0DTE Trading Rules∗
Grigory Vilkov†
November 2023
The accompanying data will be updated on a regular basis
and the analysis will be extended to conditional and dynamic trading rules.
Abstract
This empirical study is the first in a series documenting empirical properties of 0DTE options
on the S&P500 index (SPX) and popular strategies built from these options for the sample
period from 09/2016 to 05/2023. We focus on strategies established every trading day and
held to expiry (i.e., unconditional and static trading rules). We show that 0DTEs deliver
significant variance risk premium, i.e., the implied variance priced in these options is, on
average, higher than the realized variance until settlement. Realized returns of individual
options are highly volatile and skewed, though at the median, buying deep in-the-money
calls and selling out-the-money calls and puts can be profitable. Median returns for popular
options strategies are mostly negative (strangles, bull and bear spreads, call and put ratio
spreads), except for risk reversal, which produces consistently positive mean and median
returns in our sample period.
Keywords: 0DTE, ultra-short options, variance risk premium, volatility trading, option strategies, option trading
∗
Parts of the data processing methodology in this article were developed while writing Dim, Eraker, and
Vilkov (2023). The data for producing statistics in this paper and additional analysis is available online at
https://osf.io/7q86u/.
†
Frankfurt School of Finance & Management; E-mail: vilkov@vilkov.net; Web-site: www.vilkov.net.
1
Introduction
The trading volumes in zero-days to expiry options (0DTEs) have exploded in the past several
years, and due to relatively easy access to brokerage platforms, abundance of various learning
resources, and low option premiums for ultra-short maturity options, retail investors increasingly
use 0DTEs to make directional and volatility bets. While plenty of internet sites offer free and
paid recipes on making money on options markets and explaining when and how a particular
strategy should work, little is known about the performance of naked 0DTE call and put options
and various strategies combining several call and put positions.
We aim to fill the information gap and provide simple yet detailed performance statistics
for naked 0DTE options on the S&P500 market index and for several popular strategies from
these options. The first part of the analysis covers unconditional static trading rules, in which
positions are taken every day at some fixed time point during the day (we use 10:00 in the main
analysis and also include data and performance numbers for 13:00 and 15:00 in the additional
figures and data files) and held until expiry of all options at 16:00. The sample period is from
09/2016 to 05/2023, i.e., starting from the month with at least three weekly expiration days.
The data will be regularly updated to more recent periods.
For the analysis, at a given point in time on each day we interpolate prices of available
0DTE options with moneyness (defined as strike to underlying level ratio) between 0.98 and
1.02 (e.g., 3920 to 4080 for the SPX level of 4000) to fill in the available range with step 0.00125
(i.e., a 5-dollar step for the SPX of 4000), and then use these standardized options to compute
performance statistics for standalone positions and selected option strategies. As such option
strategies, we use an at-the-money (ATM) straddle and strangles with several moneyness levels,
bull call and bear put spreads, call and put ratio spreads, and risk reversals, each (except for a
straddle) for several combinations of strikes, from in-the-money (ITM) to out-the-money (OTM).
1
Figure A1 provides their sample payoff profiles. We also document the realized variance risk
premium, computed as the implied variance of SPX options until settlement time minus realized
variance for the same period.
The rest of the paper is structured as follows: Section 2 analyzes the average variance risk
premiums, prices, and returns of individual options and option-based strategies. Section 3
discusses input data and its processing. Section 4 briefly overviews relevant academic literature.
Section 5 concludes. Appendix A contains additional materials such as tables and figures for
variations in the analysis.
2
Unconditional Static Trading Rules
Suppose we establish an options position daily without considering any possible conditioning
variables (a.k.a. managing parameters) defining when and how many contracts to open. In
that case, we pursue an unconditional and static trading strategy. We calculate holding period
returns and profits and loss (PNL) to expiry for the considered options and their combinations
and then present the statistics for these returns.
Variance Risk Premium.
Over the whole sample period from 09/2016 to 05/2023, the
0DTEs deliver a positive and statistically significant variance risk premium, i.e., their implied
variance is significantly higher than the realized variance to expiry, see Figure 1, Panel B.
To trade variance, we need to sell options with different moneyness levels, with proportions
depending on the method used to compute the variance. For example, Cboe computes a wellknown volatility index VIX as the risk-neutral variance of log returns, weighting prices of outthe-money options according to the formula in equation 3. Essentially, the variance swap rate is a
weighted sum of time values of the out-the-money call and put options, with weights proportional
to the reciprocal of the moneyness (for both stock price and strikes normalized by stock price)
2
A: Variance Swap Rate to Expiration
B: Variance Risk Premiums to Expiration
Average vix_pct by Time of Day
Average vrp_pct by Time of Day
Median
25th Percentile
75th Percentile
Mean
0.008
0.007
0.0020
0.006
0.005
% to expiry
% to expiry
Median
25th Percentile
75th Percentile
Mean
0.0025
0.004
0.0015
0.0010
0.003
0.002
0.0005
0.001
15
:30
15
:00
14
:30
14
:00
Time of Day
13
:30
13
:00
12
:30
12
:00
11
:30
11
:00
10
:30
10
:00
15
:30
15
:00
14
:30
14
:00
Time of Day
13
:30
13
:00
12
:30
12
:00
11
:30
11
:00
10
:30
0.0000
10
:00
0.000
Figure 1: Variance Risk Premiums. The figure shows average variance risk premiums (VRP) to expiration
for 0DTE SPXW options by intraday 30-minute points. VRP is computed as implied minus realized variances
from a given bar to expiration at 16:00. We average realized VRPs from the end of each bar to expiration at
16:00 that day (with 95% confidence bounds based on Newey and West (1987) standard errors with three lags).
