The primary sources of the data are Taiwan Futures Exchange, and Taiwan Economic Journal Plus Database (TEL+ Database). Taiwan Futures Exchange database contains historical trading data of all futures and options traded in Taiwan. TEJ+ database provides complete trading data of indices in Taiwan.We use daily traded data of TXO index options from Taiwan Futures Exchange’s website and the period is between Dec 2011 and Dec 2013 which is one year before and after weekly option listing. Besides, we also take daily data of Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), mainly traded prices, to calculate historical volatility. Finally, the interest rates are obtained from TEJ+ database using Interbank Overnight Call-Loan Rate. We know that short-term interest rates will affect the cost of carrying of spot positions. Futures and options play an important role in hedging.
As the cost of carrying in spot positions become higher, the hedging needs and speculative trading reduce simultaneously. As a result, futures and options trading volumes will decrease.
1. Data
Liquidity Measure (LIQ)
Since option data reveals a panel nature which makes the dollar bid-ask spread to be a liquidity measure. This paper uses the proportional bid-ask spread proposed by Chordia, Roll and Subrahmanyam(2000)(CRS hereafter) as our liquidity measure,noted 𝐿𝐿𝐿𝐿𝐿𝐿𝑡𝑡:
𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕 = ∑ 𝑽𝑽𝑽𝑽𝑳𝑳𝒊𝒊(𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒂𝒊𝒊−𝒃𝒃𝒊𝒊𝒃𝒃𝒊𝒊
𝒊𝒊+𝒃𝒃𝒊𝒊𝒃𝒃𝒊𝒊)/𝟐𝟐 𝒂𝒂𝒊𝒊=𝟏𝟏
∑𝒂𝒂𝒊𝒊=𝟏𝟏𝑽𝑽𝑽𝑽𝑳𝑳𝒊𝒊
where 𝑉𝑉𝑉𝑉𝐿𝐿𝑖𝑖 is the volume of option𝑖𝑖, 𝑎𝑎𝑎𝑎𝑎𝑎𝑖𝑖 is the responding best ask price in one
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day,𝑏𝑏𝑖𝑖𝑏𝑏𝑖𝑖 is the respondingbest bid price in one day.
Trade Volume (VOL)
Trade volume, denoted by VOL, is the daily total trade volume of the two nearest month index options in one day. We take only two months for the reason that we can mainly include most of the transactions.
Open Interest (OI)
Open interest, denoted by OI, is the total open interest of the two nearest month index options in one day.
Price Volatility (𝝈𝝈)
Price volatility, denoted by 𝝈𝝈, is calculated using high-minus-low pricesas a proxy of historical volatility (Martell and Wolf (1987)), which is the gap between the highest traded price and the lowest traded price of the underlying asset in one day.
Settlement Price (SP)
Settlement price, denoted by SP, is the weighted average of index options in one day. Weights are calculated using trading volumes of each index options with different exercise prices.
Interest Rate
We take Interbank Overnight Call-Loan Rate as the interest rate. These rates are provided by the Central Bank of Taiwan.
Dummy Variables
Weekly options were introduced on Nov., 2012. In order to examine the impacts of weekly options, we take two dummy variables, 𝐷𝐷1and 𝐷𝐷2, to indicate two events respectively.𝐷𝐷1equals 1 when weekly options are introduced, while 0 represents the absence of weekly options. 𝐷𝐷2equals 1 if the trading occurs before settlement but still in the same week, while 0 represents the trading do not occur on these days.
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2. The Simultaneous Equation Approach
As suggested by Bessembinder&Seguin (1993), volume shocks had impacts on price volatility, while liquidity also affects price volatility. Further, as mentioned above, the liquidity measure proposed by Chordia, Roll and Subrahmanyam(2000) includes traded volume. These three variables influence each other so that we followWang, Chung, and Yang’s (2007) simultaneous equation modeland make adjustments of the measurement of variables to examine the relationship between traded volume, liquidity, and price volatility. Moreover, as suggested byChordia, Roll and Subrahmanyam(2001), interest rates affect liquidity as well as trading activity. Open interest is also directly related to traded volume. Finally, as settlement system influences trade position (Kumar and Seppi (1992), Devriese andMitchell (2005)), we believe that liquidity of options is strongly influenced by its settlement prices.
