Volatility and Directional Informed Trading and Option

Market Microstructure

Nick DeRobertis Yong Jin Mahendrarajah Nimalendran

Sugata Ray1

JEL Classifications: D53, G12, G28

Keywords: Option market microstructure, Probability of informed volatility

trading (VolPIN), Probability of informed direcitonal trading (DirPIN), PIN

May 14, 2016

1Nick DeRobertis, Yong (Jimmy) Jin, Mahendrarajah Nimalendran, and Sugata Ray, Warrington Col-lege of Business Administration, University of Florida, P.O. Box 117168, University of Florida, GainesvilleFL 32611-7168. DeRobertis:n ick.derobertis@warrington.ufl.edu; Jin: yong.jin@warringtonufl.edu; Nimalen-dran: mahen.nimalendran@warrington.ufl.edu; Ray: sugata.ray@ufl.edu. The authors are grateful to BingHan, Dmitriy Muravyev and seminar participants at Babson College for comments.

Volatility and Directional Informed Trading and Option

Market Microstructure

Abstract

During the past decade we have witnessed a dramatic increase in trading of volatility securi-

ties such as VIX options and ETFs on VIX (Trading of VIX options increased by 563% from

2007-2014.) In addition recently several indexes based on individual stock volatility have also

been introduced. Volatility trading is likely to have significant impact on the microstructure

of options and stock markets. To study the impact of volatility trading on markets, we

develop a sequential trade model and estimate the probabilities of volatility (V olPIN) and

directional (DirPIN) informed trading in the options market using high frequency individ-

ual stock and options data. We find that informed trading in option markets is significantly

correlated with standard market microstructure measures and future direction and volatil-

ity moves. In particular, V olPIN is positively related to future unpriced volatility, and

both option PIN measures together with StockPIN are significant determinants of option

spreads, explaining up to 31% of the effective bid-ask spread. Decomposing the effect of

V olPIN and DirPIN on option spreads,we find they contributed approximately equally to

the spread. Finally, we also document that option V olPIN are significantly higher prior to

earnings announcements indicating that volatility informed traders are significant players in

the market.

1 Introduction

The process by which information is revealed through trading has been studied extensively.2

Most of this research focuses on directional information, with much less attention given to

the question of how and where information concerning volatility is revealed.3 Compelling

evidence from the time-series and option-pricing literatures indicates that volatility is time-

varying and stochastic. Also, there is a large literature on the relation between future

volatility and option implied volatility. Yet we know little about the extent to which new

information about future volatility is revealed through the trading process. Presumably,

investors with private information about volatility will trade in instruments whose price is

sensitive to volatility, an obvious choice being the options market.4

In this paper, we investigate information based trading on the options market. We pro-

pose a structural model in the spirit of ? and ? to measure the probability of both volatility

and directional information based trading on the options market.5 The model assumes that

each period, there is some probability of an information event. Conditional on the event, the

information can be either about volatility or direction with a certain probability. Further,

we condition the volatility and directional information based on whether it is bullish or bear-

ish. This results in traders placing orders in accordance with the newly created information

structure, resulting in a rich sequential trade model. Using high frequency transaction level

data and trade direction (buyer initiated and seller initiated) for calls and puts on individ-

ual stock options we estimate the model using maximum likelihood techniques and obtain

estimates for the the probabilities of volatility and directional information-based trading in

individual stock options.

Informed directional traders will buy calls and/or sell puts if they are bullish on the price

and sell calls and buy puts when bearish. In contrast, informed volatility traders will buy

calls and buy puts (a straddle) if they are bullish on volatility and sell straddles if they are

bearish. In addition there will be noise or uninformed traders who will be buying and selling

calls and puts. These trading choices provide identification to estimate separate probabilities

2Theoretical underpinnings of this literature include ?, ?, and ? Empirical work in this area is describedin ?.

3In our study, directional information refers to information about whether a stock price is going up ordown. Volatility information refers to information regarding the future volatility of a stock either increasingor decreasing.

4Recently there have been ETFs on VIX as well as futures on VIX that can be traded. Also, there are afew individual stock volatility indexes such as the CBOE Equity Vixon Apple (∧V XAPL).

5 ? [NPP] also investigate informed trading on volatility in the options market using daily net non-marketmaker trading volume on calls and puts to construct a measure for trading on volatility information. Wediscuss the differences in our studies and findings in the following section.

1

of informed trading for directional and volatility trading, which we term DirPIN , and

V olPIN , respectively.

We validate our estimated V olPIN and DirPIN measures by confirming that they

are correlated with intuitively linked observable variables. For example, periods with high

V olPIN are followed by periods with high absolute unpriced volatility (|realized volatility

minus option price implied volatility|). Similarly, we find DirPIN is positively correlated

with the ? stock PIN measure, with a correlation of 0.22, while V olPIN has a weaker

correlation of .09. We also find that V olPIN and DirPIN are higher prior to earnings

announcements.

We use the estimated DirPIN and V olPIN together with stock PIN to estimate rel-

ative contributions to bid-ask spreads. We find that the V olPIN and DirPIN are both

significantly related to option market bid-ask spreads. A 10% increase from the mean in

the V olPIN , increases relative effective bid-ask spreads by 8 bp; and a similar increase in

DirPIN leads to a 12 bp increase. Based on an average spread of 2.23 % in the options

market, the effect of 10% increase in volatility and directional information risks in options

lead to a 9% increase in spreads.

Our findings are consistent with informed trading in option markets affecting both the

market microstructure of the options market and also future asset returns. Our main con-

tributions are the following: (1) A structural model to estimate the probability of volatility

and directional informed trading in options using signed trades; (2) Establishing a relation

between future volatility and our informed trading measures; (3) A decomposition of option

market bid/ask spreads to include the effects of asymmetric information about both direc-

tion and volatility, as well as the hedging and rebalancing costs associated delta hedging; (4)

Documenting the role of information-based trading around earnings announcements.

2 Literature review

There is a rich literature covering directional informed trading in the stock market and

its link to market microstructure6. The literature examining directional informed trading

in both the stock and the option markets is narrower, with theoretical roots in ? who

propose a theoretical model, with directionally informed traders choosing between stock

and option markets based on the relative transaction costs in the markets, and the “bang-

for-buck” in the form of leverag afforded by the options market. The authors conclude

that depending on the relative transaction costs in the markets, there can be a separating

6?, ?, ?, ?

2

equilibrium where informed traders trade only in the stock market, or a pooling equilibrium

where informed traders trade in both markets. Subsequent empirical work that focused

on directional informed trading in these two venues has largely supported the theoretical

predictions in the model. For example, ? find informed option trading prior to takeovers.

While ? allow the market makers in the option markets to hedge in the stock market.7

The literature examining informed volatility trading is more recent. ? estimate a multi-

market information asymmetry measure, similar to the PIN , for option markets using ag-

gregate unsigned volume. While simple to compute as it does not rely on estimation of a

structural model, it includes both information on volatility and direction in one measure.

? (NPP) use trades by non-market makers in the option markets to estimate demand

for volatility and show that this demand is related to “information about the future realized

volatility of underlying stocks.” In contrast to our study, which uses intraday quote and

transaction data to sign trades, NPP use non-market maker volume (NMMV ) obtained

from the Chicago Board of Options Exchange (CBOE) at the daily level for their analysis.

