V. Empirical Results
V.1 Institutional Hypothesis
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V. Empirical Results
V.1 Institutional Hypothesis
9,10Table IV contains a summary of the regression results of (1) for each series options. For the underlying asset return, the coefficients on all series options are significantly negative except DIMC; the coefficients on all series options are positive while only on ATMP is significant. The explaining ability varies. Adjusted R2srange from 5% to more than 23%.
Several results of table IV are interesting. First, implied volatility of DOTMP is affected by neither individual investors, foreign institutions, nor domestic institutions, which differs from Bollen and Whaley (2004). Nevertheless, implied volatility of DOTMP is significantly affected by both net buying pressure of ATMP from individual investors and foreign institutions. This evidence demonstrate that price of DOTMP contains information, which is consistent with the results founded by Bollen and Whaley (2004).
9 Before we proceed to the empirical test, we first employ unit-root tests to make sure the variables in our empirical models are stationary. We adopt both Augmented Dickey-Fuller (ADF) test and Phillip-Perron (PP) test (to save space, details of the results are not reported in table). Results from both ADF test and PP test show that all variables contained in (1) are stationary.
10 We also calculate correlation coefficients of the variables in (1) to avoid multicollinearity (to save space, details of the results are not reported in tables). Highest one is 0.3511, NBP for moneyness 7 options from individual investors and market return; lowest one is -0.5324, NBP for moneyness 6 options from domestic institutions and NBP for moneyness 8 options from domestic institutions. The rest of other correlation coefficients between variables are close to zero. Thus, we believe that multicollinearity should not be a major concern in this empirical model.
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Summary of Regression Results of Change in Each Type Implied Volatility for TAIFEX Options Traded on the Taiwan Futures Exchange during the Period January 2002 through December 2007
∆𝜎𝑖,𝑡= 𝛽0+ 𝛽1𝑅𝑆𝑡+ 𝛽2𝑉𝑆𝑡+ 𝛽3∆𝜎𝑖,𝑡−1+ 𝛽4𝑁𝐵𝑃𝐼𝑖,𝑡+ 𝛽5𝑁𝐵𝑃𝐹𝑖,𝑡+ 𝛽6𝑁𝐵𝑃𝐷𝑖,𝑡+ 𝛽7𝑁𝐵𝑃2𝐼𝑖,𝑡+ 𝛽8𝑁𝐵𝑃2𝐹𝑖,𝑡+ 𝛽9𝑁𝐵𝑃2_𝐷𝑖,𝑡+ 𝜀𝑖,𝑡
We report the coefficients and corresponding t-value of (1) in this table. The regression specification underlying the results reported in this table is:
where ∆𝜎𝑖,𝑡 is the change in implied volatility of moneyness i option in time t; RSt is the underlying asset return in time t; VSt is the trading volume of underlying asset in time t;
NBP_Ii,t , NBP_Fi,t , NBP_Di,t are the NBP from individual investors, foreign institutions, and domestic institutions of moneyness i option in time t respectively; NBP2_Ii,t , NBP2_Fi,t, NBP2_Di,t are the NBP from individual investors, foreign institutions, and domestic institutions of ATMP in time t respectively. But if the dependent variable is the change in implied volatility of ATMP, NBP2 would then change into the NBP of ATMC. And the ∆𝜎𝑖,𝑡−1 is the lagged change in implied volatility of moneyness i option in time t.
𝛽0 𝑅𝑆𝑡 𝑉𝑆𝑡 ∆𝜎𝑖,𝑡−1 𝑁𝐵𝑃_𝐼𝑖,𝑡 𝑁𝐵𝑃_𝐹𝑖,𝑡 𝑁𝐵𝑃_𝐷𝑖,𝑡 𝑁𝐵𝑃2_𝐼𝑖,𝑡 𝑁𝐵𝑃2_𝐹𝑖,𝑡 𝑁𝐵𝑃2_𝐷𝑖,𝑡 adj-R2
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Secondly, price impact from foreign institutions and domestic institutions for call and put seem not asymmetric. Buying pressure from foreign institutions significantly impact implied volatility of OTMP, ATMP, and DITMP but does not impact any series of call options. Results of buying pressure from domestic institutions shows similar phenomenon. Domestic institutions significantly affect implied volatility of OTMP but do not affect any series of call options. Third, not the main concern in this study but still worth mentioned, the coefficients of lagged change in implied volatility are negatively significant on all series of options, which peovides a strong support to limits to arbitrage hypothesis and has similar results to Bollen and Whaley (2004).