Bars show mean values; each bar is accompanied by median, 25th, and 75th percentiles. X-axis labels show the
endpoints of intraday bars. The sample period is from 09/2016 to 05/2023.
and empirically adding up to a number between one and two. For 0DTEs, the variance swap
rate to expiration is shown in Figure 1, Panel A. The realized variance risk premium can be
thought of as the remaining time value from selling a portfolio of OTM options after paying off
the options that were exercised. Indeed, the higher the realized variance, the further away from
the ATM point the final price realization can be, and the more we need to pay out on exercised
options. In the limiting case of the zero realized variance, the underlying price does not change,
and we keep all the collected time values.
The numbers in Panel B of Figure 1 indicate that selling 0DTE variance can, on average,
be profitable; however, because the time values of the OTM options with just hours to expiry
are minimal (see Figure 2), the variance swap rates are also very low, and even having realized
variance of zero during the day and collecting two times average time value of all the OTM calls
and puts would earn us only ≈ 0.0020% of the underlying price. Thus, the magnitude of the
variance risk premium is tiny due to the very short period to expiry, and realistic transaction
costs would hardly make it tradable for retail investors. Figure 1, Panel B puts the median
realized VRP from 10:00 to expiry to about 0.0011%, which confirms the above point.
3
A: Call
Price, 10:00
Average mid for calls time 10:00:00
B: Call Time
Value, 10:00
Average tv for calls time 10:00:00
Median
25th Percentile
75th Percentile
Mean
0.0200
0.0175
Median
25th Percentile
75th Percentile
Mean
0.0035
0.0030
0.0150
% of Underlying
% of Underlying
0.0025
0.0125
0.0100
0.0075
0.0020
0.0015
0.0010
0.0050
0.0005
0.0025
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0.1
10 25
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
0.0000
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0.0
10 00
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
0.0000
Moneyness in %
Moneyness in %
C: Put
Price, 10:00
Average mid for puts time 10:00:00
0.0200
0.0175
D: Put Time
Value, 10:00
Average tv for puts time 10:00:00
Median
25th Percentile
75th Percentile
Mean
Median
25th Percentile
75th Percentile
Mean
0.0035
0.0030
0.0025
0.0125
% of Underlying
% of Underlying
0.0150
0.0100
0.0075
0.0020
0.0015
0.0025
0.0005
0.0000
0.0000
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0.1
10 25
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
0.0010
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0.0
10 00
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
0.0050
Moneyness in %
Moneyness in %
Figure 2: 0DTE Option Prices and Time Value. The figure provides statistics on prices of 0DTE call and
put options at 10:00 ET. Panels on the left show option mid-price relative to the underlying price in %. Panels on
the right show time value relative to underlying, also in %. Bars show mean values, and each bar is accompanied
by median, 25th, and 75th percentiles. X-axis labels show the moneyness of the analyzed options. The sample
period is from 09/2016 to 05/2023.
Individual Options. We compute individual option returns for calls and puts relative to the
mid-prices and the PNL of the option positions at expiry relative to the underlying price (i.e.,
(payof f − mid price)/underlying price × 100%) at the time the option position is established
(10:00 ET for the figures and tables in the main text). The results are presented in Figure 3.
Individual call and put option returns are highly volatile, especially out-the-money ones, and
mean returns are typically not significantly different from zero. However, statistical inference
in this case can be flawed due to skewed distributions of realized returns. Computing rather
option realized PNL relative to the underlying price produces a less asymmetric (i.e., a more
normal) distribution and shows that at- and out-the-money calls and all puts are losing money
on average, and out-the-money option realized PNL is typically more compact in terms of the
4
distribution. Selling slightly OTM calls and puts delivers in up to 75 percent of observations
positive returns; for more ITM options, the realized PNL is far more volatile, with the difference
between 75th and 25th percentile of 0.7-0.8% of underlying price.
B: Call PNL/Underlying
A: Average
CallrethReturns
for calls time 10:00:00
75
Average reth_und for calls time 10:00:00
0.4
Median
25th Percentile
75th Percentile
Mean
50
0.2
0.1
0
% of Underlying
% of Option Mid-price
25
25
0.0
0.1
50
0.2
75
0.3
0.4
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
100
Moneyness in %
Moneyness in %
D: Put PNL/Underlying
C: Average
PutrethReturns
for puts time 10:00:00
40
Average reth_und for puts time 10:00:00
Median
25th Percentile
75th Percentile
Mean
Median
25th Percentile
75th Percentile
Mean
0.3
0.2
20
0.1
0
% of Underlying
% of Option Mid-price
Median
25th Percentile
75th Percentile
Mean
0.3
20
40
0.0
0.1
0.2
60
0.3
80
0.4
100
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
0.5
Moneyness in %
Moneyness in %
Figure 3: 0DTE Option Returns. The figure provides statistics on the profitability of naked 0DTE call and
put option buying at 10:00 ET and holding to expiry at 16:00 ET. Panels on the left show realized return in
% relative to option mid-price. Panels on the right show the realized profit per one unit of underlying relative
to underlying price (payof f − mid price)/underlying price × 100%. Bars show mean values, and each bar is
accompanied by median, 25th, and 75th percentiles. X-axis labels show the moneyness of the analyzed options.