Additionally, rather than estimating PIN measures, the study separates option volume into

trades that could have been used for constructing straddles and those that were not. Their

findings relating informed volatility trading, estimated using NMMV , to future changes in

volatility closely mirror our own findings regarding the V olPIN and future volatility. In

our study, we separately estimate measures for directional and volatility based information

trading in the options market. While NPP largely disregard “non-straddle” trading, exclu-

sively focusing on straddle trades, we holistically characterize trades as noise, directional, or

volatility information driven, and separately estimate measures for volatility and directions

information-based trades.

Our methodology has several advantages over that used by NPP: (1) Using intraday

data allows us to sign trades individually, rather than relying on aggregate daily volume; (2)

Separately estimating the volatility and directional information-based risk measures allows

us to examine the impact of both on market microstructure of option markets.

7Several studies have examined informed trading in option markets, for example, ?, and ? but these au-thors focus on directional information about the underlying stock price, not information about the volatility.? examine price discovery across option exchanges, but they make no attempt to differentiate between optionprice changes resulting from underlying stock price changes and those resulting from volatility changes.

3

3 Model

In this section we outline our information-based trading model that captures both directional

information and volatility information. Our sequential trade model is a generalization of ?

and ?’s probability of information-based trade (PIN) model.

Our model extends their model to the options market where agents can trade on direc-

tional information as well as volatility information on the underlying stock. Traders having

information about the future increase in stock price can use a long call/short put strategy

and long put/short call strategy for information on future decrease in stock price. If the

information is about volatility, then they can employ a long straddle (long call and long put)

when the information is about an increase in volatility and short straddle for a decrease in

future volatility.

In our model, new information arrives every 30-minutes with probability α and, con-

ditional on a information event, it is either volatility information with probability θ or

directional information with probability 1 − θ. Volatility information can be high (prob δ)

or low (prob 1− δ). Directional information is either good news (prob γ) or bad news (prob

1− γ).

Orders from informed and uninformed traders to buy/sell, call/put options follow in-

dependent Poisson processes. Uninformed buyers (seller) arrive according to independent

Poisson processes at rate ε ∈ {εBC , εSC , εBP , εSP}, where the subscripts C and P denote calls

and puts, and superscripts B and S denote buys and sells by the traders. Orders from

traders possessing volatility information arrive at rates µ ∈ {µBC , µBP } for high volatility,

and {µSC , µSP} for low volatility. Finally, orders from informed directional traders arrive at

rate ν ∈ {νBC , νSP} for high direction, and {νSC , νBP } for low direction. Figure 1 shows the

information and the decision tree for the traders’ strategies.

When there is no information in the market (1 − α), the orders are purely uninformed,

with arrival rates εBC , εSC , ε

BP , ε

SP for long call, short call, long put, short put respectively. When

information event occurs in the market (α), and the information is about volatility (θ), and

if the volatility is high (δ), the joint probability of high volatility information event is αθδ.

Under this situation, the market orders arrive rates µBC + εBC , εSC , µ

BP + εBP , ε

SP for long call,

short call, long put, short put respectively. Similarly, we have the probabilities and arrival

rates for each of the five end nodes in the tree. Based on these assumptions we can derive

the likelihood function conditional on number of buys(B), sells (S) for call (C) and put (P )

options.

4

3.1 Likelihood Function and Estimation

The likelihood function given the model is based on the following assumptions. 1) There is

only one information event in the defined unit period (in our estimation we use 30 minutes

in a day); (2) There is no possibility of volatility information and direction information

occurring simultaneously. Then the marginal likelihood function one period is given by

equation 1, where we have suppressed the subscript t.

l(Θ|Orders) =(1− α)e−εBC

(εBC)CB

CB!e−ε

SC

(εSC)CS

CS!e−ε

BP

(εBP )PB

PB!e−ε

SP

(εSP )PS

PS!

+ αθδe−(µSC+εBC ) (µ

SC + εBC)CB

CB!e−ε

SC

(εSC)CS

CS!e−(µ

BP+εBP ) (µ

BP + εBP )PB

PB!e−ε

SP

(εSP )PS

PS!

+ αθ(1− δ)e−εBC (εBC)CB

CB!e−(µ

SC+εSC) (µ

SC + εSC)CS

CS!e−ε

BP

(εBP )PB

PB!e−(µ

SP+εSP ) (µ

SP + εSP )PS

PS!

+ α(1− θ)γe−(νSC+εBC ) (νSC + εBC)CB

CB!e−ε

SC

(εSC)CS

CS!e−ε

BP

(εBP )PB

PB!e−(ν

SP+εSP ) (ν

SP + εSP )PS

PS!

+ α(1− θ)(1− γ)e−εBC

(εBC)CB

CB!e−(ν

SC+εSC) (ν

SC + εSC)CS

CS!e−(ν

BP+εBP ) (ν

BP + εBP )PB

PB!e−ε

SP

(εSP )PS

PS!(1)

3.1.1 Simplified Model

The model give by equation 1 has sixteen parameters, and estimating all the parameters using

MLE is challenging. To make the model tractable we impose several restrictions. First, we

set all the uninformed arrival rates to be the same ε = εBC = εSC = εBP = εSP . This is not a

very restrictive assumption as these are non-strategic traders. Second, we set the informed

arrival rates for high and low volatility traders to be the same, µ = µBC = µSC = µBP = µSP .

This is more restrictive as one might expect arrival rates for high volatility to be different

from low volatility. Finally, we assume that the arrival rates for the high and low directional

trader to be the same, ν = νBC = νSC = νBP = νSP . We do not expect directional traders to

prefer high or low directional trades and hence this assumption is not too restrictive. These

assumptions reduce the number of parameters to be estimated to seven from sixteen and the

likelihood function is given by equation 2:

5

l(Θ|Orders) =1

CB!CS!PB!PS!{(1− α)e−εεCBe−εεCSe−εεPBe−εεPS

+ αθδe−(µ+ε)(µ+ ε)CBe−εεCSe−(µ+ε)(µ+ ε)PBe−ε(ε)PS

+ αθ(1− δ)e−εε)CBe−(µ+ε)(µ+ ε)CSe−εεPBe−(µ+ε)(µ+ ε)PS

+ α(1− θ)γe−(ν+ε)(ν + εBC)CBe−εεCSe−εεPBe−(ν+ε)(ν + ε)PS

+ α(1− θ)(1− γ)e−εεCBe−(ν+ε)(ν + ε)CSe−(ν+ε)(ν + ε)PBe−εεPS}

=1

CB!CS!PB!PS!e−4ε{(1− α)εCB+CS+PB+PS + αθδe−2µεCS+PS(µ+ ε)CB+PB

+ αθ(1− δ)e−2µε)CB+PB(µ+ ε)CS+PS + α(1− θ)γe−2νεCS+PB(ν + ε)CB+PS

+ α(1− θ)(1− γ)e−2µεCB+PS(ν + ε)CS+PB}(2)

The log likelihood function based on the likelihood for time period T is given by Equation

3,

L(Θ|Orders) = Log(T∏t=1

lt). (3)

We use a maximum likelihood method (MLE) to estimate the parameters of the model,

Θ = {α, δ, θ, γ, ε, µ, ν}, using signed orders, Orders ∈ {CB,CS, PB, PS}, for individual

stock options. From these estimates we construct estimates for the probability of volatility

informed trading (V olPIN) and directional informed trading (DirPIN).

