![Page 1: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/1.jpg)
High Frequency Quoting:Short-Term Volatility
in Bids and Offers
Joel HasbrouckStern School, NYU
Financial Econometrics ConferenceToulouse School of Economics
![Page 2: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/2.jpg)
Disclaimers
I teach in an entry-level training program at a large financial firm that is generally thought to engage in high frequency trading has been named as a defendant in an HFT lawsuit.
I serve on a CFTC advisory committee that discusses issues related to high frequency trading.
I accept honoraria for presentations at events sponsored by financial firms.
2
![Page 3: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/3.jpg)
What does quote volatility look like?
In US equity markets, a bid or offer can originate from any market participant. “Traditional” dealers, retail and institutional
investors. Bids and offers from all trading venues are
consolidated and disseminated in real time. The highest bid is the National Best Bid (NBB) The lowest offer is the National Best Offer (NBO)
Next slide: the NBBO for AEPI on April 29, 2011
3
![Page 4: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/4.jpg)
Figure 1. AEPI bid and offer, April 29, 2011
4
09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00$27.00
$28.00
$29.00
$30.00
$31.00 AEPI 20110429
![Page 5: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/5.jpg)
Figure 1. AEPI bid and offer on April 29, 2011 (detail)
5
11:00 11:30 12:00
$29.50
$30.00
AEPI 20110429
![Page 6: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/6.jpg)
Features of the AEPI episodes
Extremely rapid oscillations in the bid. Start and stop abruptly Mostly one-sided
activity on the ask side is much smaller Episodes don’t coincide with large long-
term changes in the stock price.
6
![Page 7: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/7.jpg)
Quote volatility: why worry?
Noise The quotes are price signals. Noise degrades
the value of these signals. Execution price risk (for marketable orders
and dark trades) We don’t know and can’t time exactly when
our order will reach the market. Quote volatility links arrival uncertainty to
execution price risk.
7
![Page 8: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/8.jpg)
Quote volatility: the questions
What is its economic meaning and importance?
How should we measure it? Is it elevated? Relative to what? Has it increased along with wider adoption
of high-speed trading technology?
8
![Page 9: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/9.jpg)
Context and connections
Analyses of high frequency trading (HTF) Traditional volatility modeling Methodology: time scale resolution and
variance estimation Economic models of dynamic oligopolistic
pricing.
9
![Page 10: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/10.jpg)
Traditional volatility modeling
Mainstream ARCH, GARCH, and similar models focus on fundamental/informational volatility. Statistically: volatility in the unit-root component of
prices. Economically important for portfolio allocation,
derivatives valuation and hedging. Quote volatility is non-informational
Statistically: short-term, stationary, transient volatility
Economically important for trading and market making.
10
![Page 11: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/11.jpg)
Statistics are local variances about local means
110 50 100 150 200-10
0
10
20
30
40
![Page 12: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/12.jpg)
Connection to pre-averaging
Local averaging of price levels is used to remove microstructure noise prior to modeling fundamental variances.
The local volatility is generally not studied. Here, it is the focus.
12
![Page 13: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/13.jpg)
Computational issues
In computing a local average … How long should the averaging period be? How should the averaging periods be
aligned? Wavelet transformations simply provide
computationally efficient techniques for considering a range of averaging periods obtaining alignment-invariant estimates.
13
![Page 14: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/14.jpg)
The origins of high frequency quoting:Suggestions from economic theory
Price volatility can result from randomized strategies. Varian (1980) The Glosten-Baruch (2013) limit order book.
Edgeworth cycles Progressive undercutting until all producers but
one exit the market The remaining producer raises his price to the
monopoly level. Repeat. Masking and Tirole (1988)
14
![Page 15: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/15.jpg)
Descriptive statistics:computation and interpretation
15
![Page 16: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/16.jpg)
Local variances about local means
160 50 100 150 200-10
0
10
20
30
40
n = length of averaging interval. Depends on trader’s latency and order strategies: we want a range of n
![Page 17: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/17.jpg)
Interpretation
To assess economic importance, I present the volatility estimates in three ways. In mils ($0.001) per share In basis points As a short-term/long-term variance ratio
17
![Page 18: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/18.jpg)
The short/long variance ratio
For a random walk with per period variance , the variance of the n-period difference is .
