Ssrn id2587282

Electronic copy available at: http://ssrn.com/abstract=2587282
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Market Making and Risk Management in Options Markets
Naomi E. Boyd
Department of Finance, West Virginia University, Morgantown, WV 26505, USA
Abstract
This article examines the personal trading strategies of member proprietary traders in the
natural gas futures options market. Trading activity is found to mirror previous findings in
futures markets, specifically high frequency trading, with low risk exposure. The portfolio of
risk holdings by member proprietary traders are also examined to identify whether they are
instantaneously hedged using the underlying futures market, as well as to investigate how
they manage their inventory holding, rebalancing, and volatility risk exposures. Findings of
longer-term risk management practices by option markets indicate that instantaneous hedging
does not take place in this market. Exposure to price and volatility risks is actively managed,
while rebalancing risk exposure has a significant impact on profit for this trading group.
I would like to thank Peter Locke for his invaluable insights and comments, Li Sun, participants of the 2008
Financial Management Association doctoral consortium, the 2009 Financial Management Association and
Southern Finance Association meetings, seminar participants from West Virginia University, Kansas State
University, Clemson University and the University of Rhode Island for their helpful comments.
Naomi Boyd was a Consultant, Office of Chief Economist, Commodity Futures Trading Commission (CFTC),
Washington, D.C. when this research was conducted. The ideas expressed in this paper are those of the authors
and do not necessarily reflect those of Commodity Futures Trading Commission or its staff.
* Corresponding author: Tel.: +1-304-293-7891; fax: +1-304-293-5652.

Electronic copy available at: http://ssrn.com/abstract=2587282
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INTRODUCTION
The services of liquidity production and price determination that market makers provide
serve a vital role in the proper and orderly functioning of the aggregate financial market system.
Without the presence of market makers, the system would be less efficient and more costly to
maintain. How and why market makers provide these services should be influenced by the
structure under which they operate. Market makers can be categorized within two central
structures: (1) a designated structure under which the market maker has an assigned role and is
obligated to perform certain duties including, but not limited to, providing liquidity, filling
orders, setting prices, and maintaining price continuity or (2) an open structure under which a
market maker is governed only by the rules set forth by the exchange for all traders.
U.S. futures options (commodity options) operate under an open trading structure which
mimics the futures trading architecture, where members may broker orders or trade for their own
accounts with little constraint on their trading strategies. Floor traders (or their screen trading
equivalents) who choose to make a market with their trading are not required to maintain
inventory or price continuity and can enter and exit the market freely and without constraint,
other than risk controls imposed by their brokerage account. They have no privileged access to
pending orders, but at least on the floor have first-hand observation of trading activity and the
shouting and gesturing which predate a trade. Each trade must be categorized as a trade for the
executing members own account, the member’s clearing firm account, another member’s own
account, or a non-member account (customer). A member’s income can be derived from
proprietary trading and brokerage.
Research on futures markets has established that member proprietary trading serves the
market-making function in futures markets with trading behavior that is characterized by low

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end-of-day inventory holdings, small trades, and large volumes (Silber 1984, Kuserk and Locke,
1993, 1994). Related work shows highly volatile, short run profitability to futures proprietary
trading (Locke and Mann 2005). Proprietary options’ trading in natural gas futures options is
examined here to describe the institutional details of option market maker behavior.
It is shown that member proprietary trading in futures-options markets serves the market-
making function just as was previously documented by Kuserk and Locke (1993) in the
corresponding futures markets. This finding documents one of the many similarities between
how these markets operate. Member proprietary traders are characterized by their small trade
sizes, high volumes, small amount of time between trades, and low end-of-day inventory levels.
These characteristics are indicative of a market maker performing the tasks of providing liquidity
and price setting. This analysis also shows that these traders are profitable on average, albeit at
very low levels. Therefore, market making is a viable, profitable trading strategy for these
traders.
Since there is an active group of market makers in the futures market supplying liquidity
and making that market, futures options market makers would not benefit from similarly making
a market indirectly in the futures price. Instead, as Figlewski (1989) points out, a trader making a
market in options will benefit from eliminating futures price risk and concentrating on the other
risk factors. Trading options, unlike futures, involves more than univariate risk management. In
addition to exposure to changes in the futures price, the option value is also affected by changes
in the other factors which influence the option value, most notably the expectation of futures
price volatility. Management of the exposure to the futures price can be easily accomplished by
trading futures. Management of the exposure to volatility which arises in options trading requires
trading in other options. In terms of common option parameters, delta represents the exposure to

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futures price risk, and vega represents exposure to volatility risk1
. If option market makers use
the underlying futures market to hedge away their exposure to price risk, they could strategically
manage their residual risk and potentially earn higher profits than those who chose other trading
strategies.
In particular, we focus on the risks taken by proprietary traders, in terms of sensitivities
to parameters in an option pricing model. The manner in which these traders manage the various
risks allow us to infer market making as a strategy and describe particular characteristics of that
strategy. We focus on the ability of option market makers to dispel inventory holding risk
through simultaneous participation in the underlying futures market. The hedging practices of
market makers have been shown to reduce the costs of providing liquidity (Çetin, Protter, and
Warachka, 2006) as well as have been shown to have a direct impact on the size of bid-ask
spreads in option markets (Huh et. al. 2012). Thus, how option market markets hedge has direct
implications into market frictions such as transactions costs which will influence the price setting
practices of these traders. We also evaluate these traders exposure to gamma and vega risk to
examine whether they maintain level or changing levels of risk throughout the trading day on
average.
This paper is the first known study to attempt to formally and empirically test the theories
posited by Figlewski (1989) and Cox & Rubinstein (1985) that option traders maintain delta
neutral positions by establishing corresponding and offsetting trades in the underlying futures
market. Thus, it is thought that option market makers engage in hedging by (for example)
purchasing a quantity of futures options while simultaneously executing a certain number of
1
For example, if the delta of an option is .5, then a $.10 change in the futures price will lead to an approximately
$.05 change in the option value, holding all else constant. By selling one futures contract for every two options
contracts, this will temporarily eliminate the futures price. The residual risk would be the other option pricing
factors, such as volatility.

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contracts in the underlying futures contract, seeking instantaneous delta neutrality. The degree to
which these traders hedge by participating in both markets will determine their vulnerability to
the risk of holding positions in the option market. The short-run exposure of the futures-option
market maker to price risk, delta, is expected to be small if they are instantaneously delta-hedged
while the exposure to volatility, vega, may more accurately represent the “inventory” that the
market maker is carrying.
We find that futures-option market makers hedging practices do not coincide with
instantaneous hedging. Rather, their use of the underlying futures markets reflects a longer term
price risk management strategy. This type of strategy would be driven by option market makers
utilizing the underlying futures market to hedge when they cannot easily liquidate their inventory
in the options market or when they wish to hold onto a position for an extended period of time
(intraday) to allow prices to equilibrate or move into profitable territory. We also note that large
traders actively seek to hedge using the futures markets, which is in line with their
correspondingly larger inventory holdings; while smaller traders tend to keep most of their
trading centralized in the option market. On average, futures-option market makers maintain very
low levels of price risk over the course of a trading day while their levels of rebalancing risk and
volatility risk are much higher. Thus, futures-option market makers’ primary exposure is to
gamma and vega, or the speed at which delta changes in response to a change in the underlying
futures price and the response of the option price to a change in the volatility of the futures price,
respectively. In fact, analysis the impact of the three risk parameters on daily profits reveals that
gamma risk has the most substantial impact on the profitability of an option market maker.
The remainder of this article is organized as follows: Section II provides information
regarding the data; Section III investigates the behavior of market makers in options markets