3.2 Information-Based Measures; V olPIN and DirPIN

3.2.1 Simplified Model

The probability of volatility information event is αθ, and conditional on this the expected

informed arrival rate is 2(δµ+(1−δ)µ) = 2µ. Hence the expected rate of volatility informed

arrival is 2αθµ. Similarly, the expected directional informed arrival rate is 2α(1− θ)ν. The

total expected uninformed arrival rate is 4ε. Based on this the information measures V olPIN

and DirPIN are give by the following equations.

V olPIN =αθµ

αθµ+ α(1− θ)ν + 2ε(4)

6

DirPIN =α(1− θ)ν

αθµ+ α(1− θ)ν + 2ε(5)

We use a 30 minute interval during a day as the time period for one observation (t) and

use two weeks of data (T ) to estimate the likelihood function. Since each day has 6.5 hours of

trading, we get 13 observations per day and over two weeks we obtain 130 (T ) observations

for the estimation. In the following section, we use Monte Carlo simulation techniques to

ascertain the finite sample properties of the estimators.8

4 Monte Carlo Simulation

We follow the approach used by ? to carry our Monte Carlo simulation for estimating and

analyzing the finite sample properties of the sample parameter estimators.

In this study we use the R-Project software to generate simulated samples and obtain

the finite sample behavior using the following procedure.

1. We first set the values for the parameters (α, θ, δ, γ, ε, µ, ν).

2. Generate four independent and identical uniformly (0, 1) random variables to decide the

“No information, High Vol information, Low Vol information, High Dir information,

Low Dir information” states. For example if α = .5, and the generated Uniform

variable is less than .5 then we will be in the no information state. Similarly for the

other states of the tree.

3. Once the terminal node of the tree is determined, we use the given parameters to

simulate the number (volume) of orders of long call, short call, long put, short put for

a certain fixed number of observations per period (T = 100 or T = 300), thus a sample

including T observation of Orders ∈ {CB,CS, PB, PS} is generated.

4. Use non-linear optimization tools to estimate the parameters by maximizing the log-

likelihood function, and then record the estimated parameters as (α̂1, δ̂1, θ̂1, γ̂1, ε̂1, µ̂1, ν̂1).

8Note that the term CB!CS!PB!PS! can be factored out for the marginal likelihood function. Thisterm does not involve any of the parameters. Hence, in the MLE procedure we eliminate the term from loglikelihood function.

7

5. Repeat steps 2-4 for 200 replications and record the estimated parameters as,

(α̂i, δ̂i, θ̂i, γ̂i, ε̂i, µ̂i, ν̂i), where i = 1 : 200.

6. After obtaining the set of all the estimated parameters, we calculate the number

of replications for which the optimization converged to feasible estimates (NC), the

mean estimates MEAN = 1NC

∑NCi=1 η̂i and the standard errors of the means SEM =

1√NC

[ 1(NC−1)

∑NCi=1(η̂i −MEAN)2]1/2, where η ∈ {α, δ, θ, γ, ε, µ, ν}.

The results of our simulation is presented in Table 1. We simulate six set of parameter

choices and two sets of number of observations (100, and 300). The parameters (α, θ, δ, γ)

are chosen to be between 0.3 and 0.7. While the arrival rates for traders is chosen to be (50,

100, or 150) in different combinations. We find that the number of convergences were close

to 100%. The estimators also have very good finite sample properties. The bias for all the

estimators are very small, and the standard error of the estimates are also very small. For

example, the percentage of estimation error of α varies from 0 to 1.2% and the absolute value

of t-test which is the bias/SEM varies from 0 to 0.125, which cannot reject the null that

the estimates are different from the parameters. The efficiency of the estimators improves

when more observations enter the simulated sample. Overall, the simulations show that the

procedure is efficient and provide unbiased estimates for the parameters for our Option PIN

model using 130 observations.

5 Data and summary statistics

5.1 Data

In this study, all the option transaction level data are obtained from OPRA Option Database.

This data was provided by the OptionData warehouse, Baruch College, CUNY.9 The stock

transaction level data are extracted from the Trade and Quote (TAQ) Database. Other

option data such as option Greeks, implied volatility, and realized volatility are obtained

from Optionmetrics Database. Finally, the stock data such as end of day price, ask price, bid

9Option Price Reporting Authority (OPRA) was established as a securities information processor for mar-ket information, for collecting, consolidating and disseminating the option market data from its participantsincluding AMEX, ARCA, BATS, BX, BSE, C2, CBOE, ISE, MIAX, NASDAQ, and PHLX. OPRA OptionDatabase contains all the transaction level data (Trades and Quotes) for stock options which is traded inthe participants’ exchange.

8

price, shares outstanding, traded volume are obtained from Center for Research in Security

Prices (CRSP).

5.2 V olPIN and DirPIN Estimation Details

We construct our sample for estimation using the following procedure: 1) Compile a list of

all the stocks in TAQ and merge this list with OPRA database; 2) Sort the merged list by

the option volume in 2010 obtained from OptionMetrics, and keep the top 500 stocks. We

do this to ensure sufficient option volume to estimate our PIN measures.

For our study, we consider options within 10% of the strike price, or the nearest in- and

out- of-the-money strikes, whichever results in broader coverage. In terms of option maturity,

we keep all options expiring within 7 to 183 days. OPRA data has second level quote data

for the options markets, as well as transaction data. We use the ? algorithm to sign trades

in both stock and option markets. Finally, we use signed trades aggregated at 30-minute

intervals (CB,CS, PB, PS) to estimate our model.

The time period of our sample (2011 calendar year) is split into 2-week estimation peri-

ods. For each 2-week estimation period, we use 30 minute intervals to measure order flow to

compute V olPIN and DirPIN measures. For each day we have thirteen 30-minute obser-

vations and over two weeks we have 130 observations. These 130 observations are used to

estimate the parameters from the log likelihood function.

To estimate the PIN measure for stocks, we merge NBBO and Trades data from TAQ

and use ? to define the stock trade direction. Similar to the process for options, for every

30 minute interval, we calculate the volume of Trades-up (buys) and Trades-down (sells) for

each stock. We use two weeks or 10 trading days to obtain 130 observations to estimate PIN

using the technique outlined in ?. The stock PIN model is given in Figure 2.

5.3 Summary statistics

Table 5 presents summary statistics for option related variables in our sample. The sample

consists of 500 stocks over the twenty-six 2-week periods in 2011. Lack of option volume,

or non-convergence of log likelihood leads to the overall sample size being around 8000

observations (rather than 500 * 26 = 13000). The average quoted bid-ask spread for options

in our sample is 9.2 cents and the effective spread is 4.4 cents, which translates to a relative

bid-ask spread of 5.8% and 2.2%. The average daily volume for options is 3, 640 contracts,

and each two week period volume is 36, 315. The Greeks for the options are also presented.

The average ∆ is 0.53, reflecting the fact that only options at or around the money are used

9

in the analysis.

The average option price implied volatility is 39.2% (annualized). This is slightly higher

than realized volatility (37.9%), in line with the option volatility premium documented

in previous literature. The average unpriced volatility (realized volatility minus implied

volatility) is -1.3% and the average absolute unpriced volatility is 10.4%. Note that informed

volatility trading would be reflected in higher absolute unpriced volatility, rather than simply

unpriced volatility, as informed volatility traders may go long or short volatility and our

estimate measure does not separate these two.