An conventional variance ratio might be
For a random walk, . Microstructure: we usually find .
Extensively used in microstructure studies: Barnea (1974); Amihud and Mendelson (1987); etc.
18
![Page 19: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/19.jpg)
The empirical analysis
19
CRSP Universe 2001-2011. (Share code = 10 or 11; average price $2 to $1,000; listing NYSE, Amex or NASDAQ)
In each year, chose 150 firms in a random sample stratified by dollar trading volume
2001-2011April TAQ data
with one-second time stamps
2011 April TAQ with one-
millisecond time stamps
High-resolution analysis
Lower-resolution analysis
![Page 20: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/20.jpg)
Figure 2. Wavelet variance ratios across time scale and dollar volume quintiles
20
Nor
mal
ized
quo
te v
aria
nce
1
2
3
4
5
6
7
8
9
10
11
12 100ms 1s 10s 1m 20m
Time scale (milliseconds)
10 ms 100 ms 1,000 ms 10.0 sec 100.0 sec 16.7 min 166.7 min
Avg dollar volume rank 1 (low) 2 34 5 (high)
![Page 21: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/21.jpg)
The 2011 results: a summary
Variance ratios: short term volatility is much higher than we’d expect relative to a random-walk.
In mils per share or basis points, average short term volatility is economically meaningful, but small.
21
![Page 22: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/22.jpg)
Historical analysis
22
CRSP Universe 2001-2011. (Share code = 10 or 11; average price $2 to $1,000; listing NYSE, Amex or NASDAQ)
In each year, chose 150 firms in a random sample stratified by dollar trading volume
2001-2011April TAQ data
with one-second time stamps
2011 April TAQ with one-
millisecond time stamps
High-resolution analysis
Lower-resolution analysis
![Page 23: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/23.jpg)
High-resolution analysis …… with low resolution data
TAQ with millisecond time stamps only available from 2006 onwards
TAQ with one second time stamps available back to 1993.
Can we draw inferences about subsecond variation from second-stamped data?
Yes, if we are confident in the ordering of the data.
23
![Page 24: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/24.jpg)
Recall the constant intensity Poisson process …
no. of events in an interval If , then have the same distribution as the
order statistics in a sample of independent random variables.
This suggests that millisecond remainders can be easily simulated.
24
![Page 25: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/25.jpg)
Table 5. Summary statistics, historical sample, 2001-2011 (only odd numbered years are shown)
25
2001 2003 2005 2007 2009 2011No. firms 137 141 144 150 145 149
NYSE 106 51 48 55 56 47Amex 16 10 8 14 5 6
NASDAQ 15 80 88 81 84 96Avg. daily trades 167 231 448 970 1,993 1,346Avg. daily quotes 1,525 1,470 6,004 12,521 41,571 24,053
Avg. daily NBB changes 128 210 611 772 1,787 1,225Avg. daily NBO changes 127 226 729 789 1,789 1,146
Avg. price $20.57 $14.41 $16.10 $15.81 $11.25 $15.77Market equity cap
$ Million$976 $205 $348 $480 $382 $690
![Page 26: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/26.jpg)
Table 5. Summary statistics, historical sample, 2001-2011 (only odd numbered years are shown)
26
2001 2003 2005 2007 2009 2011No. firms 137 141 144 150 145 149
NYSE 106 51 48 55 56 47Amex 16 10 8 14 5 6
NASDAQ 15 80 88 81 84 96Avg. daily trades 167 231 448 970 1,993 1,346Avg. daily quotes 1,525 1,470 6,004 12,521 41,571 24,053
Avg. daily NBB changes 128 210 611 772 1,787 1,225Avg. daily NBO changes 127 226 729 789 1,789 1,146
Avg. price $20.57 $14.41 $16.10 $15.81 $11.25 $15.77Market equity cap
$ Million$976 $205 $348 $480 $382 $690
23% CAGR
32% CAGR
![Page 27: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/27.jpg)
What statistics to consider?