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through a descriptive analysis; Section IV analyzes how market makers hedge their exposure to
price risk as well as details their intraday rebalancing and volatility risk exposures in the option
market; Section V concludes.
II. DATA
The data for this research consist of 20 months of transaction-level data in the natural-gas
futures and futures option markets traded on NYMEX (now part of the CME group), spanning
September 2005 through April 2007. This data set is maintained by the U.S. Commodity Futures
Trading Commission and comes from the computerized trade reconstruction (CTR) records
compiled and maintained by the agency from data feeds from the exchanges.
Trading rules specify the obligations of the floor traders and how trades are to be
executed and recorded. When trades are executed on the floor, the trader on the sale side, for
either a futures or futures option, reports the transaction to the exchange for clearing. The
exchange records the relevant information regarding which futures or options expiration is
traded, the price or option premium, strike price, and information about the counterparties. The
information also requires an indication by the broker as to whether the trade was for a proprietary
account, another floor trader, the traders clearing member, or some outside customer.
Our dataset includes the records of all options floor trades and provides information
including the price, quantity of the trade, trade date, trade time to the second, trade direction (buy
or sell), delivery month and year of the contract, customer type (trade for the member’s account,
his or her house’s account, another member on the floor, or a customer), counterparty’s customer
type, and the floor trader’s identification. We also use corresponding futures and options daily
settlement prices and daily interest rates (3-month T-bill).

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As in previous research in this area, traders who executed personal options trades
infrequently are removed from the sample. We calculate a measure of incumbency as the
percentage of all possible days that each trader executed proprietary trades, and drop those
traders who participated on 5% or less of the days, reducing the number of options traders from
144 to 91.
Natural gas futures and options trade in the physical environment from 9:00 am to 2:30
pm (ET). The futures contracts trade in units of 10,000 British thermal units (mmBtu) and
contracts which are not eventually offset require physical settlement. The minimum price
fluctuation is $0.001 per mmBtu, or $10 per contract. Typical natural gas prices range from $5 to
$15 per 10,000 mmBTU, yielding a notional contract value of $50,000 to $150,000 dollars.
When delivery does occur it is a throughput at the Sabine Pipe Line Company’s Henry
Hub in Louisiana. This can take place no earlier than the first calendar day of the delivery month
and no later than the last calendar day of the delivery month. The Henry Hub is a many natural-
gas pipelines that serve markets throughout the U.S. east coast, the Gulf and the Gulf Coast, and
the Midwest up to the Canadian border. The futures seller is responsible for the movement of the
gas through the Hub and pays all Hub fees while the buyer is responsible for movement from the
Hub.
III. MARKET MAKER TRADING STRATEGIES
We follow previous research by Working (1967, 1977), Silber (1984), and Kuserk and
Locke (1993, 1994) to examine whether traders carrying out member proprietary trades take on
the role of market makers within the competitive framework of an option market. Due to the link,
both institutionally and through arbitrage conditions, of the futures and futures-options markets,

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it is an empirical question as to whether the characteristics of market makers in futures markets
universally hold in the option market.
A. Market Making Activity
The positions and levels of market-making activity are determined through an
examination of several variables that have been shown to distinguish market makers from other
types of floor traders in the futures market. These descriptive statistics for active, proprietary
traders over the first three nearest contract months for options are provided in Table 1, Panel A.
Total trades documents how many different transactions were entered into over the sample
period. Similarly, total contracts are the total option contracts bought by these traders. The
average time between trades is calculated by first taking the average number of minutes between
each trade each day, and then averaging this number across trader days. There are a total of
15,573 trader days in the sample, for our 91 traders over the 413 of days in the sample. As is
shown in Panel A, on average option proprietary trading is similar to that of proprietary trading
in futures markets: traders maintain relatively low levels of inventory and provide liquidity
services to the market by trading frequently, in small amounts, with high levels of overall
volume.
[Insert Table 1 about here]
B. Market Making Revenue
Member proprietary trader’s income can be derived from proprietary trading and
brokerage. While the analysis that follows is meant to show whether member proprietary trading
generates positive levels of income for the trader on average, certain macroeconomic and market
specific factors may also influence the level of income during certain time periods. For example,
the relationship between commodity-equity cross-market linkages could drive profitability for

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traders. This issue was examined by Buyuksahin and Robe (2013) who documented that hedge
funds that are relatively unconstrained are the only set of traders who provide these linkages in
participation. While member proprietary traders’ income from their brokerage functions may
contain a portion stemming from trading with hedge funds, it is not possible to disentangle who
the outside customers are in our dataset.
Cross market linkages with other commodity markets may also impact member
proprietary trading activities and profitability. In the past, prices of crude oil and natural gas
followed closely with one another and major users viewed the products as close to perfect
substitutes (Onur, 2009). Research has shown that this relationship has diverged (Serletis and
Ricardo, 2004; Baschmeir and Griffin, 2006; and Serletis and Shahmoradi, 2006). In the short
term, prices of oil and natural gas are driven by different fundamental factors with crude oil
prices fluctuating in response to speculative activity in world oil markets and natural gas prices
responding to productive shocks. Azzarello et al. (2014) document a 330% energy content price
gap, which is primarily attributed an increase in production in natural gas. Income stemming
from brokerage functions would be influenced by cross-commodity linkages, not necessarily
income from proprietary trading.
Here we examine the distribution of income for active, proprietary trading in Panel A of
Table 2. Daily average income for options (in dollars) for each proprietary trade across the
nearest three expirations is found by marking to market each trade over the course of a trader
day, summing the income for each individual trader, and averaging the income for each trader
over all trader days by contract expiration. If the trade is a sell, the income is found by taking the
difference between the trade price and the settlement price and multiplying by the quantity. If the
trade is a buy, the income is found by taking the difference between the settlement price and the

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trade price and multiplying by the quantity. The quartiles of daily income are found from the
total daily income levels for each trader. Thus, the minimum corresponds to the lowest level of
income made by an individual trader during the sample period for a specified contract expiration.
Panel B in Table 2 on the other hand details the distribution of average daily proprietary income
across all traders each day. Thus, we have two views of income: among traders and across
traders.
Both tables provide similar results: 25% of traders are unprofitable, while the mean profit
levels, albeit small on average, are positive across traders and days; however Table 2 documents
a slightly skewed distribution with more traders taking a positive profit than a loss on average.
The low levels of profitability beg the question of why member proprietary traders are willing to
provide liquidity to the market, if one average, they are only making low levels of returns. A
negatively skewed return distribution will increase the loss probability, while a positively
skewed return distribution will increase the probability of gaining. A preference for positive
skewness will cause investors to require lower rates of returns on these assets (Barberis and
Huang, 2008; Boyer, Mitton, and Vorkink, 2010), and, as such, a preference for skewness
represents a desire to gamble. Given that option traders often trade based on skew, the relatively
low levels of profit seen on average could be the result of member proprietary traders being
willing to take lower average daily returns for the possibility of big upside potential of these
highly skewed assets.
C. Market Making Competition
Futures and option markets have systems that can be identified as having market-making
competition, which is in stark contrast to the designated system of the NYSE specialist.