The sample period is from 09/2016 to 05/2023.
The options performance from 13:00 and 15:00 to expiry is shown in Figures A2 and A3.
The general message does not change for these position opening times.
Option Strategies. Individual option positions are bets on both volatility and the direction of
underlying, and the specific option structures allow us to bet on more specific views, benefiting
from their realizations. We build and analyze (i) an ATM straddle and strangles, which at
initiation are approximately delta-neutral and are close to a pure volatility play; (ii) risk reversals
5
that benefit from a positive skewness risk premium (i.e., realized skewness being larger than the
implied one); (iii) bull call spreads and bear put spreads, which are bets on a moderate to
a significant move in underlying, positive for the bull and negative for the bear spreads; and
(iv) call and put ratio spreads (1 × 2), which are cheap bets on zero to a moderate move in
underlying, again positive for the call and negative for the put ratio spreads.
Considered strategies have very distinct risk-return profiles (see Figure A1): the straddle and
strangles have limited downside and unlimited upside, bull, and bear spreads have limited both
downside and upside, ratio spreads have limited upside and unlimited downside, and risk reversal
has both upside and downside unlimited. It is reflected in the initial cost: Risk reversals and
ratio spreads with a narrow strike range are typically credit strategies, resulting in net premium
receipt at initiation, while the others are debit ones, with the straddle and strangles being the
most expensive ones, and we need to pay a premium at the start.
Because of the low or even negative cost of some of the option combinations, the realized
returns computed relative to the cost either do not make sense or demonstrate a very skewed and
unstable distribution. Instead, we again analyze the realized PNL of the strategies relative to the
underlying price. The results in Figure 4 and Table 1 for several moneyness combinations used
for the combos construction contain mostly negative news: the spreads and ratio spreads’ return
distributions are very volatile and, in general, show realizations all around the place, with 25th
and 75th percentiles being close to symmetric around zero. The median returns for spreads with
long positions being ATM are all negative, so shorting them could make more sense; long sides
ITM produce close to symmetric distributions with literally zero means and medians slightly
above zero for calls and below zero for puts. This result seems to be an artifact of a mostly
bullish market in 2017-2023. Buying strangles with both OTM strikes would result in relatively
compact distribution with both extreme quartiles negative, so selling them made money in at
least 75% of the historical observations. Risk reversal is the only strategy consistently producing
6
A: Strangle PNL/Underlying
B: Risk Reversal PNL/Underlying
Average reth_und for strangle time 10:00:00
Average reth_und for risk_reversal time 10:00:00
Median
25th Percentile
75th Percentile
Mean
0.04
0.03
0.0
% of Underlying
% of Underlying
0.1
0.1
0.02
0.01
0.2
1/1
0.995/1.005
Moneyness
0.99/1.01
0.00
0.98/1.02
C: Bull Call Spread PNL/Underlying
0.99/1.01
Moneyness
0.985/1.015
0.98/1.02
Average reth_und for bear_put_spread time 10:00:00
Median
25th Percentile
75th Percentile
Mean
0.3
0.995/1.005
D: Bear Put Spread PNL/Underlying
Average reth_und for bull_call_spread time 10:00:00
0.4
Median
25th Percentile
75th Percentile
Mean
0.3
0.2
0.2
0.1
0.1
% of Underlying
% of Underlying
Median
25th Percentile
75th Percentile
Mean
0.0
0.1
0.0
0.1
0.2
0.2
0.3
0.3
0.4
1/1.005
1/1.01
1/1.015
1/1.02
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
0.995/1
E: Call Ratio Spread PNL/Underlying
0.99/1.01
0.985/1.015
0.98/1.02
Median
25th Percentile
75th Percentile
Mean
0.3
0.2
0.2
0.1
0.1
% of Underlying
% of Underlying
0.98/1
0.995/1.005
Moneyness
Average reth_und for put_ratio_spread time 10:00:00
Median
25th Percentile
75th Percentile
Mean
0.3
0.985/1
F: Put Ratio Spread PNL/Underlying
Average reth_und for call_ratio_spread time 10:00:00
0.4
0.99/1
0.0
0.1
0.0
0.1
0.2
0.2
0.3
0.3
0.4
1/1.005
1/1.01
1/1.015
1/1.02
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
0.995/1
0.99/1
0.985/1
0.98/1
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
Figure 4: 0DTE Static Option Strategies. The figure provides statistics on the profitability of six wellknown option strategies based on 0DTE call and put options; positions are taken at 10:00 ET and held to expiry
at 16:00 ET. All panels show strategies’ realized profit per one unit of underlying relative to underlying price
(payof f − mid price)/underlying price × 100%. Bars show mean values, and each bar is accompanied by median,
25th and 75th percentiles. X-axis labels show the combination of moneyness of options used for a strategy. The
sample period is from 09/2016 to 05/2023.
positive mean, median, and even 25th percentile PNL. However, its average PNL is very modest,
only about 0.01% of the underlying index price, and trading 0DTE reversals may be unfeasible
for most investors. The performance of the same strategies from 13:00 and 15:00 is shown in
Figures A4 and A5.
