Capítulo III: Metodología
3. Implementación
While liquidity of stock markets has been at the focus of a large body of literature, options markets have not received as much attention. Only recently researchers have started to investigate this issue in more detail. This paper adds to this strand of the literature by analyzing the relation between daily option liquidity on the one hand and stock market activity on the other. We study a sample of German firms included in the DAX index and with stock options listed on the derivatives exchange EUREX.
Since the concept of liquidity is very broad, we explicitly differentiate be-tween transaction-based liquidity measures (volumes and trading frequency) and order-based liquidity measures (spreads and depth). The empirical analy-sis is performed separately for four groups of firms, with the categories formed according to option market transaction-based liquidity. For each group we then perform a panel regression where we relate both option transaction- and order-based liquidity measures to variables describing stock returns, volatility, stock volume, and two sets of dummies for the days of the week and for the individual firms in the given group.
Due to the fact that option trading could either be a substitute for or com-plementary to stock trading, the direction of the impact of stock volume has to be determined empirically. For our sample we find that stock trading vol-ume generally has a significantly positive impact on both option volvol-ume and trading frequency. This supports the hypothesis that option trading is comple-mentary to stock trading, for example for the purpose of risk management. On the other hand, volatility measured as a historical 20-day standard deviation of the market return does not seem to be an important explanatory factor for transaction-based option liquidity. However, short-term uncertainty, as mea-sured by the contemporaneous and the lagged positive and negative parts of the respective stock return, is a strong determinant of option liquidity.
As an innovation to the literature, we separately analyze liquidity for calls and puts as well as for buyer and seller initiated trades. The purpose of this ex-ercise is to detect potential asymmetries between the different types of options and the different types of trades, which would not show up in an aggregate analysis. Indeed, this more detailed investigation produces a number of inter-esting new results. For example, higher short-term uncertainty generally in-creases option transaction-based liquidity, where call liquidity is mainly driven by positive and put liquidity by negative returns. However, when we split up the sample into buyer and seller initiated trades, we find that on days with pos-itive stock returns the number of call purchases increases, whereas on days with negative returns it decreases significantly. Call sales, instead, increase during both downward and upward stock movements. Similar effects can be observed for put options. Thus, besides exploiting the potential further increases in stock prices when market is moving up by buying calls and decreases in stock prices when market is moving down by buying puts, market participants tend to take advantage of increased option prices by simultaneously selling calls and puts, respectively.
The results of the corresponding regressions for option order-based liq-uidity measures, like the Euro option spread, the percentage option spread, or depth do not exhibit as much explanatory power as the models for transaction-based liquidity. Volatility tends to increase liquidity when measured by depths,
while it reduces liquidity when measured by Euro spreads. Negative stock re-turns generally decrease, positive rere-turns increase liquidity. Stock volume, if significant, has a negative impact on liquidity measured by Euro and per-centage spreads, but positive on liquidity measured by depth or transaction-based liquidity proxies. This might seem counterintuitive. However, according to information-based models, it might imply the increase in information asym-metry. Market makers increase spreads since they fear the eventual presence of informed traders in the stock market, simultaneously option volume increases due to increased need for hedging of stock positions.
A further empirical issue in this paper is whether the impact of the indepen-dent variables differs across the four option liquidity categories. Stock volume impact on transaction-based liquidity increases with option market trading activity, i.e. for the stocks with the most liquid option market one additional unit of stock trading volume generates the largest number of additional option trades. For order-based liquidity proxies we observe increasing return and vol-ume variable coefficients with decreasing liquidity level, with the exception of volatility. This generally lower variability of spread and depth for more heav-ily traded firms shows that these liquidity measures may be viewed as certain characteristic of these firms and not as some exogenously determined measure.