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Competition among dealers has been found to lower spreads (Stoll, 1978; Benston & Hagerman,
1974; Tinic & West, 1972, Wahal, 1997; Klock & McCormick, 1999). Understanding the
dynamics of the price setting and trading behaviors of market makers requires an evaluation of
the competitive forces among this group of traders. The average number of traders is
documented across trade type and contract expiration in Table 3 to determine the extent of
competitive forces in each of the various trade categories. Traders in these markets can conduct
more than one type of trade. The vast majority of traders are classified as making CTI = 1 trades,
which indicates they own 10% or more in the trading account for which they are trading. On
average there are 51 traders executing trades of any type and maturity (first three nearest to
expiration contracts) per day.
D. Interdealer Trading
In inventory microstructure models market makers face exogenous demands to buy and
sell and profit from buying and selling at bid and ask prices respectively, with the spread
dependent on the underlying risk of the asset. Bid and offer placement are adjusted to manage
inventory risk (e.g. Ho and Stoll, 1983; Manaster and Mann, 1996). Further, as discussed in
Locke and Sarajoti (2004), interdealer trades are typically more costly to initiate than trades
conducted with other trade groups; thus, the only rational explanation for the existence of a
significant percentage of interdealer trades is inventory control. These traders would rather
immediately transfer their unwanted inventory than face the uncertainty of waiting for customer
orders. Table 4 details the percentage of trades by customer type in the options market through a
frequency analysis of trade combinations across the three nearest expiration contracts to examine

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the extent of interdealer trading in the options market. The levels of interdealer trading range
from 16.33% in the second deferred contract to 22.83% in the nearby contract.
E. Summary of Market Making Activities
The institutional characteristics of futures-options markets indicate that on average,
member proprietary traders in this market trade often, in small amounts, with very little time in
between trades, and are responsible for one of the highest levels of activity in terms of volume.
Thus, these traders serve similar market making roles in both the futures and futures options
markets. Further, it is shown that the levels of competition among these traders are higher than
other trade type categories and member proprietary traders are prone to engaging in interdealer
trading. Competition will lower the average levels of profitability for these traders, as will
engaging in interdealer trades. These two factors may be the driving forces behind the low levels
of profitability within this trade type. However, even given low levels of profitability, market
making in options futures markets is a profitable trading strategy. These summary measures shed
first light on the institution framework under which member proprietary traders make their
market. In order to understand more fully the constraints that these traders face and how these
frictions can help explain the behavior and price setting practices of market makers in futures-
option markets, the risk structure of member proprietary traders follows.
IV. RISK MANAGEMENT
Analysis of market-making risk dynamics in options markets has received very little
attention in the literature and has primarily focused on the overall risk that option market makers
bear. The risk exposure of the option market maker will determine how and whether the market
maker is able to dispel certain portions of risk which will ultimately drive his or her trading and

12
price setting behavior. Agarwal and Narayan (2004) characterize risk exposures and portfolio
decisions involving hedge funds, and they find that investors wishing to earn risk premia
associated with different risk factors need to differentiate hedging strategies. Research has shown
that the risk that option market makers are exposed to greatly depends on the stochastic nature of
the underlier’s returns.
Ho and Stoll (1983) showed that, if the stock return volatility is constant, the market
maker’s risk exposure per dollar of investment is nonstochastic over the interval during which
the inventory is held. However, unless the option market maker can trade continuously, an option
transaction’s contribution to the dealer’s risk exposure will be stochastic because the volatility of
an option is a function of both its (stochastic) hedge ratio and the underlying asset’s return
volatility.
Jameson and Wilhelm (1992) evaluated the risks that options market makers face and
provided empirical evidence that their risk factors are unique to option markets due to the
stochastic volatility of the stock return and the inability to rebalance the option position
continuously. Specifically, by measuring the impact of delta, gamma, and vega on bid-ask
spread, they found that gamma and vega are significant determinants of spreads. These risks can
be reduced through diversification; however, the authors’ finding of significant influence of the
risks on spreads indicates that diversification does not completely eliminate the risk due to
discrete rebalancing and stochastic volatility on the option market makers’ portfolio.
O’Hara and Oldfield (1986) utilize a dynamic framework of market makers facing
uncertainty with future order flow and future value of underlying equity, and demonstrated that
inventory and risk preferences have a pervasive influence on the market makers’ pricing policy,
influencing both the size and placement of the spread. These results were further examined by

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Giannetti, Zhong, and Wu (2004) when they developed an inventory-based approach to study
market-making behavior in option markets. They posit that the hedging practices of option
market makers have a substantial impact on the setting of bid-ask spreads and optimal inventory
control. By adding hedging mechanisms to the standard inventory-control model, the authors
derived the market makers optimum option quote setting and inventory-control policies. Huh, et
al. (2012) further develops a theoretical model which evaluates the relationship between hedging
practices of option market makers and the size of the bid ask spread. Here it is posited that the
bid-ask spread increases when option market makers use the underlying market to hedge visa-a-
via using the options market to hedge.
Of vital importance to studying market maker behavior in option markets is evaluation of
these traders’ exposure to and management of risk. Option market makers’ primary exposure to
risk comes from price movement in the option and underlying asset markets, rebalancing needs,
and volatility of the underlying assets. As noted above, much of the previous research in the
literature has focused on the price movement and stochastic nature of the underlying assets.
However, to determine the overall extent of option market makers exposure to risk, inventory
positions must be examined in terms of a vector of risk measures, which include delta, gamma,
and vega. Exposure to these risks is due to the influence of certain variables on the option price.
Several variables are known to affect option prices: the price of the underlying asset, the options
strike price, the time until expiration, the volatility of the price of the underlying asset, the risk
free rate, and the value of the dividends expected during the life of the option.
The primary purpose of this article is to explore the activities and risk management of
market makers in options markets. Here, the sensitivity of the option price to both the price of
the underlying asset and the volatility of the price of the underlying asset are evaluated through

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an examination of delta, gamma, and vega. The underlying volatility not only plays a role in the
valuation of the options being traded, but also in the ability of market makers to eliminate their
exposure to price and volatility risk. The predominant issue is whether market makers in options
futures markets maintain instantaneous delta neutrality as posited in the theoretical literature. If
market makers establish positions in both the underlier and in options that are hedged with
respect to fluctuations in the price of the underlying asset, their portfolios will be delta neutral. It
is found that the member proprietary traders examined in this article do not hedge
instantaneously, which exposes them to fluctuations in the value of their portfolios when the
underlier fluctuates.
Delta measures the degree to which an option price will move given a change in the
underlying asset or, in this case, the sensitivity of the option to the futures price. The delta is
often called the neutral hedge ratio; with a portfolio of n shares of a stock, n divided by delta
gives the number of calls needed to be written to create a neutral hedge. A positive delta
indicates that the option position will rise in value as the stock price rises and drop in value as
the stock price falls. A negative delta, on the other hand, means that the options position should
rise in value if the stock price falls and drop in value if the stock price rises. The delta of a call
option can range from 0 to 1, whereas the delta of a put option can range from -1 to 0. Thus, a
short call has a negative delta, and the long call has a positive delta with these values reversed
for puts and the same for stocks. The closer an option’s delta is to either -1 or +1, the more the
price of the option will respond like an actual long or short stock when the stock price fluctuates.
Gamma indicates how much the delta changes for a $1.00 change in the stock price. It is
the second partial derivative of the option price with respect to the underlier. If gamma is small,
delta changes slowly, and to keep a portfolio of options delta neutral one can rebalance the

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portfolio less frequently. If gamma is large, delta is extremely sensitive to changes in the
underlying price, and, therefore, the portfolio will have to be adjusted more frequently. Both long
calls and puts have positive gamma. That is, long call positions will have deltas that become
more positive and move towards 1 when the underlying price changes but move toward zero
when the underlying price falls. Long puts will have deltas that move toward -1 when the stock
price falls and move toward 0 when the stock price rises. Short calls and puts have negative
gamma; thus, the opposite effects take place. Futures will always have a gamma of zero because
the delta value is always 1.0; thus, it never changes.
The vega of an option indicates how much the price of the option will change as the
volatility of the underlying asset changes. Vega is calculated to show the theoretical price change
for every 1% point change in implied volatility. Long calls and puts both have positive vega,
which indicates that the value of the option will increase as the volatility increases and decrease
when volatility decreases. Short calls and puts both have negative vega, which means that the
value of the option will increase when volatility decreases and decrease when volatility
increases. Vega is the greek which has the most impact on option prices second to delta. Jameson
and Wilhelm (1992) showed that an options gamma and vega were important in the
determination of option market makers’ bid-ask spreads and provided an indication of the
inventory-risk exposure these traders faced.
The risk characteristics of a portfolio of options can be described by the sum of the risk
characteristics of the portfolio components. Central to the evaluation of the risk characteristic
that provides the most information about exposure to inventory-holding risk is whether market
makers in option markets maintain delta neutrality by hedging their trades in the option market
with offsetting positions in the underlying futures market. While many have speculated this to be