Overall, our analysis shows that unconditional and static trading rules in 0DTE SPX options
hardly pay off: the realized PNL is exceptionally volatile, and the variance risk premium is
7
Strategy
Moneyness Count Mean Volatility
Strangle/Straddle 1/1
0.995/1.005
0.99/1.01
0.98/1.02
Risk Reversal
0.995/1.005
0.99/1.01
0.985/1.015
0.98/1.02
Bull Call Spread 1/1.005
1/1.01
1/1.015
1/1.02
0.995/1.005
0.99/1.01
0.985/1.015
0.98/1.02
Call Ratio Spread 1/1.005
1/1.01
1/1.015
1/1.02
0.995/1.005
0.99/1.01
0.985/1.015
0.98/1.02
Bear Put Spread 0.995/1
0.99/1
0.985/1
0.98/1
0.995/1.005
0.99/1.01
0.985/1.015
0.98/1.02
Put Ratio Spread 0.995/1
0.99/1
0.985/1
0.98/1
0.995/1.005
0.99/1.01
0.985/1.015
0.98/1.02
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
1147
-0.0022
-0.0027
-0.0086
-0.0117
0.0089
0.0131
0.0130
0.0138
0.0001
0.0009
0.0024
0.0021
0.0007
-0.0016
-0.0006
-0.0008
-0.0031
-0.0014
0.0016
0.0011
-0.0024
-0.0038
-0.0014
-0.0018
0.0004
0.0055
0.0068
0.0074
-0.0001
0.0024
0.0042
0.0052
0.0062
0.0163
0.0191
0.0201
0.0057
0.0133
0.0164
0.0180
0.517
0.438
0.339
0.203
0.582
0.410
0.292
0.213
0.203
0.319
0.380
0.413
0.371
0.579
0.698
0.765
0.324
0.334
0.368
0.392
0.391
0.546
0.667
0.737
0.199
0.329
0.407
0.456
0.370
0.576
0.691
0.757
0.302
0.307
0.375
0.440
0.368
0.528
0.656
0.742
Min
1%
25%
50%
75%
99% Max Skew
-2.688 -0.985 -0.264 -0.088 0.178 1.780 2.959 1.125
-2.703 -0.826 -0.174 -0.049 0.007 1.638 2.903 1.634
-2.753 -0.568 -0.088 -0.022 -0.006 1.346 2.731 2.079
-2.136 -0.395 -0.019 -0.006 -0.002 0.733 2.120 0.630
-3.481 -1.851 0.005 0.018 0.045 1.921 5.358 0.833
-2.999 -1.336 0.003 0.012 0.030 1.441 4.917 2.135
-2.521 -0.836 0.002 0.006 0.018 0.955 4.466 4.470
-2.038 -0.345 0.000 0.003 0.010 0.453 4.010 7.936
-0.425 -0.240 -0.183 -0.087 0.228 0.363 0.500 0.482
-1.229 -0.419 -0.238 -0.106 0.179 0.745 1.000 0.826
-0.737 -0.556 -0.251 -0.114 0.163 1.108 1.360 1.206
-0.938 -0.653 -0.255 -0.116 0.161 1.385 1.613 1.399
-0.704 -0.559 -0.355 0.031 0.366 0.507 1.000 -0.133
-1.121 -1.060 -0.346 0.043 0.373 0.994 2.000 -0.157
-1.652 -1.548 -0.343 0.050 0.384 1.491 2.860 -0.157
-2.124 -2.017 -0.341 0.053 0.390 1.942 3.360 -0.208
-3.552 -1.088 -0.114 -0.023 0.150 0.532 1.798 -3.793
-3.050 -0.440 -0.209 -0.102 0.164 0.739 1.261 -1.279
-2.493 -0.431 -0.244 -0.110 0.163 1.108 1.562 0.723
-1.894 -0.514 -0.252 -0.113 0.162 1.331 1.614 1.303
-3.342 -0.879 -0.275 0.014 0.270 0.720 1.525 -1.589
-2.649 -1.024 -0.330 0.045 0.368 1.017 1.640 -0.342
-1.919 -1.511 -0.339 0.051 0.387 1.465 2.860 -0.192
-2.046 -1.994 -0.339 0.051 0.388 1.759 3.360 -0.247
-0.268 -0.215 -0.155 -0.102 0.200 0.388 0.449 0.783
-0.456 -0.378 -0.222 -0.124 0.143 0.810 0.886 1.169
-0.648 -0.492 -0.249 -0.132 0.125 1.204 1.306 1.486
-0.814 -0.570 -0.262 -0.134 0.113 1.622 1.750 1.764
-0.576 -0.508 -0.366 -0.032 0.354 0.562 0.768 0.149
-1.038 -0.993 -0.373 -0.043 0.357 1.064 1.121 0.191
-1.519 -1.478 -0.385 -0.044 0.342 1.546 1.698 0.235
-2.026 -1.921 -0.392 -0.048 0.340 2.015 2.098 0.293
-2.507 -1.281 -0.078 -0.018 0.133 0.566 1.428 -2.531
-1.680 -0.512 -0.163 -0.110 0.126 0.850 1.985 0.887
-0.788 -0.362 -0.225 -0.126 0.135 1.178 1.632 1.600
-0.483 -0.447 -0.249 -0.132 0.127 1.517 2.189 1.849
-2.318 -1.045 -0.235 -0.024 0.263 0.798 1.679 -0.550
-1.448 -0.949 -0.335 -0.016 0.343 1.194 2.459 0.299
-1.493 -1.417 -0.362 -0.030 0.351 1.532 2.317 0.287
-1.999 -1.815 -0.382 -0.039 0.355 1.974 3.023 0.383
Table 1: 0DTE Static Option Strategies Performance. The table shows the summary statistics for the
holding period returns of six well-known option strategies based on 0DTE call and put options; positions are
taken at 10:00 ET and held to expiry at 16:00 ET. The statistics are based on option strategies’ realized profit per
one unit of underlying relative to underlying price (payof f − mid price)/underlying price × 100%. The sample
period is from 09/2016 to 05/2023.