The variables used to construct V olPIN and DirPIN are given in Section 3. As a recap,

α is the probability that there is information in each 30 minute interval. The probability

that the information is regarding direction, rather than volatility, conditional on there being

information is θ. The probability that directional information is good news rather than bad

news is γ, and the probability information is regarding an increase in volatility rather than

a decrease is δ.

V olPIN and DirPIN are estimated over 2-week horizons by examining order flow in

each 30-minute interval in the 2-week horizon as independent observations. On average, the

probability of informed trading in each 30 minute horizon, α, is 0.46, with roughly an even

probability that the information is regarding direction and volatility. Information regarding

volatility is more likely to be an increase in volatility (δ = 0.615), but information regarding

direction is equally likely to reflect either good or bad news (γ = 48.6%). The overall

V olPIN and DirPIN are estimated at 0.223 and 0.200 respectively, suggesting roughly an

equal probability of informed volatility and directional trading. In table 5 we provide the

summary statistics for the model estimates.

Table 6 presents corresponding summary statistics for the underlying stocks in our sam-

ple. The average quoted bid-ask spread is 1.6 cents, corresponding to a relative quoted

bid-ask spread of 4.5bps.

The daily volume is 5.6 million shares and the market capitalization is $12 billions. The

stock PIN is computed using the model outlined in ?. The probability of informtion in each

30 minute windows is 0.339, and informed traders are equally likely to trade on good news

and bad news. The overall stock PIN is estimated as 0.170, which is similar to the numbers

reported by ?.

Figure 3 presents distributions of V olPIN and DirPIN estimates for our sample of

stock options. Figure 4 presents distributions of stock PIN parameters in our sample. The

three distributions are quite symmetric about the mean.

Table 7 presents the correlations across the various variable in the study. In line with

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intuition, PIN measures (V olPIN and DirPIN and Stock PIN) are negatively correlated

with stock and option volume, as well as stock market captalization. They are positively

correlated with stock and option bid-ask spreads. Also in line with expectations, DirPIN

is more positively correlated with Stock PIN than V olPIN .

Table 8 presents selected summary statistics sorted by market capitalization quintiles.

The probability of directional and volatility informed trading decreases with market cap-

italization, reflecting the greater transparency of larger companies. The PIN measures of

companies in the largest quintile are significantly different from the PIN measures of com-

panies in the smallest quartile by market capitalizations.

6 Results and Analysis

6.1 Unpriced volatility and the V olPIN

In this section we study the relation between our option PIN measures and unpriced volatility,

UV = (|RV − IV |) using the following empirical model.

UV = β0 + β1(V olPIN) + β2(DirPIN) + γX + ε (6)

The vector X refers to control variables and additional interaction terms. Table 9 presents

regressions estimating the above equation and analysing the explanatory power of our PIN

measures on the absolute unpriced volatility (absolute value of the realized volatility over

the next 2-week minus the implied volatility in the option prices at the end of the current

2-week period). We find V olPIN is positively related to the unpriced volatility, with a one

standard deviation increase (0.066) in V olPIN associated with a 0.5% increase in absolute

unpriced volatility (based on model 3 estimate of 0.0752 reported in Table 9). This change

translates to a 4.8% increase based on the average unpriced volatility of 10.4%.

The positive relation is strongest when the realized volatility is higher than the implied

volatility. The coefficient estimate increases to 0.182 after including a dummy variable for

the instances when the realized volatility is lower than the implied volatility. This leads to

nearly double (1.2% increase and a 11.6% change from the average) the impact of V olPIN on

future unpriced volatility. Our findings suggest that informed volatility trading, as estimated

using our V olPIN measure, is indeed linked to significantly large differences between implied

and realized volatility. Furthermore, the informed trading captured by our measure is more

likely to be trading on an increase in volatility, rather than decrease in volatility.

In addition to V olPIN we find that DirPIN too is positively but weakly related to

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absolute unpriced volatility. Though, the sensitivity of 0.0421 is about half of the V olPIN

effect. However, when we interact DirPIN with the I(IV −RV ), the estimate increases to

0.0873. This is consistent with an increase in volatility being positively related to a decrease

in stock price. Our results suggest that there is more directional informed traders in the

options market when the future volatility is higher than the implied volatility.

6.2 Determinants of Option Bid-Ask Spreads

6.2.1 Adverse Selection Cost

Adverse selection costs play an important role in determining stock spreads. On the options

market, the extant evidence is mixed. If informed agents can trade strategically on the

stock and the options markets to maximize their returns from private information, and if

option market makers cannot instantaneously hedge the option exposure to adverse selection,

then the option market makers will face the same information disadvantage as stock market

makers do, and the option spread must compensate for this cost.10

? argues that informed agents might prefer the options market for its high leverage.

On the other hand, ? find that informed agents may trade in both the option and the

stock markets simultaneously. This has implications for where price discovery occurs. The

empirical evidence on this issue is mixed. For example, ? and ? find that option market

makers do not face significant adverse selection costs, while ? and ? find evidence consistent

with informed trading on the options market.

To proxy for adverse selection costs we will use DirPIN , V olPIN and Stock PIN. These

are measures of information based trading in the options market and the stock market.

6.2.2 Hedging Costs

? show that in a “perfect” market the payoff to an option can be replicated by continu-

ously rebalancing a portfolio of stocks and bonds. If the conditions necessary for a perfect

market hold, then option spreads should only compensate option market makers for order

processing costs, and perhaps for informed volatility trading. However, when there are mar-

ket frictions such as transaction costs, it is no longer possible to replicate the option payoff

using a dynamic strategy involving continuous rebalancing. Therefore, option market makers

must be compensated for the costs associated with rebalancing at discrete time intervals, as

10The bid-ask spreads on stocks compensate market makers for order processing, inventory (?), and adverseselection costs (?, ?, ?, ?).

12

well as costs due to market frictions such as bid-ask spread on the underlying stock, price

discreteness, information asymmetry, and model misidentification.

The costs consist of the cost of setting up and liquidating the initial delta neutral position,

and the cost to continuously rebalance the portfolio to maintain a delta neutral position.

Several papers, including ?, ?, and ?, have theoretically examined the impact of stock bid-ask

spreads on the hedging costs imposed on option dealers due to discrete rebalancing. They

show that the option spread (the difference between the prices of long and short calls) due

to the discrete rebalancing is positively related to the proportional spread on the underlying

asset, inversely related to the revision interval, and positively related to the sensitivity of

the option to changes in volatility (vega).