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the case, due to data limitations, it has not been formally tested. This unique data set facilitates
the evaluation of traders’ positions in both the futures and option markets, which allows for
incorporation of information about whether these traders are maintaining delta neutral positions
by conducting simultaneous, off-setting trades. Two issues are addressed in the analysis that
follows: (1) Do option market makers use the underlying futures market to maintain delta
neutrality? and (2) How are market makers managing their exposure to sources of rebalancing
and volatility risk? These questions are addressed by evaluating the market maker’s risk
holdings at varying intervals intraday.
A. Position Risk Parameters
If a trader simultaneously trades in both the option and futures markets, position delta
will reflect the extent to which the trader is maintaining a delta-neutral portfolio at the end of
each day by creating offsetting trades from participation in both markets. If the trader is only
participating in the option market, the position delta is calculated using only the trades from the
option market and will also provide information about end-of-day delta neutrality. The gamma
and vega of futures are zero; thus, those values incorporate only information about trades in the
option market.
In order to facilitate the analysis of the position parameter levels, several simplifying
assumptions must be made. First, it is assumed that traders conducting member proprietary
trades begin each trading day with an inventory level of zero. Manaster and Mann (1996)
provided evidence that daily changes in inventory are concentrated around zero, so we follow the
previous literature which assumes that all traders begin the day with a zero-inventory position.
Second, while the analysis for the option market is performed by broker identification numbers,
which are unique for a particular trader, in order to track trades from the option to the futures

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market, account numbers must be used when matching trades in both markets2
. The trades are
matched by account number and time; thus, it is assumed that if a trade occurs within a specified
time frame for the same account, it is instigated by the same broker. There may be more than one
broker per account number; therefore, noise will be introduced into the matching process.
Finally, trades in the options market will contain only those performed by traders conducting
CTI 1 trades, whereas they are matched with both CTI 1 and CTI 3 trades from the futures
market because a trader in either category of trade in the futures market could in practice be
executing offsetting trades for the option market makers.
In order to calculate the parameter estimates, a price series must be formed for the option
and futures markets. There are two issues to address in forming a matched price series for the
option and futures markets: (a) which contract expiration to use and (b) how to address
nonsynchronous trading issues. The first issue arises because the contract with the highest
volume may not be the nearby contract. Volume is well known to be a proxy for information and
is highly related to open interest; thus, we use both the nearby and first deferred contracts which
contain the highest overall levels of volume for this analysis. The second issue arises because
futures markets are much more active than the relatively illiquid option market; thus, issues
involving nonsynchronous trading must be addressed. NYMEX requires that trades be reported
within one minute of execution, so we aggregate prices over a one-minute time span in order to
form a price series that reflects the volume weighted average price for a minute for both the
futures and options markets.
2
A subsample was also studied that evaluated the position risk positions matched by executing broker IDs after
electronic trading in futures markets began because in theory option market makers could simultaneously trade in
both markets using hand held devices. Our findings were insignificantly different and robust to the matching
procedure using account numbers.

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Volume-weighted average prices for observations from proprietary trades (CTI 1 trades)
for the nearby and first deferred contracts are computed over one minute interval for both the
option and the futures markets. The volume weighted average prices are found by multiplying
the trade price for a given observation by the quantity traded at that price with the average taken
over all observations in a minute. The last observation at each strike, for each option type (put
and call) is taken along with the futures-settlement price in an increment, where the last volume-
weighted average futures price in the increment is used as a proxy for the settlement price.
These values are used in a binomial pricing model to estimate the option premiums.
The binomial option-pricing models the underlying instrument over time, as opposed to a
particular point in time; thus, it is used to allow for the early exercise component of futures
contracts. Also known as American-style options, which can be exercised at any point in time,
early exercise is a unique feature of options on futures contracts that stems from the minimal
time value associated with in-the-money futures options. It is advantageous to exercise in-the-
money futures options early and reinvest the proceeds at the risk free rate in order to earn a
higher overall rate of return, which unique to these types of options.
An implied standard deviation is used as a proxy for F which, along with the time
duration of a step t, measured in years, is used to calculate the probability that the price of the
underlying asset will move up or down at each step in the binomial tree. This implied standard
deviation is calculated from the most actively traded, near-the-money option for the settlement
futures price3
. A grid search is used to find the implied standard deviation, which minimizes the
mean-squared error over the trading day by comparing the average option premium to the
observed premium for each hypothetical sigma.
3
Bloomberg implied volatilities were also used with no significant changes in the results. Thus, our estimation of
the implied volatility is robust to the methodology described.

19
This method ensures that the tree is recombinant, which reduces the number of tree nodes
and speeds up the computation of the option price. This property also allows for the underlying
price to be calculated directly from a formula at each node rather than from having to build the
entire tree. It is well known that option valuations cycle from high to low as the number of steps
increases, holding time to maturity constant; therefore, two separate steps are used, 30 and 31, to
calculate the average option value for each hypothetical sigma.
Once the premiums, futures prices, and implied standard deviation have been found, the
delta, gamma, and vega are calculated as in Hull (2000). An estimate of delta, gamma, and vega
are computed for each strike price and option type (put and call) in each increment. The
estimated risk parameters are merged back with the trader level data to compute position
parameter values for each trade. This is done by summing the quantity of trade for a particular
strike and option type for each trader in an increment, which is then multiplied by the
corresponding (option type and strike) estimated parameter values to compute the position
parameter value for each trader in each increment. The position levels are marked to market at
the end of each increment to account for open positions (either long or short) in the computation
of the position parameter levels.4
These position parameter values are examined in greater detail
to examine option market makers exposure to various sources of intraday risk in the sections that
follow.
B. Delta Neutrality
The theoretical literature on option risk management postulates that option market
makers may hedge inventory risk exposures by maintaining delta-neutral positions (Figlewski,
4
Marking the position parameter levels to market each increment entails summing the positions of each increment to
carry forward the balance (if the trader is net long in the increment) or debit (if the trader is net short in the
increment) of trades. The balance is then added to the first trade in the increment and multiplied by the increment’s
parameter estimate to calculate the increment’s parameter position level.