tiny due to the short time to expiry. The results demonstrated by some strategies may be a
consequence of an on-average growing S&P500 index during our sample period, and their future
average performance may be different in case the market growth slows down.
Note that conditioning trading decisions on the current environment and making trading
rules dynamic, i.e., adjusting complete combos or individual options positions during the day,
8
can be crucial in improving the performance of 0DTE trading. We will extend the analysis in
these directions in the next version of the paper.
3
Data Preparation
Data on Options and Underlying Markets. We use option 30-minute bars from Cboe
that include national best bid and offer (NBBO) with size, open/high/low/close (OHLC) prices,
trade volumes, and price of the underlying instrument, focusing on the SPX Weeklys with root
SPXW. These options are European and cash-settled at the SPX index’s close at 16:00 ET.
Our analysis runs from 09/2016 until 05/2023. Starting from late August 2016, SPXW options
have three weekly expiration dates, and then on April 18, 2022, and May 11, 2022, two more
days per week were added, so we have SPXW 0DTE options every weekday. We obtain the
end-of-the-day (EOD) closing prices for all underlying instruments and also one-minute OHLC
(open, high, low, close) prices for SPX from DTN IQFeed.
Returns, Variances and Variance Risk Premiums. We compute implied variance (IV )
to expiration at the end of each available bar t during the expiration day using VIX Cboe (2023)
methodology applied to 0DTE options observed at the end of that bar:
IVt = 2erT
X ∆Ki
i
Ki2
Q(Ki ) − [F/K0 − 1]2 ,
(1)
where Ki is the strike price of out-the-money (OTM) call and put options, K0 is the first strike
equal to or otherwise immediately below current option-implied forward price F , Q(Ki ), i ̸= 0
is the mid-quote of OTM call and put options, and Q(K0 ) is the average of the K0 put option
price and K0 call option price, r is the risk-free rate, for which we use 1-month T-bill rate from
FRED, and T is time to expiration (in years).
9
We compute forward-looking realized variance (RV ) at the end of each bar t for periods
matching each computed IV as the sum of squared one-minute log returns from the end of a
bar to the end of the day:
RVt =
T
−1
X
2
rt,t+1
,
(2)
t
where rt,t+1 is log return for the minute ending at t + 1 computed as close to close from t until
T =16:00 on the same day.
We define ex post realized variance risk premium V RP to expiration at a given bar t as the
payment on a short variance swap from t to expiry, which is equal to the implied minus realized
variances from the end of a given intraday bar until expiration time:
V RPt = IVt − RVt .
(3)
We do not annualize it to get a better feeling of the total return from selling variance until
expiry at 16:00 at some point during the day.
For individual options with today’s expiration, observed at a given point in time during the
day (e.g., 10:00 ET), we first compute their moneyness (defined as strike to underlying price
ratio) and then select all options within moneyness bounds [0.98, 1.02], i.e., ±2% from the ATM
level. For each of these options, we express the mid-price and bid-ask spread in terms of the
underlying price (i.e., compute the ratio of a variable and underlying price), and then interpolate
main variables of interest (mid-price, bid-ask spread, implied volatility, and Greeks) as a function
of moneyness with step 0.00125, for calls and puts separately.1 For each interpolated option, we
1
The step corresponds to the standard 5-dollar step in strikes for the index level of 4000. We interpolate the
options to have standard moneyness levels comparable in time, and we can use them without modifications to
construct option strategies. We use 1-dimensional interpolation using piecewise cubic polynomials developed by
Akima (1970), and implemented in Akima1DInterpolator function in SciPy Interpolate package. The results
are robust to using other interpolation routines.
10
compute the payoff:
P ayof ft (M, T ype) =



(M − S /S )+
if T ype = Call,


(ST /St − M )+
if T ype = P ut,
T
t
(4)
where M is the moneyness level for a given option, and ST /St is the total return on the index
S from time t to expiry T =16:00. We also compute for each option its intrinsic value as the
payoff from an immediate exercise and the time value as the difference between the mid-price
and intrinsic value. For options that get a negative time value (due to using mid-price instead of
the effective or true price), we set the time value to zero and the intrinsic value to the mid-price.