Initial Hedging Cost

An option market maker would set up a delta neutral position by purchasing ∆ shares of

the stock at the ask price and close the position by selling at the bid price. This would lead

to a cost,

IC = kS∆ (7)

where, IC represents the initial hedging cost, k is the proportional stock spread, S is

the stock price, and ∆ is the option delta. And the relative initial heding cost (Rel IC) is

defined as

RelIC = k∆ (8)

Rebalancing Cost

The initial hedging cost does not include the cost of rebalancing the portfolio to maintain

a delta-neutral position. Following ? and ?, we define the rebalancing cost as follows:

RC =2νk√2π(δt)

(9)

where ν is the option Vega, k is the proportional stock spread and δt is the rebalancing

interval. And the relative rebalancing cost (Rel RC) is defined as

RelRC =2νk√2π(δt)

/S (10)

13

The rebalancing cost is proportional to the option’s Vega and the spread on the underlying

stock, and is inversely related to the rebalancing interval. Since Vega is highest when the

stock price is equal to the present value of the exercise price, ceterisparibus, we would

expect at-the-money options to have the highest rebalancing costs. The expression for the

rebalancing costs also has an intuitive explanation: the bid-ask spread on the stock gives

rise to an extra volatility when the option is replicated. For example, if you replicate a long

call option, then when the stock price increases, rebalancing would require you to purchase

more stock. But this has to be done at the ask price. Similarly, when the stock price falls,

the stock has to be sold at the bid price to maintain a delta neutral position. This effectively

increases the volatility of the asset, and this increase in volatility would be proportional to

the bid-ask spread (?).

In constructing the above measure of rebalancing cost we do not observe the rebalancing

frequency. Therefore, we assume that this frequency is the same across all option contracts

and drop the term√

2π(δt) in our construction of the rebalancing cost. Hence, we obtain

the following expression for rebalancing costs and relative rebalancing costs:

RC = νk (11)

and

RelRC = νk/S (12)

Order Processing Costs

Since order-processing costs are likely to be fixed for any particular transaction, the

order processing costs should decrease as the expected trading volume increases. ? suggest

a negative relation between bid-ask spreads and trading volume in the long run, and . ?

develop a model that implies spreads decrease with an increase in expected trading volume.

We use trading volume of the option contract (number of contracts traded), denoted as

OptV ol, to proxy for order processing costs. Since we control for adverse selection, we

expect the trading volume to be negatively related to spreads.

6.2.3 A Model of Option Bid-Ask Spread

We propose the following empirical model for the determinants of option spreads.11

11We do not include the inventory costs as a determinant for two reasons. First, the literature on stockspreads suggests that its magnitude is trivial (? and ?). Second, option market makers rarely take directionalrisks. Even if they carry inventory, it is likely to be hedged.

14

OptSprd = β0 + β1(V olPIN) + β2(DirPIN) + β3(StkPIN)

+ β4(RelIC) + β5(RelRC) + β6(OptV ol) + ε(13)

Table 10 provides OLS (models 1 - 3) and fixed effect (models 4 - 6) regression model

estimates for the above model with dependent variable option effective bid-ask spread. We

find that in all the specification, the option PIN measures and the stock PIN measure

has significant positive impact on option spreads. In pooled OLS models, they explain

nearly 31 % of the option spreads. The economic significant of the information measures are

also significant. A 10 % higher probabilities of the option volatility information (V olPIN)

increases effective spread by 8 bp, and a one 10 % higher probabilities of the option directional

information (DirPIN) increases effective spread by 12 bp. The totally 20 bp increase leads

to a 9% increase in effective spread from the mean value of 2.23%. Interestingly, the stock

PIN too has a significant economic impact and a 10 % increases option effective spread by

17 bp (7.6%). The findings are consistent with models where informed traders splitting their

trades between the option and the stock markets.

Since there are potentially omitted variables such as firm opaqueness, which could influent

the spread and informed trading, we use the a fixed effect panel regression model to re-

estiamte the coefficients, and the estimates are given in models 4 - 6. We find that the

results are consistent and significant after controlling for time and firm effects. A 10 %

higher probabilities of the option volatility information (V olPIN) increases effective spread

by 3 bp, and a 10 % higher probabilities of the option directional information (DirPIN)

increases effective spread by 3.4 bp. Then the totally 6.4 bp increase leads to a 2.9% increase

in effective spread from the mean value of 2.23%. And 10 % higher in stock PIN increases

option spread by 5 bp (2.9%).

6.2.4 Information Based Trading Around Earnings Announcements

Earnings announcement are information sensitive events and several studies have examined

the changes in information measures on the stock market around earnings announcements

(?). Other studies have examined options trading around important events such as takeovers

and find significant trading on options that are related to information about the outcomes

(?). NPP examine the changes in their volatility information measure around earnings an-

nouncements. In particular, they construct a measure of volatility price impact by creating

securities from options that are sensitive to volatility but insensitive to directional informa-

15

tion by using a straddle. Since a straddle will increase (decrease) in value when volatility

increases (decreases) but is insensitive to small directional changes. NPP use the average of

the call and put implied volatilities as the price of volatility and examine the the volatility

price impact with respect to non-market maker volume around earnings announcements.

They find an increase in price impact prior to earnings announcement dates suggesting that

market makers are reacting to informed traders. The NPP measure of volatility informed

trading depends on using the Black-Scholes model to estimate the implied volatilities. In

this section we examine the effect of earnings announcement on our PIN measures. We esti-

mate our OPIN measures for two (two-week) intervals before the announcement and for one

(two-week) interval after the announcement. The two-weeks immediately preceding and the

two-week interval following the earning announcement date are denoted as “pre-earnings”

and “post-earnings”. We then analyze the effects of earnings announcement by regressing

V olPIN , DirPIN and the relative bid-ask spread for options on dummy variables for each

of the pre-earnings and post-earnings in addition to other control variables. The results are

presented in Table 11.

We find that our estimated PIN measures are consistent with higher levels of informed

trading before an earnings announcement. Both V olPIN and DirPIN measures are sig-

nificantly higher before the earnings announcements. The V olPIN is higher by 4.2% and

the DirPIN is also higher by 4.45% compared to post-earnings period estimates. Similarly

in the stock market, the StockPIN is higher by 3.3%. We also find that the relative ef-

fective bid-ask spreads in option markets does not change significantly around the earning

announcement. Finally, we also document a 2.1% decrease in Implied V olatility after the

announcement and a very significant 13% increase in option volume after the announcement.

The increase in option market volume is similar to what previous studies have documented

for the stock market (?).

These results suggest that, the probability of informed trading on volatility and direc-

tional information is higher prior to the announcement, and the higher volume of trading

and lower volatility after the announcement is consistent with uninformed traders concen-

trating their trading after the announcement to avoid the information uncertainty about the

earnings.

7 Conclusion

Volatility plays an increasingly significant role in the financial markets as evident by large

increase in trading of VIX options as well as the VIX ETFs. During the same period, the

16

total volume of equity options traded on the CBOE decreased by 16% from 2007 to 2013.

In addition to increased activity on VIX, we also see the introduction of futures on VIX

and also the introduction of options on individual stock volatility such as the (∧V XAPL,

option on Apple stock implied volatility) . In this study we examine how information about

volatility is traded and how this information is impounded in future volatility, and market

microstructure of options and stock markets. We propose a structural model to estimate

separate measures for the probability of informed trading based on directional and volatility

information in option markets. Our measures of informed trading are based on the signed

trade volume and do not depend on the option prices. This has an advantage over using

prices as the prices have to be adjusted for changes in the underlying Greeks of the options

to obtain measures such as the price impact.

We have three main results. First, we find that our option PIN measures predict fu-

ture unpriced volatility. This is consistent with option PIN measures capturing information

based trading about future volatility. It may also reflect a growing trend of using option

markets to trade on information. Second, we examine the market microstructure of the

option and the stock markets. We find that the both volatility and directional option PIN

measures contribute to the high bid-ask spreads in option markets, even after controlling for

the underlying stock PIN . The option PIN measures explain 31% of the cross-sectional

variation. We also find that the DirPIN for option markets is a better measure for di-

rectional informed trading in the underlying stocks compared to the stock PIN measure.