Although this paper has generated new insights into option liquidity, a number of issues still remain unsolved and pose challenging problems for fu-ture research. For example, market participants generally seem to prefer call trading to put trading, and currently the motives for this behavior are not at all clear. Furthermore, order-based liquidity in the options market is much harder to grasp than transaction-based liquidity, although in studies of stock markets both are usually well explained by certain exogenous factors. Such a weak exogenous impact is further surprising since there is much more infor-mation available on order- than on transaction-based liquidity. Especially the behaviour of spreads indicate the potential presence of asymmetric informa-tion in the market. Taken together these findings seem to indicate that opinforma-tion markets are much more ’autonomous’ than would be implied by the fact that options are derivative securities relative to the stock.
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Table1: Summarystatisticsfordifferentliquidityvariables SymbolFirmCallsPuts OTOVOEVSPSDOTOVOEVSPSDSV SIESiemens324.77,771.824,506.70.220.1590.2302.46,810.059,147.90.270.1058.55,780,941.1 DCXDaimlerChrysler238.17,004.111,820.20.140.16104.4197.56,112.225,791.80.160.1281.94,257,580.2 DBKDeutscheBank212.75,789.916,701.20.190.1580.8183.44,956.323,960.10.190.1068.93,656,119.8 VOWVolkswagen95.72,167.64,298.20.160.1877.955.21,375.44,054.40.170.1663.91,008,135.2 BAYBayer95.42,743.53,924.10.130.1949.976.71,976.16,374.50.130.1459.93,205,043.5 ALVAllianz90.71,458.213,901.20.680.1894.083.91,177.315,988.40.750.1240.43,788,074.7 IFXInfineon85.41,789.73,091.70.220.2467.476.51,534.64,834.60.230.1567.11,991,999.2 BASBASF82.92,288.93,353.60.100.17115.357.31,532.29,761.60.130.1269.42,474,207.1 CBKCommerzbank75.32,463.52,126.10.100.2088.559.11,825.04,207.80.120.1379.51,759,282.2 EOAEON52.01,499.02,454.80.140.1877.837.41,131.36,465.90.160.1473.72,491,248.2 LHALufthansa35.01,272.2980.90.100.2381.726.6838.21,218.40.120.1976.6486,039.5 EPCEpcos32.8530.11,480.40.480.2744.433.9549.33,411.20.490.1743.31,636,953.8 RWERWE32.0898.61,284.20.160.2179.025.1739.11,568.60.150.1973.8691,897.6 HVMHypoVereinsbank31.2800.61,327.90.160.1867.332.8821.92,499.10.180.1364.42,063,545.8 MUVM¨unchnerR¨uck28.7521.04,672.20.770.1841.629.9486.65,079.80.840.1736.61,521,874.7 BMWBMW27.6727.41,165.40.150.1666.021.2658.31,039.80.120.1773.71,913,105.9 PRSPreussag20.2452.5550.20.180.2764.813.6261.0651.60.210.1859.3549,690.9 SCHSchering18.3280.1537.50.210.2256.012.8190.9663.80.230.1749.3697,118.2 MEOMetro16.7513.7661.20.170.2265.210.6338.3509.80.180.1962.1758,189.3 LINLinde11.4209.6294.50.190.2554.57.9136.3336.90.190.1850.1467,484.2 MANMAN9.3199.8181.10.160.3055.88.0143.0282.00.190.1953.3318,722.9 KARKarstadt4.5155.9126.20.210.2544.53.785.3158.60.180.2641.4216,677.1 Thereportedvaluesaredailyaverages.OTrepresentsthenumberofoptiontransactions,OVisoptionvolumeinnumberofcontracts,OEVisoptionvolumeinEuro,Sistheoption spreadinEuro,PSisthespreadinpercentofthemidpointquote,Disdepth,andSVisstocktradingvolumeinshares.Thefirmsaresortedbythenumbercallofoptiontransactions.
Table 2:
Average cross-sectional correlations between dependent variables
OV OEV S P S D
Calls
OT 0.81 0.77 0.01 -0.06 0.13
OV 1 0.73 -0.04 0.06 0.30
OEV 1 0.07 -0.17 0.16
S 1 0.38 -0.08
P S 1 0.13
Puts
OT 0.86 0.52 0.06 0.02 0.15
OV 1 0.56 -0.01 0.02 0.33
OEV 1 0.22 -0.12 0.19
S 1 0.20 -0.05
P S 1 0.07
N represents the number of option transactions, OV is option volume in number of contracts, OEV is option volume in Euro, S is the option spread in Euro, P S is the spread in percent of the midpoint quote, and D is depth.
