKIS

GEORGE FILIS

GRIGORIOS SIOUROUNIS

LORENZO TRAPANI

Superkurtosis

Very little is known on how traditional risk metricsbehave under intraday

trading. Well this void by examining the niteness of the returns’ moments

and assessing the impact of their innity in a risk management framework.

Weshow that when intraday trading is considered, assuming nite higher or-

der moments, potential losses are materially larger than what the theory pre-

dicts, and they increase exponentially as the trading frequency increases—a

phenomenon we call superkurtosis. Hence, the use of the current risk man-

agement techniques under intraday trading imposes threats to the stability

of nancial markets, as capital ratios are severely underestimated.

JEL codes:C12, C54, F30, G10, G15, G17

Keywords:nite moments, risk management, superkurtosis, ultra-high

frequency trading

H     computer

technology have originated a new class of trading known as “intraday trading.” Intra-

day trading has numerous advantages: it offers a great deal of liquidity in the market;

it facilitates the instantaneous transmission of information into prices, pushing mar-

kets to be more efcient; and it creates a market place for small (retail) as well as

large investors (institutions).

However, intraday trading also presents unique challenges (see, e.g., the Final

Project Report from The Government Ofce for Science, London - 2012). Chiey,it

has been criticized as liable to cause large market crashes that may be amplied by the

S D is a Professor of Econometrics and Statistics, Department of Economic and

Regional Development, Panteion University of Social and Political Science, & Research and Economic

Analysis Department, Bank of Greece (E-mail: sdegiannakis@panteion.gr).G F is an Assis-

tant Professor of Economics, Department of Economics, University of Patras(E-mail: glis@upatras.gr).

G S is an Assistant Professor of Economics, Department of Economic and Regional

Development, Panteion University of Social and Political Science, & Department of Economics, Brown

University (E-mail: grigorios_siourounis@brown.edu).L T is a Professor of Economet-

rics, School of Economics, University of Nottingham (E-mail: lorenzo.trapani@nottingham.ac.uk).

Received March 25, 2020; and accepted in revised form March 28, 2022.

Journal of Money, Credit and Banking, Vol. 55, No. 8 (December 2023)

© 2022 The Ohio State University.

2062 :MONEY,CREDIT AND BANKING

inux of algorithmic trading and the order clustering caused by unintended trading

strategy coordination (see, e.g., Beddington et al. 2012; Kirilenko et al. 2017; Man-

hire 2018; and media coverage such as Brush, Schoenberg, and Ring 2015). Hence,

regulators (see the Press Release, European Parliament, MEPs Vote Laws to Regulate

Financial Markets and Curb High Frequency Trading (April 15, 2014)), economists

(e.g., Kirilenko and Lo 2013), and law scholars (e.g., Yadav 2015) have proposed

measures to mitigate such trading behavior.

As a consequence of the issues discussed above, market participants are required

to measure and report several market risk metrics, and to take them into account

when calculating their regulated capital requirements. For example, on January 16th,

2016, the Basel Committee on Banking Supervision (henceforth, “the Committee”)

published a document that revised standards for minimum capital requirements for

Market Risk. In addition, the Committee had also produced three consultative papers

on the Fundamental review of the trading book, namely (i) fundamental review of

the trading book, May 2012, (ii) a revised market risk framework, October 2013, and

(iii) fundamental review of the trading book: Outstanding issues, December 2014.

Furthermore, ECB imposes capital requirements (via the Capital Requirements Reg-

ulation) on institutions who engage in intraday trading. Such requirements are based

on risk metrics or asset volatility. 1However, standards set by regulators are based

on risk metrics that are calculated—at most—at daily frequency. Given that intra-

day trading takes place at higher frequencies, this leaves the market risk, generated

by such trading activity, largely as a dark pool. Indeed, very little is known about

market risk associated with intraday trading; similarly, only little analysis has been

conducted on how traditional risk metrics such as value-at-risk (VaR, hereafter) or

Expected Shortfall (ES, hereafter) behaveat such high-frequency trading. The inves-

tigation of this issue is arguably of immense importance, due to the fact that typical

risk metrics users assume that high-order moments of asset returns at intraday fre-

quency are nite. This assumption is based on the fact that such moments are nite

at lower, for example, daily, frequency, which may be not hold true for higher fre-

quencies. Consequently, the VaR and ES are calculated under the assumptions that

high-order moments are nite, typically using the quantiles of the normal distribution.

In turn, such risk metrics computations are assumed to adequately capture capital re-

quirements, which may be grossly incorrect in the presence of heavy tails. Of course,

it is perfectly possible to compute the VaRand ES without assuming normality. How-

ever, existing methodologies require several assumptions that may not be satised:

for example, extreme-value-theory-based methodologies usually require the i.i.d.as-

sumption (see Manganelli and Engle 2001), which is highly unlikely to be satised by

intraday returns. Thus, prior to calculating any risk metric, it is of vital importance

to have a deep understanding of the properties of the data. Despite its importance,

1. For details, see https://www.bankingsupervision.europa.eu/press/publications/newsletter/2019/

html/ssm.nl190213-5.en.html