4.1 Data description and matching procedure
The TAIFEX introduced the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) futures and European –style options contracts at July 1, 1998 and December 24, 2001, respectively. Delivery months for the futures and options contracts are spot month, the next two calendar months followed by two additional months from the March quarterly Cycle (March, June, September, and December), and the contract multipliers for the futures and options contracts are NT$ 200 and NT$ 50 per index point, respectively. The difference in the multiplier values implies that every four pairs of TAIFEX options can be hedged by one future contract.
However, despite the difference in multiplier values, the parity condition for the TAIEX contracts is identical to Equation (1). To reduce the impact of illiquidity trading on the test results, we analyze only the spot month contract. For the spot month transaction, there were 204,239 contracts, 2,870,856 contracts, and 2,800,920 contracts within one-minute basis for TX and TXO calls and TXO puts, respectively.
Time-stamped, intraday bid-and-ask quotes and transaction price records were obtain from the Taiwan Economic Journal (TEJ) for the period January 2, 2002 to August 31, 2004. The data were extracted from CD-ROMs containing the tick data.
The source files are checked whether there are typographical problems to avoid large pricing errors. The one-month time deposit of the PSS (postal savings system) also retrieved from TEJ is used as the risk-free interest rate.
This thesis refers to data-matching methods of Fung and Mok (2001). For bid/ask quotes, we have two steps. First, we match every bid quote of call with the ask quote of the put of the same exercise price and maturity, and then match the options pair with the ask price of the futures contract, restricting the maximum time difference of the trio to be within a one-minute interval. Second, we match every bid quote of call with the ask quote of the put of the same exercise price and maturity, and then match the options pair with the ask price of the futures contract, restricting the maximum time difference of the trio to be within a one-minute interval. Similarly, the matching procedure for the traded options prices and for the futures is the same. To lighten the nonsynchronous price problem, we match the options and futures prices
within one-minute time intervals. And we discard quotes and prices that are mismatched in time by more than one minute. Using the 1-min matching procedure and the filtering criteria, we obtain 490,033 and 2,314,900 matched trios for transaction price and bid/ask quotes.
4.2 Trading costs of the hold-to-expiration strategy
The Taiwan Futures Exchange charges member firms (market marker) various trading fees per contract & per trade. The exchange fees include one one-way trading fee per trade for the futures or option contract, a settlement fee for a futures position that is not closed out before expiration, and an exercise fee on each expired in-the-money option. No charge is imposed on expired out-of-the-money option.
The total exchange charges against members per arbitrage trade for the buy-and-hold strategy include one trading fee and one settlement fee for the futures contract, two one-way trading fees, and one exercise fee for the options portfolio. In this study, member arbitrageurs are charged only for trading and settlement tax. The trading tax rate for futures and options are 0.025% and 0.125%, respectively. The settlement tax rates are both 0.025%. Thus, the trading costs for member arbitrageurs are (futures price * 0.025% + settlement price * 0.025%) + 4*(call price * 0.125% + put price * 0.125% + settlement price * 0.025% * 0.25). Because the settlement cost equals settlement price times settlement tax and times multiplier, 0.25 is multiplied to settlement cost of option. The average trading costs for member arbitrageur are 6.18 index points for the sample period.
Non-members must pay trading commissions and also compensate the member firms for the exchange charges. For non-members, each arbitrage trade with the hold-to-expiration strategy involves one round-trip commission for the futures position and three way commissions for the options portfolio. The additional one-way commission for the in-the-money option, but no commission is charged on the expired out-of-the-money option. The one way commission for futures and options are estimated as 1.5 and 0.5 index points, respectively. Thus, the trading costs for non-member arbitrageurs are (futures price * 0.025% + settlement price * 0.025%) + 2*1.5 + 4*(call price * 0.125% + put price * 0.125% + settlement price * 0.025% * 0.25) +4*(0.5*3). The average trading costs for nonmember arbitrageur are 15.38
index points for the sample period.