The last one is that change in implied volatility could be affected by both individual investors and foreign institutions. Previous investigations suggest that institutional investors trade options to hedge their spot positions and thus lead the market supply/demand imbalance as well as volatility smile. However, our results demonstrate that change in implied volatility not only can be affected by institutional investors but also individual investors. Thus, we may infer that factors causing volatility smile/smirk proposed by existing papers could be imperfect due to following reasons. 1) Institutional investors indeed have price impact on options, but other factors besides hedging demand could also impact motives for institutional investors to trade options. 2) Individual investors have price impact on options as well; previous
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investigations do not provide explanations to demonstrate the reason for individual investors to trade options however. Under these backdrops, we build up our second hypothesis, hedging hypothesis, to examine the motives to trade options for each trader type.
Before proceeding to empirical results of next hypothesis, we present the numbers of call/put options contracts traded for hedging purpose as a percentage of total trading volume in a specific option series by each trader type in table V and table VI. The results in table V and table VI could somewhat provide support of our inference. In table V and VI, we report the numbers of contracts traded for hedging purpose as a percentage of trading volume of all series of options. We define call (put) options traded for hedging purpose as the call (put) traded by a particular trader account with open position of short selling (long) in TAIFEX in the same trading day.
As shown in table V and VI, numbers of contracts traded for hedging purpose of all series of options initiated by all types of investors count relatively low portion of overall market volume. Since trading volume initiated by domestic institutions in entire sample period of all series of options count less than 0.2% of corresponding market volume, the volume is too low to move the market; therefore, we consider foreign institutions only. For call options, volume initiated by foreign institutions count 0.51% to 2.30% over corresponding market volume; for put options, volume initiated
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Table V
Numbers of Call Option Contracts Traded for Hedging Purpose by Trader Type during the Period January 2002 through December 2007
In this table, type is the moneyness of call options; Quantity is the numbers of call options contracts traded for hedging purpose in the corresponding period in each panel;
%tage is the numbers of call options contracts traded for hedging purpose as a percentage of total market volume for a specific moneyness option. We define call options traded for hedging purpose as the call traded by a particular trader account with open position of short selling in TAIFEX in the same trading day.
Panel A: Year 2002
Trader Individual Investors Foreign Institutions Domestic Institutions
Type 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
Quantity 149 1393 4667 6208 526 n.a n.a 502 601 n.a n.a 2 680 563 n.a
%tage 0.91 1.64 1.66 1.69 0.57 n.a n.a 0.18 0.16 n.a n.a 0.00 0.24 0.15 n.a
Panel B: Year 2003
Quantity 2323 9727 51658 66591 5136 21 3957 65116 54973 1601 36 323 1479 1467 298
%tage 0.94 0.86 1.22 1.24 0.57 0.01 0.35 1.54 1.02 0.18 0.01 0.03 0.04 0.03 0.03