Because the moneyness of an option is its strike level relative to the underlying price, the payoff,
time value, and intrinsic are already expressed in terms of the underlying price. To compute
the PNL of an option position relative to the underlying price, we need to take the difference
between the payoff and the mid-price, assuming that the latter is the effective option price:
P N Lt (M, T ype) = P ayof ft (M, T ype) − M idt (M, T ype),
(5)
where M idt (M, T ype) is the mid-price at time t of an option with moneyness M and type T ype.
The realized return to expiry is then computed as the ratio of PNL to the mid-price:
Rett (M, T ype) =
P ayof ft (M, T ype)
P N Lt (M, T ype)
=
− 1.
M idt (M, T ype)
M idt (M, T ype)
(6)
To express PNL and return in percentage terms, we multiply both by 100. For the structures
created as predefined combinations of options, we compute their PNL as the sum of PNLs of
individual options scaled by the number of particular options included in the structure. By
construction, this PNL will be expressed in terms of underlying price.
The interpolated options and relevant structures data are available at https://osf.io/7q86u/.
11
4
Relevant Literature
Some recent papers study 0DTE options trading. Beckmeyer, Branger, and Gayda (2023) look
at the performance of retail vs. professional traders in 0DTE options. They use the methodology
of Bryzgalova, Pavlova, and Sikorskaya (2022) to classify trades as retail or professional and show
that retail investors incurred significant trading losses in 0DTE options, averaging losses of more
than $500,000 per day since the introduction of five expiration days per week in 2022. Retail
investors’ losses are primarily from taking long positions, while short positions are generally
profitable. Bandi, Fusari, and Renò (2023) derive a theoretical pricing model for short-term
options without distributional assumptions. Brogaard, Han, and Won (2023) examine the impact
of trading activity in 0DTEs (using the proportion of 0DTEs in total options trading) on the
intraday volatility, finding that higher relative turnover in ultra-short-term options is positively
related to the intraday volatility of underlying. Dim, Eraker, and Vilkov (2023) show that
high open interest gamma in 0DTE options is not contributing to the propagation of past
volatility (specifically, last day and overnight volatilities) and that the current state of liquidity
in underlying markets absorbs any potential delta-hedging flows from option markets without
generating abnormal volume patterns.
5
Conclusion
Our empirical study of zero-days to expiry (0DTE) options trading strategies on the S&P 500
index, spanning from 09/2016 to 05/2023, provides valuable insights into this dynamic trading
sector. The surge in 0DTE options trading, mainly driven by easy access to user-friendly brokerage platforms and the attraction of low option premiums, has produced a diverse range of
outcomes in terms of profitability.
12
Our analysis has uncovered several key findings. First, 0DTE options offer a substantial
variance risk premium, with implied variance consistently higher than realized variance until
settlement. However, the success of various strategies is not guaranteed. In the initial part
of our analysis, we considered unconditional static trading rules, revealing high volatility and
skewed returns in individual 0DTE options held to expiry.2 Some tactics, such as buying deep
in-the-money calls and selling out-of-the-money calls and puts, show promise for profitability.
Nevertheless, the median profit and loss (PNL) for most popular strategies tend to be negative,
with a wide distribution of potential outcomes. Notably, the risk reversal strategy consistently
yields positive PNL, though the magnitude is modest.
Furthermore, our study highlights the challenges of applying unconditional and static trading
rules in 0DTE SPX options. These strategies often lead to highly volatile realized PNL and a
minimal variance risk premium due to the short time to expiry. Additionally, the upward trend
of the S&P 500 index during our study’s timeline may have influenced some of the observed
outcomes.
Our research underscores that while specific 0DTE unconditional static trading rules can
yield profitability, this domain is inherently risky and unpredictable. Traders should be mindful
of the volatility and mixed success rates associated with various strategies, emphasizing the
importance of a comprehensive and nuanced understanding of the 0DTE options market. These
insights provide valuable guidance to market participants navigating this complex and evolving
trading landscape.
2
We call such rules unconditional and static because we do not condition our decision about the direction and
size of the position on any environmental variables and do not adjust the positions during the day to fix profits,
limit losses, or change the exposure profile. Later, we will extend the analysis to conditional and dynamic rules.
13
References
Akima, H., 1970, “A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures,”
J. ACM, 17(4), 589–602.
Bandi, F. M., N. Fusari, and R. Renò, 2023, “0DTE option pricing,” Working paper.
Beckmeyer, H., N. Branger, and L. Gayda, 2023, “Retail Traders Love 0DTE Options... but should
they?,” working paper.
Brogaard, J., J. Han, and P. Y. Won, 2023, “How does Zero-Day-to-Expiry options trading affect the
volatility of underlying assets?,” working paper.
Bryzgalova, S., A. Pavlova, and T. Sikorskaya, 2022, “Retail trading in options and the rise of the big
three wholesalers,” Journal of Finance, forthcoming.
Cboe, 2023, “Volatility Index Methodology: Cboe Volatility Index,” working paper, Cboe Global Indices,
LLC.
Dim, C., B. Eraker, and G. Vilkov, 2023, “0DTEs: Trading, Gamma Risk and Volatility Propagation,”
Working Paper, Frankfurt School of Finance and Management.
