Electronic copy available at: http://ssrn.com/abstract=2587282 1 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.
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Electronic copy available at: http://ssrn.com/abstract=2587282
1
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.
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
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
Personal Personal 17.82%
Personal House 3.42%
Personal Other floor 2.29%
Personal Customer 71.30%
House House 0.07%
House Other floor 0.09%
House Customer 1.41%
Other floor Other floor 0.02%
Other floor Customer 0.53%
Customer Customer 3.05%
Second Deferred Contract
Personal Personal 16.33%
Personal House 2.98%
Personal Other floor 1.99%
Personal Customer 72.82%
House House 0.07%
House Other floor 0.10%
House Customer 1.58%
Other floor Other floor 0.02%
Other floor Customer 0.60%
Customer Customer 3.51%
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
First Deferred Contract
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
First Deferred Contract
Increment Options Delta Options and Futures Delta Difference 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
Increment Options Delta Options and Futures Delta Difference 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
First Deferred Contract
Increment Options Delta Options and Futures Delta Difference 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
Increment Options Delta Options and Futures Delta Difference 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
First Deferred Contract
Increment Options Delta Options and Futures Delta Difference 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
Increment Options Delta Options and Futures Delta Difference 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
First Deferred Contract
Increment Options Delta Options and Futures Delta Difference 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
First Deferred Contract
Increment Gamma Vega
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
Increment Gamma Vega
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
First Deferred Contract
Increment Gamma Vega
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
Increment Gamma Vega
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
First Deferred Contract
Increment Gamma Vega
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.