| Summary: | 碩士 === 國立中正大學 === 財務金融所 === 95 === Theoretical research suggests that in the absence of market friction and bias, transaction prices should be uniformly distributed across all possible pricing grids （Niederhoffer, 1965；De Grauwe and Decupere, 1992). However, empirical evidence refutes this uniform distribution by extensively documenting the clustering of transaction prices and quoted prices （Harris, 1991； Grossman et al., 1997).
We document trade price clustering in the futures markets. Most of the analyses in this study use tick-by-tick and daily trade data for Taiwan Stock Exchange Capitalization Weighted Stock Index Futures（TAIEX Futures) contract over the period from Jan 2nd , 2004 to Dec 30th, 2005. In this paper, we begin by documenting price clustering of TAIEX Futures. Next, we examine whether open prices and close prices make any difference to the degree of price clustering （testing the intraday patterns of price clustering). Finally, we regress the percentage of trades that occur at xxx0 and xxx5（proxy of price clustering) against several factors associated with price clustering.
The main findings of this thesis can be summarized as follows. First, the phenomenon of price clustering does exist in TAIFEX. About 32% trades of TAIEX Futures contracts cluster at 0 and 5 ending digit prices. Which is more than MSCI Taiwan stock index futures contracts, but less than S&P 500 futures contracts. Second, there is a slight increase in clustering for daily open prices and close prices of TAIEX Futures contracts. Third, we identified six factors associated with price clustering such as open interest, open price, close price, volatility, volume and maturity and found that open prices and close prices are near perfect positive correlated. Also the two series are I(1). We rank the open prices and close prices respectively and replace the original variables with the logarithm of the rank value to assure all the variables are I(0)（with no unit root). Fourth, according to our empirical result, price clustering is a positive function of volatility or volume and a negative function of open interest, rank of open prices or rank of close prices. We also find that there is a dramatic change in the degree of price clustering when a contract moves to maturity.
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