20
1989; Cox & Rubinstein, 1985). This would require option market makers to engage in hedging
by (for example) purchasing a quantity of futures options while simultaneously executing a
certain number of contracts in the underlying futures contract, seeking instantaneous delta
neutrality. The degree to which these traders hedge by participating in both markets will
determine their vulnerability to the risk of holding positions in the option market. The short-run
exposure of the futures-option market maker to price risk, delta, is expected to be small if they
are instantaneously delta-hedged while the exposure to volatility, vega, may more accurately
represent the “inventory” that the market maker is carrying.
As specified above, the futures and options data are matched by account numbers and
time to determine whether (1) instantaneous hedging is taking place and (2) if instantaneous
hedging is not being used, examining the process by which option market makers use futures
markets to hedge during the course of a trading day. Table 5 reports the results that depict
whether option market makers are instantaneously delta neutral by matching the options and
futures data by account number and time; where we make the assumption that if a trade takes
place under the same account number in the same minute the futures trade corresponds to the
options trade that was executed in that same time frame. We find that contrary to theory, option
market makers do not maintain instantaneous delta neutrality.
Due to this finding, an additional analysis is performed to determine whether option
market makers tend to specialize in hedging in a particular market. To evaluate whether option
market makers specialize in hedging only in options or in futures the first month of the sample,
September 2005, is evaluated. A frequency analysis of the number of traders engaging trades in
both the futures and option markets versus the option market only is performed. The frequency

21
provides a count of the number of trades for a particular trader. Of the 65 option market makers
who were trading in September 2005, 25, or 38.64%, traded only in the option market and did
not use the futures market to hedge. Of these traders, their overall trading activity is very low,
capturing only 3.8% of the overall number of trades conducted that month. Forty, or 61.54%, of
the options market makers engage in trading in both markets. The number of trades in the futures
market far surpasses the number of trades in the options market with 3020 and 4452 trades in
options and futures respectively.
Thus, hedging options trades in the futures market is not a one-for-one strategy. Trading
in options captures 38.88% of the overall number of trades for the month, whereas trades in the
futures market are at about 57.32%. Higher amounts of trading in the futures market may be one
explanation for why the levels of position delta are higher when both option and futures trades
are evaluated than when only the options trades are evaluated. Market makers who are using both
markets to hedge may be overestimating their exposure to price risk, resulting in holding (or
selling) too many of the underlying futures contracts to offset their positions in the options
market.
There are other explanations as well however: first, option market makers trade
frequently and in small amounts as is documented in Table 1; therefore, many of their option
trades are liquidated quickly which would eliminate the need for hedging in the futures market.
Further, if they are unable to unwind these positions efficiently and quickly, it may be an impetus
to eventually go into the futures market to offset their inventory holding risk exposure. The
desire to keep bid-ask spreads to a minimum as postulated in Huh et. al. (2012) in order to keep
liquidity high may also be a reason for the above findings.

22
The ability of market makers to liquidate their inventory holdings quickly and efficiently
using futures markets is examined by widening the interval by which options are matched with
the futures trades to better capture the hedging activity being employed by the option market
makers. Two primary filters are used: (1) 600 seconds and (2) the trading increment which
consists of one hour of trading, except the initial increment that consists of the first 2 hours of
trading.5
The results from this analysis are presented in Table 6, with Panel A presenting the
merge base of 600 seconds and Panel B containing the results from the increment merge base.
From this analysis it appears that market makers actively seek to utilize the underlying futures
market to hedge their nearby contracts more than the further to expiration contracts. Further
when comparing the alternative merge base specifications of 600 seconds and an increment with
the instantaneous hedging (within one minute), it appears that lengthening the time frame
captures greater amounts of market maker hedging activities. This analysis supports the notion
that while market makers in options markets do not maintain instantaneous delta neutrality, they
do utilize the underlying futures market to hedge inventory that either was not easily liquidated
quickly or is being held onto for a period of time to possibly allow for prices to adjust to some
acceptable level.
We also examine whether there are differences between large and small traders in their
risk management. We split the sample into two categories of traders: large traders, or those who
maintain an absolute value of quantity traded during an increment of 30 contracts or more and
small traders, or those who fall below 30 contracts in any given increment. The results of this
analysis are presented in Table 7, which indicates that large traders are the primary users of the
futures market for hedging purposes. Small traders do not maintain delta neutrality as shown by
5
Due to the lack of trading in the first hour, the first 2 hours of trade are combined for the incremental analysis.

23
the larger levels of position risk when including the futures trades than when not. It may be that
larger traders are more adept at managing their inventory holding risk due to their frequent needs
to dispel this risk because of their much larger holdings on average. The levels for the position
risk holdings are significantly lower when including the futures trades corresponding to the
options transactions made within the same increment across both maturity spectrums (nearby and
first deferred). Small traders on the other hand are primarily trading frequent, small amounts in
the options market with limited trading taking place in the futures market, thus eliminating the
need for futures market hedging.
C. Intraday Analysis of Gamma and Vega
Of further importance is whether and how the market maker’s other position risks are
changing over the course of the trading day. Examining the intraday values of gamma and vega
allows for a decomposition of the characteristics that option market makers manage in order to
mitigate their exposure to various sources of risk. By evaluating the distribution of the risk
characteristics over the trading day, it can be determined whether any intraday patterns in risk
management exist for market makers in the options market.
Intraday market-maker gamma and vega risk is evaluated over five time increments in
Table 8. Panel A denotes the position risk parameters averaged over all traders. Both gamma
and vega exhibit a u-shaped pattern across the increments indicating increased levels of risk on
average at the beginning and end of the trading day when volume is also the highest. Significant
differences for position gamma correspond to the higher volumes at the beginning and end of the
trading day, while position vega has a significant drop at midday when volumes are typically at

24
their lowest levels. Thus, on average the risk management practices of market makers seem to
follow typical trends in volume.
Panel B (C) of Table 8 provides the position gamma and vega by increment for large
(small) traders. For large traders both gamma and vega experience relatively flat levels over the
course of the trading day with a significant increase in the last increment. Interesting differences
can be noted between the contract expirations where the first deferred levels of position vega are
of three orders of magnitude larger than the nearby contract. It appears that large option market
makers focus their volatility risk management on the nearby contract. For small traders, position
gamma decreases with contract expiration while position vega is two orders of magnitude larger
in the first deferred contract.
D. The Microstructure of Risk Management
In Table 9 we partition the increment position risk parameters based on number of trades,
trade size, and volume to determine whether any of these market microstructure characteristics
play a role in the management of intraday risk by option market makers. Across all of the sample
partitions we see a very large amount of dispersion among the quartiles especially between the
lower 50% and upper 50%, which again suggests that significant differences in trading and risk
characteristics are present among large versus small traders. Those with the highest levels of
trading activity, with the largest trades, and those who generate the highest amounts of volume,
all exhibit the greatest amounts of risk management: delta risk appears to exhibit an inverted U-
shape across the trading increments; vega risk is highest in the first two increments and virtually
flat across the latter three time increments; gamma risk seems to fluctuate within some

25
acceptable range. No discernible pattern exists for the lowest quintile for vega risk, but delta risk
for this group also exhibits an inverted u-shape across the trading day.
E. Does Moneyness Matter?
Due to the various costs in trading different types of options market makers may tend to
trade in particular categories of moneyness. This issue is evaluated with the results presented in
Table 10. It is reasonable to assume that certain traders may choose to specialize in a group of
options determined by moneyness due to the relative differences in cost and structure of the
various option types. For instance, deep in-the-money options are almost perfect substitutes for
the underlying security, while in-the-money options are the cheapest. If option market makers
have certain trading strategies based on the differences between moneyness categories, patterns
in trading certain options should emerge.
A moneyness level of 3% is chosen because it offers the greatest range of observations in
each moneyness group. A frequency analysis is performed to determine whether market makers
specialize in moneyness groups. This analysis reveals that the vast majority of options market
makers trade in all types of moneyness with only 11 of the 65 trading in only one or two
categories of option moneyness. For those 11 traders, all but two conduct only one trade during
the sample period. Of the remaining 54 traders who participate in trading across all levels of
moneyness, 66.17% of their trades are in out-of-the-money options, 18.87% are in at-the-money
options, and 14.12% of their trades are in in-the-money options as shown in Table 10. Thus, it
does not appear that market makers focus on only one category of moneyness, but instead trade