Newey, W. K., and K. D. West, 1987, “A Simple, Positive-semidefinite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,” Econometrica, 55(3), 703–708.
14
A
Additional Tables and Figures
B:Strangle
Strangle
Strategy Payoff Profile
A:Straddle
Straddle
Strategy Payoff Profile
50
40
35
40
30
Payoff
Call
Put
Straddle
Payoff
25
30
20
Call
Put
Strangle
20
15
10
10
5
0
0
0
20
40
Stock Price at Expiry
60
80
100
0
20
40
80
100
Stock Price at Expiry
60
80
100
C: Risk
Risk
ReversalReversal
Strategy Payoff Profile
40
Long Call
Short Put
Risk Reversal
30
20
Payoff
10
0
10
20
30
40
0
20
40
60
Stock Price at Expiry
D: Bull
Call Spread
Call Bull Spread Strategy Payoff Profile
E: Bear
Put Spread
Put Bear Spread Strategy Payoff Profile
Long Call
Short Call
Call Bull Spread
60
Long Put
Short Put
Put Bear Spread
60
20
20
Payoff
40
Payoff
40
0
0
20
20
40
40
0
20
40
60
Stock Price at Expiry
80
100
0
F: Call
Ratio Spread
Call Ratio Spread Strategy Payoff Profile
80
100
Long Put
Short Put x2
Put Ratio Spread
40
20
20
0
Payoff
0
Payoff
40
60
Stock Price at Expiry
G: Put
Ratio Spread
Put Ratio Spread Strategy Payoff Profile
Long Call
Short Call x2
Call Ratio Spread
40
20
20
20
40
40
60
60
80
80
0
20
40
60
Stock Price at Expiry
80
100
0
20
40
60
Stock Price at Expiry
80
100
Figure A1: Sample Payoffs of Option Strategies. The figure provides sample final payoffs of the popular
strategies used in our analysis. The payoff does not account for the cost of the strategy. To compute PNL of each
strategy we need to subtract the premium, and it will shift the payoff down in case of a debit strategy and up in
vcase of a credit strategy.
15
B: Call PNL/Underlying, 13:00 ET
A: Call Average
Returns,
13:00 ET
reth for calls time 13:00:00
Average reth_und for calls time 13:00:00
0.1
0
% of Underlying
% of Option Mid-price
25
25
0.2
Median
25th Percentile
75th Percentile
Mean
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
0.3
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
100
0.0
0.1
50
75
Moneyness in %
Moneyness in %
D: Put PNL/Underlying, 13:00 ET
C: Put Returns,
13:00 ET
Average reth for puts time 13:00:00
40
Average reth_und for puts time 13:00:00
Median
25th Percentile
75th Percentile
Mean
Median
25th Percentile
75th Percentile
Mean
0.2
20
0.1
0
% of Underlying
% of Option Mid-price
Median
25th Percentile
75th Percentile
Mean
0.2
50
20
40
0.0
0.1
60
0.2
80
100
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
0.3
Moneyness in %
Moneyness in %
Figure A2: 0DTE Option Returns, 13:00 ET to Expiry. The figure provides statistics on profitability
of naked 0DTE call and put option buying at 13:00 ET and holding to expiry at 16:00 ET. Panels on the left
show realized return in % relative to option mid-price. Panels on the right show option realized profit (payoff mid-price) per one unit of underlying relative to underlying price, in %. Bars show mean values, and each bar is
accompanied by median, 25th and 75th percentiles. X-axis labels show moneyness of the analyzed options. The
sample period is from 09/2016 to 05/2023.
16
B: Call PNL/Underlying, 15:00 ET
A: Call Average
Returns,
15:00 ET
reth for calls time 15:00:00
Average reth_und for calls time 15:00:00
60
40
0.10
0.05
0
% of Underlying
% of Option Mid-price
20
20
40
0.05
0.15
Median
25th Percentile
75th Percentile
Mean
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0.0
10 00
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
0.20
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
100
0.00
0.10
60
80
Moneyness in %
60
Moneyness in %
D: Put PNL/Underlying, 15:00 ET
C: Put Returns,
15:00 ET
Average reth for puts time 15:00:00
Average reth_und for puts time 15:00:00
Median
25th Percentile
75th Percentile
Mean
40
Median
25th Percentile
75th Percentile
Mean
0.15
0.10
20
0.05
% of Underlying
0
20
40
0.00
0.05
0.10
80
0.15
100
0.20
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0.0
10 00
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
60
98
.
98 000
.
98 125
.
98 250
.
98 375
.
98 500
.
98 625
.
98 750
.
99 875
.
99 000
.
99 125
.
99 250
.
99 375
.
99 500
.
99 625
.
99 750
10 .875
0
10 .000
0
10 .125
0
10 .250
0
10 .375
0
10 .500
0
10 .625
0
10 .750
0
10 .875
1
10 .000
1
10 .125
1
10 .250
1
10 .375
1
10 .500
1
10 .625
1
10 .750
1
10 .875
2.0
00
% of Option Mid-price
Median
25th Percentile
75th Percentile
Mean
0.15
Moneyness in %
Moneyness in %
Figure A3: 0DTE Option Returns, 15:00 ET to Expiry. The figure provides statistics on profitability
of naked 0DTE call and put option buying at 13:00 ET and holding to expiry at 16:00 ET. Panels on the left
show realized return in % relative to option mid-price. Panels on the right show option realized profit (payoff mid-price) per one unit of underlying relative to underlying price, in %. Bars show mean values, and each bar is
accompanied by median, 25th and 75th percentiles. X-axis labels show moneyness of the analyzed options. The
sample period is from 09/2016 to 05/2023.