Table 3:
Determinants of number of option transactions (OT )
Trading activity group
Calls lowest low high highest
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday -0.02 0.82 0.22 0.01 0.16 0.05 0.29 0.02
Tuesday -0.01 0.95 0.06 0.41 -0.03 0.70 0.22 0.05
Wednesday -0.05 0.55 0.03 0.65 -0.05 0.51 -0.08 0.45
Thursday -0.02 0.84 0.10 0.18 -0.03 0.72 0.22 0.05
OT−1 0.18 0.00 0.20 0.00 0.25 0.00 0.15 0.00
SV 14.92 0.00 11.22 0.00 20.49 0.00 38.22 0.00
OT C 0.04 0.04 0.04 0.00 0.03 0.00 0.05 0.00
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday 0.06 0.55 0.09 0.23 0.05 0.55 0.28 0.02
Tuesday -0.03 0.72 0.01 0.91 -0.04 0.58 0.04 0.74
Wednesday 0.00 0.99 0.07 0.39 0.05 0.51 0.00 0.99
Thursday 0.08 0.38 0.14 0.07 0.05 0.56 0.12 0.32
OT−1 0.28 0.00 0.20 0.00 0.27 0.00 0.20 0.00
SV 10.14 0.00 9.08 0.00 14.28 0.00 32.87 0.00
OT C 0.06 0.00 0.05 0.00 0.08 0.00 0.08 0.00
Firm dummies are not reported. OT is measured in number of transactions. SV is measured in millions of shares, while OT C in contracts. All return variables as well as volatility entered the regressions as percentage numbers.
Table 4:
Determinants of signed number of option transactions (OT )- calls
Trading activity group
Buyer initiated lowest low high highest
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday -0.02 0.81 0.21 0.01 0.22 0.01 0.26 0.04
Tuesday 0.09 0.23 0.05 0.46 0.07 0.35 0.15 0.17
Wednesday -0.05 0.50 -0.03 0.67 -0.02 0.75 -0.12 0.27
Thursday -0.01 0.86 0.10 0.20 0.09 0.28 0.23 0.06
OT−1 0.22 0.00 0.23 0.00 0.28 0.00 0.21 0.00
SV 8.14 0.00 5.38 0.00 10.25 0.00 19.20 0.00
OT C 0.01 0.38 0.02 0.00 0.02 0.00 0.02 0.02
Seller initiated lowest low high highest
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday 0.01 0.91 0.12 0.14 0.05 0.54 0.25 0.04
Tuesday -0.05 0.56 -0.01 0.92 -0.09 0.25 0.20 0.08
Wednesday -0.01 0.88 0.05 0.47 -0.03 0.70 0.01 0.96
Thursday 0.02 0.85 -0.01 0.93 -0.10 0.23 0.17 0.16
OT−1 0.14 0.00 0.15 0.00 0.20 0.00 0.13 0.00
SV 5.13 0.00 5.07 0.00 8.70 0.00 18.26 0.00
OT C 0.02 0.02 0.01 0.00 0.01 0.01 0.03 0.00
Firm dummies are not reported. OT is measured in number of transactions on buy or sell side, respectively.
SV is measured in millions of shares, while OT C in contracts. All return variables as well as volatility entered the regressions as percentage numbers.