26
across moneyness groups, with the majority of their trading focused on out-of-the-money
options, probably due to their cost-relative to at-the-money or in-the-money options.
F. Risk and Return
Previous research has documented the impact of the position greeks on bid-ask spread but
since we are interested here in market making as a trading strategy, we evaluate the impact of
each of the position risk parameters on profit. If the risk/return model holds true we expect to
see significant levels of risk being related to profit. The univariate analysis above indicates that
option market makers actively seek to manage their exposure to delta risk over both the nearby
and first deferred contracts, albeit not instantaneously, focus their vega hedging on primarily the
nearby contract, and are subject to significant levels of gamma risk. A simple regression of daily
profit for each trader on the position risk parameters (Delta, Vega, and Gamma respectively)
yielded the following results for the nearby contract where Position Gamma was the only risk
parameter found to have a significant effect on market maker profit:
𝑃𝑖,𝑡 = 4.31 − 14.05𝛿𝑖,𝑡 − 6.14𝜗𝑖,𝑡 + 𝟖𝟏. 𝟕𝟑𝛾𝑖,𝑡 + 𝜀𝑖,𝑡
These results are in line with those of Jameson and Wilhelm (1992) who found Gamma to have a
positive and significant effect on the spread and also correspond to the theoretical design
constructed in Huh et. al. (2012) with respect to the ability of a market maker to rebalance
increasing the costs associated with trading.
V. CONCLUSION
The institutional characteristics of traders behind four different trade classifications are
evaluated for the futures option NYMEX natural-gas market in order to decompose trade-type
characterization. It is found that traders conducting member proprietary trading in the natural-gas

27
option market behave as though they are market makers, on average, trading often in small
amounts with very little time in between trades, and are responsible for the highest levels of
activity in terms of volume. They also end the trading day with very low levels of inventory in
order to mitigate their exposure to overnight inventory-holding risk. Evaluation of the extent of
competitive forces in each trade category and the use of interdealer trades to expel unwanted
inventory are also conducted in order to provide more information on the institutional details of
option market making. It is shown that traders who conduct member proprietary trading are one
of the largest trader groups and engage in significant amounts of interdealer trading in order to
maintain their preferred inventory levels.
The portfolios of option market makers are examined in terms of their exposure to daily
levels of risk as measured by delta, gamma, and vega. It is found that end-of day positions are
very small, a result that supports the hypothesis that market makers try to mitigate their exposure
to overnight risk. Intraday, position delta and vega are found to be relatively constant. Position
vega has a significant drop at midday (increment 3) but has insignificant changes and small
levels throughout most of the trading day. Gamma has significant changes between increments 1
and 2 and then again at the end of the trading day between increment’s 4 and 5, which likely
results from higher volumes at the beginning and end of the trading day. These results lend
support to the hypothesis that market makers in options markets work to maintain their exposure
to both price and volatility risk, and are primarily exposed to the effects of rebalancing risk.
Analysis of the relationship between the position risk parameters and profits shows a significant
and positive relationship between profitability and position gamma risk exposure.
When comparisons are made between large and small traders it is found that large traders
utilize the underlying futures market to hedge price risk, but only at longer time horizons. One

28
explanation for this is that the underlying futures market is used by option market makers
wanting to dispel their inventory holding risk that cannot be eliminated in the option market;
indicating a preference for managing risk using options. The exposure of large traders to
rebalancing and volatility risk is significantly higher than that of smaller traders, as larger traders
inventories are more cumbersome to manage throughout the trading day.
This article provides an in-depth, descriptive analysis of how market makers in option
markets make their market and lays the foundation for a wealth of future research paths. Future
research directly stemming from this analysis should evaluate how changes in risk holdings
affect the prices that market makers maintain. Patterns in bid-ask spreads are well documented;
thus, the intraday changes in risk holdings and the movement of traders into and out of the
market may serve as additional measures to help explain their U-shaped patterns. Other issues
that deserve further examination include how option market makers are using the option market
to mitigate their exposure to price risk, the impact of a market event on the number and ability of
traders providing market-making services, as well as the extent to which interdealer trading
impacts risk levels and, ultimately, market prices. These are largely unaddressed areas in the
literature and warrant further investigation. This paper serves as the basis for a fruitful stream of
future research surrounding market making in option markets.

29
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32
Table 1: Summary Statistics for NYMEX Natural-Gas Options Trading
Table 1 displays summary statistics for the most active traders for all trade categories over the first three nearest contract months for
options. The level of analysis used to conduct the testing of whether member proprietary trader behavior is indicative of that of market
makers in futures options is meant to provide an indication of how an average trader conducting a certain type of trade behaves and
the characteristics of each type of trade. The total number of trades each day is determined through a frequency analysis that provides
a count of the number of trades every day by each trade group across the three nearest contract expirations. The daily average number
of trades is found by taking the average of the total number of daily trades obtained from the frequency analysis (the total number of
trades divided by the number of trader days). The daily average volume is found by first summing the total quantity of purchases
traded in a day (buy observations only) by an individual trader for a trade type and contract expiration. This provides the total sum of
quantity traded for each trader on every day for a trade type and contract expiration. This total is averaged over the total trader days by
trade category and contract expiration to obtain a daily average level of trading volume. The average trade size is found by evaluating
the average quantity traded for each trade category and expiration. The average time between trades is found by evaluating the average
time between each trade for each trade category and expiration.
Summary Statistics for NYMEX Natural-Gas Options
CTI
Daily average
number of trades
Total number
of trades
Daily average
volume
Total
volume
Average
trade size
Average time
between trades
Nearby contract
1 89 36,646 167 2,154,761 29.43 18.42
2 5 1,511 263 226,920 66.13 15.06
3 4 1,499 145 176,675 55.23 15.07
4 55 22,617 259 1,928,015 43.39 15.06
First deferred contract
1 47 19,179 121 1,232,891 32.13 15.93
2 4 864 324 189,577 95.27 12.42
3 2 501 133 63,144 60.52 17.31
4 33 33 225 1,281,987 48.52 15.92
Second deferred contract
1 26 10,789 99 691,003 31.23 12.76
2 3 470 272 99,440 95.26 14.74
3 2 266 154 43,036 80.16 15.37
4 20 8,010 193 837,020 53.95 14.01

33
Table 2: Distribution of Proprietary Trader Income
Panel A in Table 2 displays the distribution of income for active, proprietary trading. Daily average income for options (in dollars) for each proprietary trades
across the nearest three expirations is found by marking to market each trade over the course of a trader day, summing the income for each individual trader, and
averaging the income for each trader over all trader days by contract expiration. If the trade is a sell, the income is found by taking the difference between the
trade price and the settlement price and multiplying by the quantity. If the trade is a buy, the income is found by taking the difference between the settlement
price and the trade price and multiplying by the quantity. The quartiles of daily income are found from the total daily income levels for each trader. Thus, the
minimum corresponds to the lowest level of income made by an individual trader during the sample period for contract expiration. Panel B in Table 2 displays
the distribution of daily income where each day a proprietary trader’s income is calculated by marking to market all of their trades at daily settlement prices. An
average across all traders is taken to obtain a daily average income for each day in the sample. This table represents the distribution of the daily average incomes
across 413 days with the top row containing all trades and the next three incomes broken out by expiration.
Panel A: Income Distribution
Contract N Mean Minimum 25% Median 75% Maximum
All trades 15,573 $228 -$1,799,279 -$162 $60 $500 $1,779,416
Nearby 13,503 $245 -$422,450 -$375 $50 $800 $445,018
First Deferred 10,944 $267 -$5,396,627 -$150 $25 $470 $5,333,350
Second Deferred 7,760 $331 -$122,190 -$40 $0 $250 $697,990
Panel B: Daily Income Distribution
Contract N Mean Minimum 25% Median 75% Maximum
All trades 413 $224 -$8,842 -$175 $145 $585 $10,820
Nearby 413 $229 -$20,966 -$350 $188 $970 $12,717
First Deferred 413 $254 -$6,864 -$289 $113 $732 $16,068
Second Deferred 413 $331 -$12,777 -$195 $49 $444 $53,248