Long-term volatilities changed dramatically over the sample period.
Variance ratios (normalized to long-term volatility) are the most reliable indicators of trends.
27
![Page 28: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/28.jpg)
Table 6. Wavelet variance ratios for bids and offers, 2001-2011
28
Time scale 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
50 ms 5.29 7.36 5.96 10.31 6.56 8.57 6.96 6.07 4.53 7.09 4.71100 ms 5.52 6.75 5.20 9.71 6.38 8.07 6.27 5.39 4.12 6.27 4.33200 ms 5.35 6.44 5.05 9.06 6.10 7.34 5.33 4.65 3.68 5.41 3.75400 ms 4.65 5.35 4.92 8.18 5.64 6.30 4.25 3.84 3.21 4.54 3.07800 ms 3.16 4.12 3.86 5.59 4.93 5.10 3.41 3.11 2.76 3.71 2.56
1,600 ms 2.13 2.56 3.19 4.11 4.06 4.05 2.89 2.59 2.42 3.04 2.233.2 sec 2.00 2.25 2.91 3.39 3.42 3.37 2.56 2.28 2.16 2.53 2.016.4 sec 1.95 2.12 2.61 2.91 2.88 2.92 2.35 2.08 1.94 2.16 1.82
Panel A: Computed from unadjusted bids and offers
![Page 29: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/29.jpg)
Summary 2001-2011
Quote volatility is surprisingly high in the early years.
This reflects large temporary shifts in bids and offers (a consequence of manual markets).
When the bid and offer series are filtered, volatility is lower in the early years.
But over 2001-2011 no evidence of a broader trend.
29
![Page 30: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/30.jpg)
Follow-up questions
What strategies give rise to the episodic oscillations?
Are the HFQ episodes unstable algos? Are they sensible strategies to detect and access
liquidity?
30
![Page 31: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/31.jpg)
31
09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00
$9.00
$9.50
$10.00
$10.50
$11.00
LSBK 20110401
![Page 32: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/32.jpg)
32
09:30 10:00 10:30 11:00
$41
$42
$43
$44
$45
$46
$47
$48CVCO 20110420
![Page 33: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/33.jpg)
33
09:45 09:50 09:55 10:00 10:05 10:10
$79.50
$80.00
$80.50
$81.00 PRAA 20110414
![Page 34: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/34.jpg)
34
11:10 11:20 11:30 11:40
$18.50
$19.00
TORM 20110401
![Page 35: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/35.jpg)
35
10:00 11:00 12:00 13:00 14:00 15:00 16:00
$13.50
$13.55
$13.60
$13.65
$13.70
$13.75
$13.80
$13.85
$13.90
WSTG 20110404
![Page 36: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/36.jpg)
36
10:00 11:00 12:00 13:00 14:00 15:00 16:00
$1.94
$1.96
$1.98
$2.00
$2.02
$2.04
$2.06
AAME 20110418
![Page 37: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/37.jpg)
37
10:00 11:00 12:00 13:00 14:00 15:00 16:00
$3.55
$3.60
$3.65
$3.70
$3.75
$3.80
$3.85
$3.90
$3.95
$4.00 ACFN 20110412
![Page 38: High Frequency Quoting: Short-Term Volatility in Bids and Offers](https://reader036.vdocuments.mx/reader036/viewer/2022062811/56815efa550346895dcdb7b2/html5/thumbnails/38.jpg)
38
12:00 13:00 14:00 15:00 16:00
$3.90
$4.00
$4.10
$4.20
$4.30
$4.40 ADEP 20110427