Finally, we study the evolution of the information measures around information sensitive

earnings announcement dates. We find that the both option PIN measures are significantly

higher before the announcement.

We believe that analyzing the effect of informed trading on option markets will play a

significant role as more information about both the future direction and volatility of stocks

is revealed through trading on options, and we hope the V olPIN and DirPIN measures,

as proposed in this study, will help with this analysis.

17

Figure 1: Option PIN model.

18

Figure 2: Stock PIN model.

19

Figure 3: Parameter distribution with pooled data in Option PIN model.

This figure provides the empirical distribution of the estimated Option PINmodel parameters with 26 bi-weeks and all the options in our sample. PanelA shows the empirical distribution of Option α, the probability that aninformation event occurs. Panel B shows the empirical distribution of Optionθ, the probability of volatility information happens when information occurs.Panel C shows the empirical distribution of Option δ, the probability of highvolatility information happens when volatility information occurs. Panel Dshows the empirical distribution of Option γ, the probability of high directioninformation happens when direction information occurs. Panel E shows theempirical distribution of Volatility PIN. Panel F shows the empirical distributionof Direction PIN.

Panel A: Empirical distribution of Option α, the probability that an information eventoccurs.

Panel B: Empirical distribution of Option θ, the probability of volatility informationhappens when information occurs.

20

Panel C: Empirical distribution of Option δ, the probability of high volatility informationhappens when volatility information occurs.

Panel D: Empirical distribution of Option γ, the probability of high direction informationhappens when direction information occurs.

21

Panel E: Empirical distribution of Volatility PIN.

Panel F: Empirical distribution of Direction PIN.

22

Figure 4: Parameter distribution with pooled data in Stock PIN model.

This figure provides the empirical distribution of the estimated Stock PIN modelparameters with 26 bi-weeks and all the options in our sample. Panel A showsthe empirical distribution of Stock α, the probability that an information eventoccurs. Panel B shows the empirical distribution of Stock γ, the probabilityof good news happens when information occurs. Panel C shows the empiricaldistribution of Stock PIN.

Panel A: Empirical distribution of Stock α, the probability that an information event occurs.

Panel B: Empirical distribution of Stock γ, the probability of good news happens wheninformation occurs.

23

Panel C: Empirical distribution of Stock PIN.

24

Table 1: Finite sample properties of the MLE estimators of the Option PIN model based onMonte Carlo Simulations

The finite sample properties are based on 200 replications of either 100 or 300observation days, that is, 100 or 300 sets of number of long call, short call, longput and short put orders. NC is the number of replications for which the opti-mization converged to feasible estimates, MEAN is the mean estimates, whichis calculated by MEAN = 1

NC

∑NCi=1 η̂i, and SEM is the standard error of the

MEANs, which is calculated by SEM = 1√NC

[ 1(NC−1)

∑NCi=1(η̂i −MEAN)2]1/2,

where η ∈ {α, δ, θ, γ, ε, µ, ν}.T = 100 T = 300

Set Parameter Sim Val NC Mean SEM NC Mean SEM1 α 0.50 200 0.494 0.048 200 0.501 0.031

θ 0.50 200 0.491 0.074 200 0.500 0.043δ 0.50 200 0.503 0.103 200 0.502 0.062γ 0.50 200 0.496 0.100 200 0.500 0.057ε 100.00 200 100.063 0.612 200 100.012 0.340µ 100.00 200 100.291 2.162 200 100.035 1.157ν 100.00 200 99.877 2.127 200 100.004 1.183

2 α 0.50 200 0.506 0.051 200 0.501 0.030θ 0.50 200 0.497 0.070 200 0.495 0.038δ 0.50 200 0.509 0.105 200 0.504 0.056γ 0.50 200 0.498 0.092 200 0.495 0.063ε 100.00 200 99.911 0.559 200 99.971 0.353µ 50.00 200 50.108 1.808 200 50.046 1.169ν 50.00 200 50.200 1.827 200 49.990 1.131

3 α 0.30 200 0.299 0.046 200 0.298 0.025θ 0.70 200 0.704 0.088 200 0.702 0.049δ 0.50 200 0.493 0.114 200 0.497 0.065γ 0.50 200 0.498 0.173 200 0.500 0.093ε 100.00 200 99.960 0.567 200 99.996 0.310µ 100.00 200 100.174 2.261 200 99.914 1.296ν 100.00 200 100.148 3.687 200 99.991 2.019

4 α 0.30 200 0.295 0.049 200 0.298 0.026θ 0.70 200 0.696 0.085 200 0.699 0.046δ 0.40 200 0.388 0.103 200 0.402 0.061γ 0.40 200 0.405 0.177 200 0.397 0.098ε 100.00 200 99.969 0.547 200 100.005 0.324µ 100.00 200 99.870 2.287 200 100.025 1.339ν 100.00 200 100.104 3.508 200 100.201 2.079

5 α 0.30 200 0.301 0.051 200 0.300 0.025θ 0.70 200 0.702 0.086 200 0.702 0.047δ 0.40 200 0.403 0.108 200 0.401 0.060γ 0.40 200 0.393 0.178 200 0.395 0.100ε 50.00 200 49.726 3.484 200 49.989 0.216µ 100.00 200 100.252 1.902 200 99.893 1.066ν 100.00 200 99.796 4.385 200 99.897 1.738

6 α 0.30 200 0.299 0.086 200 0.301 0.029θ 0.70 200 0.681 0.143 200 0.704 0.047δ 0.40 200 0.402 0.154 200 0.404 0.062γ 0.40 200 0.409 0.193 200 0.401 0.095ε 50.00 200 47.852 9.450 200 49.929 0.852µ 100.00 200 99.427 4.285 200 100.194 2.323ν 150.00 200 146.982 13.883 200 150.218 2.191

25

Table 2: Variable Description for Option

Variable Description Frequency / Estimation Pe-riod

OptionOption Spread ($) Option’s ask price minus bid price from OPRA database Transaction / BiweekOption Effective Spread ($) Twice the difference between the actual execution price and the

mid-point of the market quote priceTransaction / Biweek

Option Rel Spread (%) Option spread divide by the mid-point of the bid-ask spread fromOPRA database

Transaction / Biweek

Option Rel Effective Spread(%)

Option Effective Spread divide by the mid-point of the bid-askspread from OPRA database

Transaction / Biweek

Log(Option Volume) Natural logarithm of the option volume from OPRA database Transaction / BiweekLog(Daily Option Volume) Natural logarithm of daily average option volume from OPRA

databaseTransaction / Average Daily

∆ The data is from Optionmetrics. ∆ of the option is calculated bythe change in option premium for a $1.00 change in underlying price

Last day of period t

Θ The data is from Optionmetrics. Θ is calculated by the change inoption premium as time passes, in terms of dollars per year.

Last day of period t

V ega The data is from Optionmetrics. Vega is calculated by the changein option premium, in cents, for one percentage point change involatility.

Last day of period t

Γ The data is from Optionmetrics. Γ is calculated by the absolutechange in ∆ for a $1.00 change in underlying price.