34
Table 3: Number of Traders
The table presents the daily average number of traders executing the various types of trades in options market across
our sample. A trader trades a CTI=1 trade when they own 10% or more in the trading account for which they are
trading. CTI=2 executed trades are for the traders clearing member account. CTI=3 trades are executing for other
floor traders who are present on the floor. A trader executes a CTI=4 trade when the principal behind the trade is a
non-member, or a customer. Traders may execute all 4 of the trade types for all contract maturities. There are on
average 51 traders executing trades of any type and any maturity per day.
CTI Average number of traders
Nearby contract
1 31
2 2
3 3
4 18
First deferred contract
1 25
2 2
3 2
4 14
Second deferred contract
1 17
2 1
3 1
4 10

35
Table 4: Interdealer Trading Options
The percentage of trades by customer type in the options market is determined through a frequency analysis of trade
combinations across the nearest three expiration contracts to examine the extent of interdealer trading in the options
market. Interdealer trades are identified when both the initiator of the trade and the opposite trader are both trading
for their personal accounts.
Trader Opposite trader Percentage of trades by customer type
Nearby Contract
Personal Personal 22.83%
Personal House 3.30%
Personal Other floor 3.96%
Personal Customer 64.79%
House House 0.05%
House Other floor 0.17%
House Customer 1.29%
Other floor Other floor 0.03%
Other floor Customer 0.61%
Customer Customer 2.97%
First Deferred Contract
House House 0.07%
Second Deferred Contract
House House 0.07%

36
Table 5: Delta Risk Analysis Merge Base of 60 Seconds
Table 5 provides evidence testing the hypothesis that option market makers maintain instantaneous delta neutral
positions. The trading day is partitioned into five increments. Using the last trade for both options and futures in a
time increment, an implied standard deviation is found for each time increment, which minimizes the sum of
squared errors between the options price estimated by the binomial option pricing model and the observed options
incremental settlement price. This implied standard deviation is then used to compute the delta for all option strikes
and types (puts and calls) in each increment. For each trader, the quantity of trade is summed over the increment and
multiplied by the estimated parameter values to compute the trader’s exposure to portfolio risk as measured by
position delta. The variable options and futures delta include futures trades placed within 60 seconds of the options
trade under the same account number. The absolute value of each trader’s position risk parameter for each trade is
taken and averaged over all traders trading in a given increment. The positions are marked to market each increment
by summing the quantity traded over a particular increment for a trader and using that level as the beginning
inventory level for the next increment.
Delta Risk Analysis: Merge Base of 60 Seconds
Nearby Contract
Increment
Options
Delta Options and Futures Delta Difference
t-
Value DF
p-
Value
1 13.80 15.57 -1.77 -6.69 9224 <.0001
2 18.31 19.99 -1.68 -5.67 11257 <.0001
3 21.83 23.81 -1.98 -5.73 12200 <.0001
4 23.72 26.21 -2.49 -6.72 12892 <.0001
5 26.11 29.32 -3.21 -7.81 13265 <.0001
Increment
Options
Delta Options and Futures Delta Difference
t-
Value DF
p-
Value
1 7.67 9.11 -1.43 -5.92 6598 <.0001
2 10.49 12.02 -1.53 -4.77 8595 <.0001
3 13.04 14.44 -1.40 -4.1 9584 <.0001
4 14.53 16.04 -1.52 -3.93 10333 <.0001
5 16.04 18.23 -2.19 -4.96 10787 <.0001

37
Table 6: Delta Risk Analysis with Alternative Merge Base Specifications
Table 6 explores alternate matching specifications of futures and options trades to explore option market markets
position delta risk management strategies. The trading day is partitioned into five increments. Using the last trade
for both options and futures in a time increment, an implied standard deviation is found for each time increment,
which minimizes the sum of squared errors between the options price estimated by the binomial option pricing
model and the observed options incremental settlement price. This implied standard deviation is then used to
compute the delta for all option strikes and types (puts and calls) in each increment. For each trader, the quantity of
trade is summed over the increment and multiplied by the estimated parameter values to compute the trader’s
exposure to portfolio risk as measured by position delta. The variable options and futures delta include futures
trades placed within either (1) 600 seconds (Panel A) or (2) increment (Panel B) of the executed options trade under
the same account number. The absolute value of each trader’s position risk parameter for each trade is taken and
averaged over all traders trading in a given increment. The positions are marked to market each increment by
summing the quantity traded over a particular increment for a trader and using that level as the beginning inventory
level for the next increment.
Panel A: Delta Risk Analysis: Merge Base of 600 Seconds
Nearby Contract
Increment Options Delta Options and Futures Delta Difference
t-
Value
DF
p-
Value
1 19.68 15.41 4.28 6.1 3738 <.0001
2 18.75 13.10 5.65 7.57 3069 <.0001
3 20.15 14.84 5.32 6.12 2545 <.0001
4 17.60 14.29 3.31 4.27 2435 <.0001
5 16.43 18.75 -2.32 -2.73 2216 0.0063
t-
Value
DF
p-
Value
1 11.99 13.48 -1.49 -2.42 2054 0.0157
2 13.54 14.59 -1.06 -1.22 1558 0.2232
3 13.32 14.72 -1.4 -1.62 1175 0.1061
4 13.70 15.71 -2.01 -2.31 1129 0.0208
5 17.16 20.63 -3.46 -2.02 1069 0.0435
Panel B: Delta Risk Analysis: Merge Base of Increment
Nearby Contract
t-
Value
DF
p-
Value
1 20.61 19.49 1.12 1.72 4517 0.0859
2 19.38 16.92 2.46 3.69 3732 0.0002
3 20.74 18.47 2.28 2.92 3125 0.0035
4 18.16 17.98 0.18 0.24 2981 0.8083
5 17 21.22 -4.22 -4.92 2548 <.0001

38
t-
Value
DF
p-
Value
1 12.1 16.19 -4.09 -6.99 2658 <.0001
2 13.17 16.45 -3.28 -4.28 2036 <.0001
3 13.08 16.21 -3.12 -3.95 1570 <.0001
4 14.18 18.35 -4.17 -5.41 1499 <.0001

39
Table 7: Delta Risk Analysis By Trader Size with a Merge Base of Increment
Table 7 explores differences between large and small traders with regards to the management of their position delta
risk. A large trader is defined as one whose absolute value of quantity of trade in a given increment is 30 contracts
or more, while a small trader is one who trades below this same threshold. The trading day is partitioned into five
increments. Using the last trade for both options and futures in a time increment, an implied standard deviation is
found for each time increment, which minimizes the sum of squared errors between the options price estimated by
the binomial option pricing model and the observed options incremental settlement price. This implied standard
deviation is then used to compute the delta for all option strikes and types (puts and calls) in each increment. For
each trader, the quantity of trade is summed over the increment and multiplied by the estimated parameter values to
compute the trader’s exposure to portfolio risk as measured by position delta. The variable options and futures delta
include futures trades placed within an increment of the executed options trade under the same account number. The
absolute value of each trader’s position risk parameter for each trade is taken and averaged over all traders trading in
a given increment. The positions are marked to market each increment by summing the quantity traded over a
particular increment for a trader and using that level as the beginning inventory level for the next increment.
Panel A: Large Traders with Merge Base of Increment
Nearby Contract
t-
Value
DF
p-
Value
1 84.13 54.84 29.28 9.46 782 <.0001
2 83.53 48.79 34.74 10.29 600 <.0001
3 91.93 55.92 36.01 10.48 510 <.0001
4 82.42 53.7 28.71 7.26 457 <.0001
5 89.61 68.87 20.73 4.68 336 <.0001
t-
Value
DF
p-
Value
1 71.48 58.57 12.91 3.07 256 0.0024
2 85.87 61.59 24.28 3.94 187 0.0001
3 78.26 56.82 21.44 3.85 155 0.0002
4 81.2 62.87 18.33 4.24 171 <.0001
5 100.97 68.89 32.08 3.86 146 0.0002
Panel B: Small Traders with Merge Base of Increment
Nearby Contract
t-
Value
DF
p-
Value
1 7.29 12.08 -4.79 -12.7 3734 <.0001
2 7.07 10.8 -3.74 -10.19 3131 <.0001
3 6.83 11.15 -4.31 -7.65 2614 <.0001
4 6.5 11.5 -4.99 -10.63 2523 <.0001
5 5.94 13.96 -8.02 -11.67 2211 <.0001