Panel C: Year 2004
Quantity 5020 40576 165611 201335 50441 5557 30959 118421 192471 52997 158 317 6025 6156 2354
%tage 1.09 1.81 2.18 2.01 1.61 1.21 1.38 1.56 1.92 1.69 0.03 0.01 0.08 0.06 0.07
Panel D: Year 2005
Quantity 22728 186164 403175 376905 71158 5361 29640 147797 217971 30556 883 1886 16514 15098 2617
%tage 1.82 2.90 2.76 2.44 1.36 0.43 0.46 1.01 1.41 0.58 0.07 0.03 0.11 0.10 0.05
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Quantity 1713 3827 21248 14094 1161 n.a 369 13596 2703 1340 n.a 36 316 1269 n.a
%tage 1.41 1.42 1.99 1.31 0.27 n.a 0.14 1.27 0.25 0.31 n.a 0.01 0.03 0.12 n.a
Panel F: Year 2007
Quantity 16794 83225 241181 365260 108966 4772 29610 259714 659916 218520 225 3450 13229 16219 9690
%tage 1.71 2.21 2.39 2.17 1.49 0.49 0.79 2.57 3.92 2.98 0.02 0.09 0.13 0.10 0.13
Panel G: Year 2002 - 2007
Quantity 48727 324912 887540 1030393 237388 15711 94535 605146 1128635 305014 1302 6014 38243 40772 14959
%tage 1.58 2.33 2.34 2.10 1.38 0.51 0.68 1.60 2.30 1.78 0.04 0.04 0.10 0.08 0.09
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Table VI
Numbers of Put Option Contracts Traded for Hedging Purpose by Trader Type during the Period January 2002 through December 2007
In this table, type is the moneyness of put options; Quantity is the numbers of put options contracts traded for hedging purpose in the corresponding period in each panel;
%tage is the numbers of put options contracts traded for hedging purpose as a percentage of total market volume for a specific moneyness option. We define put options traded for hedging purpose as the put traded by a particular trader account with open long position in TAIFEX in the same trading day.
Panel A: Year 2002
Trader Individual Investors Foreign Institutions Domestic Institutions
Type 6 7 8 9 10 6 7 8 9 10 6 7 8 9 10
Quantity 680 6542 3523 143 55 4458 6473 11100 n.a n.a 11 27 10 n.a n.a
%tage 0.80 2.06 1.92 0.26 0.46 5.25 2.04 6.05 n.a n.a 0.01 0.01 0.01 n.a n.a
Panel B: Year 2003
Quantity 13047 52240 34943 5805 438 5795 31009 7685 157 n.a 240 1613 1195 67 225
%tage 1.25 1.17 1.22 0.93 0.40 0.55 0.69 0.27 0.03 n.a 0.02 0.04 0.04 0.01 0.21
Panel C: Year 2004
Quantity 53179 156933 114423 22612 5548 46835 187339 94037 19089 4980 3379 8968 3314 270 150
%tage 1.60 2.01 2.58 1.80 1.65 1.41 2.40 2.12 1.52 1.48 0.10 0.12 0.07 0.02 0.04
Panel D: Year 2005
Quantity 112217 275535 160344 48413 14759 107550 254271 183432 19336 1309 6953 19388 10639 2048 529
%tage 2.10 2.01 1.88 2.02 1.97 2.02 1.85 2.16 0.81 0.18 0.13 0.14 0.13 0.09 0.07
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Quantity 3881 5301 13061 4382 731 18438 84692 9241 1170 n.a 36 292 110 116 n.a
%tage 1.00 0.92 1.84 2.33 1.56 4.76 14.64 1.30 0.62 n.a 0.01 0.05 0.02 0.06 n.a
Panel F: Year 2007
Quantity 196028 307899 160376 36111 8769 363688 855292 227034 26084 8192 15468 33938 16508 1379 98
%tage 1.93 2.24 2.58 1.98 1.40 3.58 6.21 3.66 1.43 1.31 0.15 0.25 0.27 0.08 0.02
Panel G: Year 2002 - 2007
Quantity 379032 804450 486670 117466 30300 546764 1419076 532529 65836 14481 26087 64226 31776 3880 1002
%tage 1.87 1.98 2.13 1.85 1.61 2.69 3.49 2.33 1.04 0.77 0.13 0.16 0.14 0.06 0.05
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by foreign institutions count 0.77% to 3.49% over corresponding market volume.
2.30% and 3.49% may not be high enough to move the market price; thus that options volatility smile/smirk is led by hedging demand of institutional investors seems imperfect, and we therefore can infer that some other motives besides hedging demand are concerned by investors while trading options.