Last day of period t

Unpriced Volatility (annu-alized)

Realized Volatility of time period t+ 1 minus Implied volatility atthe last day of time period 1 from Optionmetrics

Biweek

Implied Volatility (annual-ized)

The data is from Optionmetrics. IV is calculated for options withstandard settlement at last day of time period t.

Last day of period t

Realized Volatility (annual-ized)

The data is from Optionmetrics. Biweek at t+ 1

Abs(Unpriced Volatility)(annualized)

Absolute Value of Unpriced Volatility from Optionmetrics Biweek

26

Table 3: Variable Description for Option PIN

Variable Description Estimation Period

Option PINα The probability that an information event occurs Biweekθ The probability of volatility information happens when information

occursBiweek

δ The probability of high volatility information happens when volatil-ity information occurs

Biweek

γ The probability of high direction information happens when direc-tion information occurs

Biweek

ε Uninformed trading arrival rate. Biweekµ Volatility informed trading arrival rate. Biweekν Direction informed trading arrival rate. BiweekVol PIN The probability of option volatility information-based trading,

which is calculated by αθµαθµ+α(1−θ)ν+2ε

Biweek

Dir PIN The probability of option volatility information-based trading,which is calculated by α(1−θ)ν

αθµ+α(1−θ)ν+2ε

Biweek

27

Table 4: Variable Description for Stocks

Variable Description Estimation Period

StockReturn (Per Day) Raw return from CRSP database BiweekS&P 500 Return (Per Day) S&P 500 return from CRSP database BiweekExcess Return (Per Day) Raw return minus S&P 500 Return from CRSP database BiweekStock Spread ($) Stock ask price minus bid price from CRSP database BiweekStock Rel Spread Stock bid-ask spread divide by mid-point of ask and bid price from

CRSP databaseBiweek

Log(Daily Stock Volume) Natural logarithm of biweek daily stock volume from CRSPdatabase

Average Daily

Log(Market Cap) Natural logarithm of market capital at last day of period t fromCRSP database

Last day of period t

Stock PINStock α The probability that an information event occurs. BiweekStock δ The probability of good news happens when information occurs. BiweekStock ε Uninformed trading arrival rate. BiweekStock µ Informed trading arrival rate. BiweekStock PIN The probability of stock information-based trading, which is calcu-

lated by Stock δ∗Stock µStock δ∗Stock µ+2Stock ε

.Biweek

28

Table 5: Summary Statistics for Options

Variable Obs Mean Std. Dev. Min Max

OptionOption Bid-Ask Spread ($) 8160 0.092 0.202 0.014 1.829Option Effective Spread ($) 8013 0.044 0.153 0.006 1.466

Option Rel Bid-Ask Spread (%) 8160 5.835 4.320 1.505 22.999Option Rel Effective Spread (%) 8013 2.230 1.613 0.612 8.840

Log(Option Volume) 8154 10.460 1.281 7.896 14.056Log(Daily Option Volume) 8154 8.194 1.280 5.663 11.817

∆ 8094 0.526 0.016 0.508 0.615Θ 8094 -12.899 12.727 -81.909 -1.583

V ega 8094 5.862 5.669 0.522 38.453Γ 8094 0.138 0.110 0.012 0.614

Unpriced Volatility 8093 -0.013 0.153 -0.334 0.646Implied Volatility 8094 0.392 0.171 0.128 0.998

Realized Volatility 8095 0.379 0.226 0.081 1.286Abs(Unpriced Volatility) 8093 0.104 0.113 0.000 0.646

Initial Hedging Cost 8064 0.0087 0.011 0.0046 0.0893Rebalancing Cost 8064 0.0018 0.0020 0.0010 0.0159

Rel IC (%) 8064 0.024 0.021 0.005 0.125Rel RC (%) 8064 0.005 0.0045 0.001 0.028

Option PINα 8162 0.459 0.064 0.023 0.838θ 8162 0.492 0.115 0.023 0.989δ 8162 0.615 0.202 0.013 0.988γ 8162 0.486 0.176 0.035 0.962ε 8162 158.454 851.465 4.731 26794.070µ 8162 371.276 1239.278 10.783 35848.180ν 8162 301.447 1013.220 9.841 33978.800

Vol PIN 8162 0.223 0.066 0.088 0.409Dir PIN 8162 0.200 0.066 0.076 0.393

29

Table 6: Summary Statistics for Stocks

Variable Obs Mean Std. Dev. Min Max

StockReturn (%) 8130 -0.030 0.739 -2.410 1.982

S&P 500 Return (%) 8130 0.004 0.303 -0.849 0.706Excess Return (%) 8130 -0.034 0.639 -2.147 1.773

Stock Bid-Ask Spread ($) 8131 0.016 0.020 0.009 0.172Stock Rel Bid-Ask Spread (%) 8131 0.045 0.039 0.010 0.235

Log(Daily Stock Volume) 8137 15.546 0.977 13.247 18.248Log(Mkt Cap) 8131 16.296 1.412 12.893 19.147

Stock PINStock α 8151 0.339 0.050 0.168 0.574Stock δ 8151 0.489 0.178 0.041 0.928Stock ε 8151 286508 631814 3492 16900000Stock µ 8151 339981 815049 6671 24400000

Stock PIN 8151 0.170 0.033 0.113 0.284

30

Table 7: Correlation MatrixDirPIN

VolPIN

StockPIN

Log(DailyOptionVol-ume)

Log(DailyStockVol-ume)

Log(MktCap)

ImpliedVol

RealizedVol

RelIC

RelRC

Dir PIN 1.00Vol PIN -0.04 1.00Stock PIN 0.22 0.09 1.00Log(Daily Option Volume) -0.55 -0.39 -0.14 1.00Log(Daily Stock Volume) -0.29 -0.11 -0.15 0.70 1.00Log(Market Cap) -0.33 -0.11 -0.39 0.43 0.34 1.00Implied Vol 0.05 -0.03 0.03 -0.14 0.03 -0.53 1.00Realized Vol 0.04 -0.02 0.01 -0.09 0.03 -0.38 0.72 1.00Rel Initial Hedging Cost 0.22 0.15 0.33 -0.18 0.11 -0.49 0.49 0.34 1.00Rel Rebalancing Cost 0.22 0.15 0.33 -0.18 0.11 -0.48 0.46 0.31 0.99 1.00

31

Table 8: Sorted by Market Cap

Log(MktCap) Log(Stock Vol) Log(Option Vol) VolPIN DirPIN StockPIN1 (Low) 14.208 15.250 7.679 0.229 0.224 0.190

2 15.593 15.271 7.754 0.232 0.218 0.1773 16.358 15.444 8.026 0.221 0.203 0.1664 17.147 15.532 8.168 0.225 0.195 0.159

5 (High) 18.176 16.238 9.319 0.208 0.161 0.156(1-5) -3.968 -0.987 -1.640 0.021 0.064 0.034

(-193.015) (-30.828) (-42.492) (9.074) (29.690) (29.870)

32

Table 9: Regression on Abs(Unpriced Volatility)

This table reports the coefficients from fixed effect panel regression of absoluteunpriced volatility. The absolute unpriced volatility is defined as the t − 1 pe-riod last day implied volatility (IV) minus the t period realized volatility (10days). VolPIN is the probability of option volatility information-based trading instock/option i of biweek t− 1, which is calculated by αθµ

αθµ+α(1−θ)ν+2εand DirPIN

is the probability of option volatility information-based trading in stock/option

i of biweek t− 1, which is calculated by α(1−θ)ναθµ+α(1−θ)ν+2ε

. The dummy is defined to

be 1 if IV>Realized Volatility(RV), 0 otherwise. Log(Market Cap) is the naturallogarithm of t−1 period last price times total shares outstanding. Log(Daily Op-tion Volume) is the natural logarithm of t−1 period daily average option volume.All the variables are winsorized at 1% level. Time and firm effects are controlledand s.e. is adjusted using robust option. T-stat is reported in parentheses with*** p < 0.01, ** p < 0.05, * p < 0.1.