40
t-
Value
DF
p-
Value
1 5.74 11.65 -5.91 -13.09 2401 <.0001
2 5.78 11.86 -6.08 -11.59 1848 <.0001
3 5.9 11.73 -5.83 -9.96 1414 <.0001
4 5.5 12.58 -7.09 -11.3 1327 <.0001
5 5.59 14.64 -9.04 -7.74 1161 <.0001

41
Table 8: Intraday Gamma and Vega Risk Position Levels by Increment
Table 8 evaluates the option market maker’s intraday exposure to Position Gamma and Position Vega, or
rebalancing and volatility risk respectively. The trading day is partitioned into five increments. Using the last trade
for both options and futures in a time increment, an implied standard deviation is found for each time increment,
which minimizes the sum of squared errors between the options price estimated by the binomial option pricing
model and the observed options incremental settlement price. This implied standard deviation is then used to
compute the gamma and vega for all option strikes and types (puts and calls) in each increment. For each trader, the
quantity of trade is summed over the increment and multiplied by the estimated parameter values to compute the
trader’s exposure to portfolio risk as measured by position gamma and vega. The absolute value of each trader’s
position risk parameter for each trade is taken and averaged over all traders trading in a given increment. The
positions are marked to market each increment by summing the quantity traded over a particular increment for a
trader and using that level as the beginning inventory level for the next increment. Bolded values indicate a
significant difference from the previous increment’s value.
Panel A: All Position Gamma and Vega
Nearby Contract
Increment Gamma Vega
1 54.95 14.17
2 51.78 14.73
3 45.57 12.99
4 45.86 13.49
5 64.40 15.02
1 33.03 27.00
2 27.29 25.82
3 27.20 25.87
4 29.36 26.72
5 36.60 31.30
Panel B: Large Traders Position Vega and Gamma
Nearby Contract
1 157.35 37.53
2 150.82 41.90
3 126.75 39.77
4 130.96 42.64
5 242.15 54.60
1 155.33 114.53
2 121.01 124.70
3 103.55 112.92
4 116.89 105.74
5 161.43 139.49

42
Panel C: Small Traders Position Vega and Gamma
Nearby Contract
1 34.27 9.46
2 32.12 9.34
3 29.51 7.70
4 30.58 8.25
5 37.52 9.03
1 20.08 17.73
2 17.61 15.61
3 18.64 16.11
4 17.93 16.40
5 20.10 17.01

43
Table 9: Subsample Analysis of the Intraday Risk Parameter Position Levels Over Five Time Increments
Table 9 evaluates whether the option market maker’s intraday exposure to their portfolio of position risk holdings is influenced by their number of trades (Panel
A), trade size, or volume traded. The trading day is partitioned into five increments. Using the last trade for both options and futures in a time increment, an
implied standard deviation is found for each time increment, which minimizes the sum of squared errors between the options price estimated by the binomial
option pricing model and the observed options incremental settlement price. This implied standard deviation is then used to compute the delta, gamma, and vega
for all option strikes and types (puts and calls) in each increment. For each trader, the quantity of trade is summed over the increment and multiplied by the
estimated parameter values to compute the trader’s exposure to portfolio risk. The absolute value of each trader’s position risk parameter for each trade is taken
and averaged over all traders trading in a given increment. The positions are marked to market each increment by summing the quantity traded over a particular
increment for a trader and using that level as the beginning inventory level for the next increment.
Panel A: Quartiles Based on the Number of Trades
Variable Increment 1 Increment 2 Increment 3
1 2 3 4 1 2 3 4 1 2 3 4
Position Delta 2.22 2.84 17.38 19.94 5.28 3.58 25.30 33.29 4.23 4.58 28.48 34.86
Position Delta without Futures 2.19 2.92 15.40 18.18 5.10 3.42 19.16 23.83 4.26 3.85 20.85 23.91
Position Gamma 2.16 2.79 30.58 36.16 10.30 5.89 39.20 52.04 7.64 4.55 37.65 41.95
Position Vega 1.28 2.17 13.04 16.25 4.27 3.47 19.08 24.91 3.80 3.84 18.27 24.80
Increment 4 Increment 5
1 2 3 4 1 2 3 4
Position Delta 4.46 4.38 25.77 30.13 2.31 4.98 34.68 28.19
Position Delta without Futures 4.72 3.59 19.28 19.39 2.41 4.45 25.48 20.41
Position Gamma 9.12 6.13 44.80 49.12 4.53 9.51 48.49 53.27
Position Vega 5.62 2.91 18.75 21.04 2.60 3.71 16.64 23.89
Panel B: Quartiles Based on Trade Size
1 2 3 4 1 2 3 4 1 2 3 4
Position Delta 2.91 5.15 13.28 30.82 3.82 7.55 20.98 51.26 4.26 7.60 21.87 53.35
Position Gamma 4.29 4.58 22.55 58.43 7.97 9.12 32.01 79.84 6.21 7.62 23.26 69.88
Position Vega 2.47 2.97 10.72 24.96 3.42 6.28 15.47 37.53 3.47 5.15 13.57 37.67

44
1 2 3 4 1 2 3 4
Position Delta 4.22 6.83 18.27 45.21 3.03 6.75 17.09 47.25
Position Gamma 6.86 9.48 29.58 76.52 7.18 11.23 29.58 83.90
Position Vega 3.84 4.59 11.61 31.36 3.00 4.18 12.66 34.08
Panel C: Quartiles Based on Volume
1 2 3 4 1 2 3 4 1 2 3 4
Position Delta 1.30 3.47 7.74 27.70 1.60 4.80 11.39 46.69 2.23 6.23 11.01 48.86
Position Gamma 1.73 3.22 12.83 51.76 3.39 7.51 19.58 70.19 3.77 6.18 14.33 59.67
Position Vega 1.50 2.13 5.92 23.78 2.07 4.14 9.15 35.89 2.72 4.48 7.26 32.98
1 2 3 4 1 2 3 4
Position Delta 3.43 5.23 10.74 42.88 2.90 5.05 9.10 44.03
Position Gamma 4.03 7.73 19.13 70.06 10.54 9.90 19.92 73.72
Position Vega 2.32 3.86 7.33 32.93 3.42 3.55 7.05 32.89

45
Table 10: Percentage of Trades in Each Moneyness Category
Table 10 presents the percentage of trades in each category of option moneyness for traders who trade in all
categories, where moneyness is defined by a 3% range. In other words, for a range of 3%, an at-the-money (ATM)
option is one whose strike price is within 3% of the price of the futures settlement price, an out-of-the-money
(OTM) option is one whose strike price is above 3% of the futures settlement price, and an in-the-money (ITM)
option is one whose strike price is below 3% of the futures settlement price.
Category Percentage of trades
OTM 66.17%
ATM 18.87%
ITM 14.12%

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