Table 5:
Determinants of signed number of option transactions (OT )- puts
Trading activity group
Buyer initiated lowest low high highest
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday 0.05 0.53 0.07 0.35 0.04 0.67 0.24 0.05
Tuesday 0.05 0.48 0.06 0.44 -0.06 0.45 0.01 0.95
Wednesday 0.05 0.47 0.00 0.98 -0.06 0.44 -0.06 0.59
Thursday 0.05 0.56 0.04 0.58 -0.04 0.63 -0.02 0.89
OT−1 0.21 0.00 0.21 0.00 0.28 0.00 0.21 0.00
SV 5.48 0.00 4.78 0.00 7.48 0.00 17.82 0.00
OT C 0.02 0.09 0.03 0.00 0.04 0.00 0.04 0.00
Seller initiated lowest low high highest
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday -0.01 0.92 0.07 0.41 0.03 0.71 0.20 0.11
Tuesday -0.11 0.18 -0.04 0.61 -0.07 0.40 -0.01 0.93
Wednesday -0.14 0.11 0.14 0.08 0.11 0.14 0.03 0.77
Thursday -0.02 0.83 0.20 0.01 0.11 0.17 0.18 0.13
OT−1 0.17 0.00 0.21 0.00 0.24 0.00 0.19 0.00
SV 4.49 0.00 4.25 0.00 6.95 0.00 14.39 0.00
OT C 0.04 0.00 0.02 0.00 0.03 0.00 0.04 0.00
Firm dummies are not reported. OT is measured in number of transactions on buy or sell side, respectively.
SV is measured in millions of shares, while OT C in contracts. All return variables as well as volatility entered the regressions as percentage numbers.
Table 6:
Determinants of percentage option spreads (P S)
Trading activity group
Calls lowest low high highest
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday 0.02 0.82 0.15 0.06 0.24 0.00 0.17 0.14
Tuesday 0.01 0.86 0.08 0.30 0.23 0.00 0.23 0.03
Wednesday -0.07 0.42 0.07 0.35 0.12 0.11 0.07 0.52
Thursday -0.10 0.26 -0.01 0.92 0.13 0.12 0.15 0.18
P S−1 0.13 0.00 0.22 0.00 0.27 0.00 0.25 0.00
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday -0.01 0.94 0.14 0.09 0.29 0.00 0.33 0.01
Tuesday 0.11 0.24 0.11 0.12 0.22 0.01 0.16 0.19
Wednesday 0.14 0.12 -0.03 0.65 0.11 0.17 0.05 0.67
Thursday -0.01 0.94 0.06 0.44 0.05 0.52 -0.05 0.67
P S−1 0.07 0.02 0.15 0.00 0.27 0.00 0.28 0.00
Firm dummies are not reported. P S is measured as spread relative to the midpoint quote and multiplied by
−1. SV is measured in millions of shares, while OT C in contracts. All return variables as well as volatility entered the regressions as percentage numbers.
Table 7:
Determinants of option depth (D)
Trading activity group
Calls lowest low high highest
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday -0.01 0.95 0.06 0.42 0.12 0.14 0.13 0.34
Tuesday -0.02 0.82 -0.01 0.96 -0.05 0.51 0.14 0.27
Wednesday -0.11 0.20 -0.02 0.82 0.04 0.65 -0.01 0.95
Thursday -0.11 0.23 0.04 0.60 0.03 0.77 -0.06 0.66
D−1 0.04 0.16 0.04 0.08 0.17 0.00 0.13 0.00
SV 13.33 0.01 3.52 0.01 1.76 0.34 -3.22 0.17
OT C 0.32 0.00 0.11 0.00 0.25 0.00 0.03 0.10
Coeff. p-value Coeff. p-value Coeff. p-value Coeff. p-value
Monday -0.07 0.44 -0.10 0.18 0.03 0.70 -0.16 0.18
Tuesday -0.07 0.44 -0.10 0.21 0.00 0.99 -0.18 0.11
Wednesday -0.15 0.09 -0.10 0.20 0.05 0.54 -0.27 0.01
Thursday -0.11 0.23 0.05 0.51 0.15 0.09 -0.18 0.13
D−1 0.15 0.00 0.06 0.01 0.07 0.01 0.14 0.00
Firm dummies are not reported. D is measured in number of contracts. SV is measured in millions of shares, while OT C in contracts. All return variables as well as volatility entered the regressions as percentage numbers.