(1) (2) (3) (4) (5)

VolPIN 0.0796*** 0.187*** 0.0752** 0.182*** 0.144***(2.737) (6.035) (2.518) (5.789) (3.470)

I(IV > RV )*VolPIN -0.182*** -0.183*** -0.124***(-15.29) (-15.39) (-3.781)

DirPIN 0.0596** 0.0452 0.0570* 0.0421 0.0873**(2.025) (1.573) (1.848) (1.397) (2.063)

I(IV > RV )*DirPIN -0.0707**(-1.995)

Log(Market Cap) -0.0421*** -0.0425*** -0.0428***(-4.910) (-4.980) (-4.991)

Log(Daily Option Volume) 0.00717*** 0.00707*** 0.00705***(2.800) (2.804) (2.804)

Constant 0.0740*** 0.0794*** 0.703*** 0.716*** 0.720***(6.692) (7.423) (5.025) (5.142) (5.151)

Time Effect YES YES YES YES YESFirm Effect YES YES YES YES YES

Observations 8,093 8,093 8,056 8,056 8,056R-squared 0.001 0.037 0.006 0.042 0.043

33

Table 10: Regression on Option Effective Rel Bid-Ask Spread

This report reports the coefficients from OLS and fixed effect panel regression of option effective relativebid-ask spread. The option effective relative bid-ask spread is defined as the option effective bid-ask spreaddivide by the average quote price (ask+bid

2); Stock PIN is the probability of information-based trading in stock

i of biweek t − 1, which is calculated by Stock α∗Stock µStock α∗Stock µ+2Stock ε

; VolPIN is the probability of option volatility

information-based trading in stock/option i of biweek t− 1, which is calculated by αθµαθµ+α(1−θ)ν+2ε

and DirPIN

is the probability of option direction information-based trading in stock/option i of biweek t − 1, which

is calculated by α(1−θ)ναθµ+α(1−θ)ν+2ε

; Initial hedging cost (IC) is the cost to set up a delta neutral position bypurchasing ∆ shares of the stock at the ask price and close the position by selling at the bid price, which iscalculated by kS∆; Rebalance hedging cost is calculated by νk; Rel IC (RC) is IC (RC) divided by the stockprice; Log(Daily Option Volume) is the natrual logarithm of the average daily option volume at biweek t.Time and firm effects are controlled and s.e. is adjusted using robust option. T-stat is reported in parentheseswith *** p < 0.01, ** p < 0.05, * p < 0.1.

(1) (2) (3) (4) (5) (6)

VolPIN 0.0367*** 0.0314*** 0.0312*** 0.0137*** 0.0132*** 0.0129***(12.34) (10.61) (10.52) (4.672) (4.803) (4.765)

DirPIN 0.0581*** 0.0515*** 0.0514*** 0.0168*** 0.0163*** 0.0162***(16.49) (14.76) (14.70) (5.720) (5.727) (5.693)

Stock PIN 0.101*** 0.0845*** 0.0844*** 0.0302*** 0.0307*** 0.0304***(17.78) (14.74) (14.75) (5.852) (6.162) (6.253)

Rel IC 8.963*** 5.036(9.020) (1.518)

Rel RC 41.41*** 33.68**(8.789) (2.254)

Log(Daily Option Volume) -0.00289*** -0.00294*** -0.00295*** -0.000724** -0.000665** -0.000649**(-15.82) (-16.62) (-16.69) (-2.258) (-2.008) (-2.020)

Constant 0.00967*** 0.0132*** 0.0134*** 0.0173*** 0.0157*** 0.0152***(3.802) (5.311) (5.382) (4.664) (3.842) (3.888)

Time Effect NO NO NO YES YES YESFirm Effect NO NO NO YES YES YES

Observations 7,998 7,909 7,909 7,998 7,909 7,909R-squared 0.305 0.311 0.311 0.030 0.034 0.037

34

Table 11: Event Study on Information Measures

This table reports the coefficients from fixed effect panel regression of the information measures. The informa-tion measures include DirPIN, VolPIN, Stock PIN and Option Rel Spread. In addition we also include impliedvolatility and option volume. We only keep the data from t− 4(weeks) to t + 2(weeks) (totally 3 biweeks),where t is earning announcement date; the event period is from t− 2(weeks) to t+ 2(weeks), and the controlperiods are from t − 4(weeks) to t − 3(weeks); Stock PIN is the probability of information-based tradingin stock i of every biweek, which is calculated by Stock α∗Stock µ

Stock α∗Stock µ+2Stock ε; VolPIN is the probability of option

volatility information-based trading in stock/option i of every biweek, which is calculated by αθµαθµ+α(1−θ)ν+2ε

and DirPIN is the probability of option direction information-based trading in stock/option i of every biweek,

which is calculated by α(1−θ)ναθµ+α(1−θ)ν+2ε

; option effective relative bid-ask spread is defined as the current effective

bid-ask spread divide by the average quote price (ask+bid2

) at the first day of t−4(weeks); Implied Volatility isthe standardized at-the-money option’s implied volatility; Log(Daily Volume) is the natural logarithm of theaverage daily option volume of every biweek; Pre-Earning Dummy is defined as 1 if the biweek is right beforethe earning announcement date, 0 otherwise; Post-Earning Dummy is defined as 1 if the biweek is right afterearning announcement date, 0 otherwise. We control the option greeks for the regressions with dependentvariables DirPIN, VolPIN, Option Rel Bid-Ask Spread, Implied Volatility and Option Volume. Time andfirm effects are controlled and s.e. is adjusted using robust option. T-stat is reported in parentheses with ***p < 0.01, ** p < 0.05, * p < 0.1.

(1) (2) (3) (4) (5) (6)Variables VolPIN DirPIN Stock PIN Rel Spread Implied Volatility Log(Daily Volume)

Pre-Earning Dummy (β1) 0.00238 -0.00575** 0.00172* 0.0033 -0.00452** 0.135***(0.973) (-2.490) (1.717) (0.710) (-2.178) (7.038)

Post-Earning Dummy (β2) -0.0103*** -0.0147*** -0.00401*** 0.0130** -0.0128*** 0.261***(-3.453) (-5.175) (-3.770) (2.481) (-3.054) (11.52)

Constant 0.198*** 0.216*** 0.179*** 0.0703 -0.751*** 7.766***(2.879) (3.708) (301.4) (0.567) (-2.718) (12.05)

H0 : β2 − β1 = 0 (t stat) -3.287*** -2.445** -3.922*** 1.378 -1.770* 4.244***Control for Option Greeks YES YES NO YES YES YES

Time Effect YES YES YES YES YES YESFirm Effect YES YES YES YES YES YES

Observations 2,458 2,458 4,681 4,616 4,726 4,726R-squared 0.021 0.020 0.007 0.003 0.326 0.045

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