When there is opportunity for unwinding, the trading costs for member arbitrageurs are (future price * 0.025% - settlement price * 0.025%) + 4*(call price * 0.125% + put price * 0.125% - settlement price * 0.025% * 0.25). Because the settlement costs have been considered at the initial trade, we save the settlement costs.
The average unwinding trading costs for member arbitrageur are 0.32 index points for the sample period. For non-member arbitrageurs, the unwinding trading costs are (futures price * 0.025% - settlement price * 0.025%) + 4*(call price * 0.125% + put price * 0.125% - settlement price * 0.025% * 0.25) +4*(0.5). As described at section 3.2.2, the commissions for futures have been considered round trip fees at the initial.
The average unwinding trading costs for nonmember arbitrageur are 2.48 index points for the sample period.
The margin deposit per arbitrage portfolio is estimated to be between 630 and 835 index points. The initial margin for options and futures are shown at table 1.
Table 1 The initial margin for futures and options
Date 2001/12/20~Since a put-call-futures arbitrage portfolio comprises of one futures position, one long and one short position in the options, we use table above to calculate total initial margin per arbitrage portfolio. The average interest cost for the margin deposit is estimated as 0.276 index points.
The options are divided into five levels of moneyness5—from -2 to +2, where Level =0 indicates the at-the-money options. Level = -1 donates near out-of-the-money options; and Level = 1 denotes near in-the-money. Level = 2 and Level = -2 denotes deep in-the-money and far out-of-the-money, respectively.
The percentage spread cost per transaction in the contracts is calculated
5
The fraction F/X is used to define moneyness because the asset that is hedged by the options contracts is the futures contract. At-the-money is defined as 0.95≦F/X≦1.05, near-the-money is defined as 0.85
≦F/X<0.95 and 1.05<F/X≦1.15, and far-from-the-money is defined as F/X<0.85 and 1.15<F/X.
according to the following formula (see ap Gwilymm, Buckle & Thomas, 1997;
For the options contract, we sort the contracts for any particular day into two different maturities: less than 30 days and greater than 30 days. For each maturity series, the contracts are further sorted according to the moneyness of the contract as mentioned above. Hence, we obtain ten different average percentage spreads for both the call and the put on each trading day. The one-way spread cost is equal to the price multiplied by the average percentage spread for the contract that belongs to the particular category. For futures contract, they are classified into two different categories as with the different maturities of option quotes. The one-way spread cost is equal to the futures price multiplied
−
=
Ask
spread Percentage
by the average percentage spread for the aturity subgroup for that particular day.
. Level = 2 and Level = -2 denotes deep in-the-money and far out-of-the-money, s ectively.
m
Table 2 Spread costs for call options and put options, January 2002 – August 2004
The options are divided to five levels of moneyness—from -2 to +2, where Level =0 indicates the at-the-money options. Level = -1 donates near out-of-the-money options; and Level = 1 denotes near
-the-money The statistical descriptions of spread cost are in in
**Indicate statistical significance at the 0.01 level
dex points.
tistical significance at the 0.05 level
*Indicate sta
Table 2 presents the spread cost for call options and put options for the matched
trios. Most of the trios occur at the moneyness of at-the-money. The spread cost is higher when the call and put options are deep in-the-money than if they are far out-of-the-money. The average spread cost of futures is estimated as 0.9 index points
r the sample period.
4.3 Empirical methodology for three-equation model
The specific e calculated as below:
fo
variables in three-equation model ar
*
0
F
F
− , whereF is defined in equation (
0*Bias
t = 1).AL equals the average of implied volatility of matched call and put options.
erially correlated and heteroskedastic error terms of our simultaneous equations model.
pread equals best ask price minus best bid price.
tS
t equals the quantity of best bid price plus the quantity of best ask price.
Depth V
tTo mitigate the econometric problems, all variables in Equation (15) through (17) were transformed into log form. This enabled us to stabilize the variance of the error terms and approximate error terms toward a symmetric distribution. In addition, to avoid any spurious relationship among the variables because of the presence of a unit root in the time series, we applied the augmented Dickey-Fuller test (ADF) to test for differenced stationary. Results from ADF tests indicate that only ln(