The model is as follows:
𝐕𝐕𝐕𝐕𝐕𝐕𝒕𝒕 = 𝒂𝒂𝟎𝟎+ 𝒂𝒂𝟏𝟏𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕+ 𝒂𝒂𝟐𝟐𝝈𝝈𝒕𝒕+ 𝒂𝒂𝟑𝟑𝑳𝑳𝑰𝑰𝑰𝑰𝒕𝒕+ 𝒂𝒂𝟒𝟒𝑽𝑽𝑳𝑳𝒕𝒕−𝟏𝟏+ 𝒂𝒂𝟓𝟓𝑽𝑽𝑽𝑽𝑳𝑳𝒕𝒕−𝟏𝟏+ 𝒂𝒂𝟔𝟔𝑫𝑫𝒕𝒕+ 𝜺𝜺𝟏𝟏𝒕𝒕 𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕 = 𝒃𝒃𝟎𝟎+ 𝒃𝒃𝟏𝟏𝑽𝑽𝑽𝑽𝑳𝑳𝒕𝒕+ 𝒃𝒃𝟐𝟐𝝈𝝈𝒕𝒕 + 𝒃𝒃𝟑𝟑𝐒𝐒𝐒𝐒𝒕𝒕+ 𝒃𝒃𝟒𝟒𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕−𝟏𝟏+ 𝒃𝒃𝟓𝟓𝑫𝑫𝒕𝒕+ 𝜺𝜺𝟐𝟐𝒕𝒕
𝝈𝝈𝒕𝒕 = 𝒄𝒄𝟎𝟎+ 𝒄𝒄𝟏𝟏𝑽𝑽𝑽𝑽𝑳𝑳𝒕𝒕+ 𝒄𝒄𝟐𝟐𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕+ 𝒄𝒄𝟑𝟑𝐕𝐕𝐕𝐕𝐕𝐕𝒕𝒕−𝟏𝟏+ 𝒄𝒄𝟒𝟒𝝈𝝈𝒕𝒕−𝟏𝟏+ 𝒄𝒄𝟓𝟓𝑫𝑫𝒕𝒕+ 𝜺𝜺𝟑𝟑𝒕𝒕 (𝟏𝟏) where𝐕𝐕𝐕𝐕𝐕𝐕𝒕𝒕is the aggregate daily trading volume; 𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕 indicates the daily liquidity of monthly options;𝝈𝝈𝒕𝒕is the daily volatility, which is the difference between the highest and lowest transaction prices in one day. 𝑳𝑳𝑰𝑰𝑰𝑰𝒕𝒕is the three-month interest rate; 𝑽𝑽𝑳𝑳𝒕𝒕−𝟏𝟏is the open interest of t-1 period; 𝐒𝐒𝐒𝐒𝒕𝒕 is the settlement price for option contracts; 𝑫𝑫𝒕𝒕indicates whether short-term options are introduced.
Following the approach above, we evaluate another dummy variable,𝑫𝑫𝟐𝟐,to separate data into two periods: before the introduction of weekly options and that after. These two dummy variables are used in simultaneous equation approach again, and the model becomes
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𝐕𝐕𝐕𝐕𝐕𝐕𝒕𝒕= 𝒂𝒂𝟎𝟎+ 𝒂𝒂𝟏𝟏𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕+ 𝒂𝒂𝟐𝟐𝝈𝝈𝒕𝒕+ 𝒂𝒂𝟑𝟑𝑳𝑳𝑰𝑰𝑰𝑰𝒕𝒕+ 𝒂𝒂𝟒𝟒𝑽𝑽𝑳𝑳𝒕𝒕−𝟏𝟏+ 𝒂𝒂𝟓𝟓𝑽𝑽𝑽𝑽𝑳𝑳𝒕𝒕−𝟏𝟏+ 𝒂𝒂𝟔𝟔𝑫𝑫𝟏𝟏𝒕𝒕+ 𝒂𝒂𝟕𝟕𝑫𝑫𝟐𝟐𝒕𝒕+ 𝜺𝜺𝟏𝟏𝒕𝒕
𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕 = 𝒃𝒃𝟎𝟎+ 𝒃𝒃𝟏𝟏𝑽𝑽𝑽𝑽𝑳𝑳𝒕𝒕+ 𝒃𝒃𝟐𝟐𝝈𝝈𝒕𝒕+ 𝒃𝒃𝟑𝟑𝐒𝐒𝐒𝐒𝒕𝒕+ 𝒃𝒃𝟒𝟒𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕−𝟏𝟏+ 𝒃𝒃𝟓𝟓𝑫𝑫𝟏𝟏𝒕𝒕+ 𝒃𝒃𝟔𝟔𝑫𝑫𝟐𝟐𝒕𝒕+ 𝜺𝜺𝟐𝟐𝒕𝒕
𝝈𝝈𝒕𝒕 = 𝒄𝒄𝟎𝟎+ 𝒄𝒄𝟏𝟏𝑽𝑽𝑽𝑽𝑳𝑳𝒕𝒕+ 𝒄𝒄𝟐𝟐𝑳𝑳𝑳𝑳𝑳𝑳𝒕𝒕+ 𝒄𝒄𝟑𝟑𝐕𝐕𝐕𝐕𝐕𝐕𝒕𝒕−𝟏𝟏+ 𝒄𝒄𝟒𝟒𝝈𝝈𝒕𝒕−𝟏𝟏+ 𝒄𝒄𝟓𝟓𝑫𝑫𝟏𝟏𝒕𝒕+ 𝒄𝒄𝟔𝟔𝑫𝑫𝟐𝟐𝒕𝒕+ 𝜺𝜺𝟑𝟑𝒕𝒕 (𝟐𝟐) 𝑫𝑫𝟏𝟏indicates whether the data lies in the last week before every monthly settlement before the introduction of short-term options, while 𝑫𝑫𝟐𝟐 indicates whether weekly options were introduced or not.
Nevertheless, due to the fact that weekly options are launched only one year, our data period is one year before and after Nov., 2012, which is totally two years. We anticipate there exists significant difference in market liquidity,especially in the last week to settlement, before and after the introduction of weekly options.
Moneyness
Option market differs from futures market and stock market in the way that options can be three-fold classified into moneyness categories: in-the-money, at-the-money, and out-of-the-money. Moneyness affects the behavior of investors, especially near the settlement. We follow Chernov&Ghysels’s(2000) moneyness range to separate the dataset into three parts to examine whethermoneyness do any effects to the market.
CALL
⎩⎪
⎨
⎪⎧K
S < 0.93, 𝑖𝑖𝑖𝑖 − the − money 0.93 ≤K
S ≤ 1.07, 𝑎𝑎𝑡𝑡 − the − money K
S > 1.07, 𝑜𝑜𝑜𝑜𝑡𝑡 − of − the − money
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PUT
⎩⎪
⎨
⎪⎧K
S < 0.93, out − of − the − money 0.93 ≤K
S ≤ 1.07, at − the − money K
S > 1.07, in − the − money