17
A: Strangle PNL/Underlying
B: Risk Reversal PNL/Underlying
Average reth_und for strangle time 13:00:00
0.05
Median
25th Percentile
75th Percentile
Mean
0.020
% of Underlying
0.00
% of Underlying
Average reth_und for risk_reversal time 13:00:00
0.025
Median
25th Percentile
75th Percentile
Mean
0.10
0.05
0.015
0.010
0.10
0.005
0.15
0.20
1/1
0.995/1.005
Moneyness
0.99/1.01
0.000
0.98/1.02
C: Bull Call Spread PNL/Underlying
0.99/1.01
Moneyness
0.985/1.015
0.98/1.02
D: Bear Put Spread PNL/Underlying
Average reth_und for bull_call_spread time 13:00:00
Average reth_und for bear_put_spread time 13:00:00
Median
25th Percentile
75th Percentile
Mean
0.2
0.995/1.005
Median
25th Percentile
75th Percentile
Mean
0.2
0.1
% of Underlying
% of Underlying
0.1
0.0
0.0
0.1
0.1
0.2
0.2
1/1.005
1/1.01
1/1.015
1/1.02
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
0.995/1
E: Call Ratio Spread PNL/Underlying
0.98/1
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
Average reth_und for put_ratio_spread time 13:00:00
Median
25th Percentile
75th Percentile
Mean
Median
25th Percentile
75th Percentile
Mean
0.2
0.1
% of Underlying
0.1
% of Underlying
0.985/1
F: Put Ratio Spread PNL/Underlying
Average reth_und for call_ratio_spread time 13:00:00
0.2
0.99/1
0.0
0.0
0.1
0.1
0.2
0.2
1/1.005
1/1.01
1/1.015
1/1.02
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
0.995/1
0.99/1
0.985/1
0.98/1
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
Figure A4: 0DTE Static Option Strategies, 13:00 ET to Expiry. The figure provides statistics on
profitability of six well-known option strategies based on 0DTE call and put options; positions are taken at 13:00
ET and held to expiry at 16:00 ET. All panels show option strategy realized profit (payoff - mid-price) per one
unit of underlying relative to the underlying price, in %. Bars show mean values, and each bar is accompanied by
median, 25th and 75th percentiles. X-axis labels show combination of moneyness for options used for a strategy.
The sample period is from 09/2016 to 05/2023.
18
A: Strangle PNL/Underlying
B: Risk Reversal PNL/Underlying
Average reth_und for strangle time 15:00:00
0.075
0.050
Average reth_und for risk_reversal time 15:00:00
0.010
Median
25th Percentile
75th Percentile
Mean
Median
25th Percentile
75th Percentile
Mean
0.008
0.025
% of Underlying
% of Underlying
0.000
0.025
0.050
0.006
0.004
0.075
0.100
0.002
0.125
1/1
0.995/1.005
Moneyness
0.99/1.01
0.000
0.98/1.02
C: Bull Call Spread PNL/Underlying
0.985/1.015
0.98/1.02
0.10
0.10
0.05
0.05
0.00
0.05
Median
25th Percentile
75th Percentile
Mean
0.15
% of Underlying
% of Underlying
Moneyness
Average reth_und for bear_put_spread time 15:00:00
Median
25th Percentile
75th Percentile
Mean
0.00
0.05
0.10
0.10
0.15
0.15
1/1.005
1/1.01
1/1.015
1/1.02
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
0.995/1
E: Call Ratio Spread PNL/Underlying
0.985/1
0.98/1
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
Average reth_und for put_ratio_spread time 15:00:00
Median
25th Percentile
75th Percentile
Mean
0.15
0.99/1
F: Put Ratio Spread PNL/Underlying
Average reth_und for call_ratio_spread time 15:00:00
0.10
0.10
0.05
0.05
0.00
0.05
Median
25th Percentile
75th Percentile
Mean
0.15
% of Underlying
% of Underlying
0.99/1.01
D: Bear Put Spread PNL/Underlying
Average reth_und for bull_call_spread time 15:00:00
0.15
0.995/1.005
0.00
0.05
0.10
0.10
0.15
0.15
1/1.005
1/1.01
1/1.015
1/1.02
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
0.995/1
0.99/1
0.985/1
0.98/1
0.995/1.005
Moneyness
0.99/1.01
0.985/1.015
0.98/1.02
Figure A5: 0DTE Static Option Strategies, 15:00 ET to Expiry. The figure provides statistics on
profitability of six well-known option strategies based on 0DTE call and put options; positions are taken at 15:00
ET and held to expiry at 16:00 ET. All panels show option strategy realized profit (payoff - mid-price) per one
unit of underlying relative to the underlying price, in %. Bars show mean values, and each bar is accompanied by
median, 25th and 75th percentiles. X-axis labels show combination of moneyness for options used for a strategy.
The sample period is from 09/2016 to 05/2023.
19