Pricing Behavior in an Off-Hours Computerized Market
Price Clustering: Average Tick Frequencies
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- Panel A: SP 500 Futures Contract
- Panel B: Currency Futures Contracts
- Table VII Price Clustering: Stationary State Probabilities
- Table VIII Price Resolution: Intensity Effects in a Static Framework
- Panel B: DM Futures Contracts
- Panel C: Yen Futures Contracts
Price Clustering: Average Tick FrequenciesThis table contains average price category frequencies. Prices in the S&P 500 are written to two decimal places, e.g., 470.05. The five price clustering categories are denoted by xxx.05 (8 possible prices), xxx.10 (8 possible prices), xxx.25 (2 possible prices), xxx.50, and xxx.00. For example, the stationary probability reported in panel A for the xxx.05 category is 0.037, representing the probability of price being in any one of the eight possible subcategories divided by 8. Prices in the currency futures are written to four decimal places, e.g., 0.7651. The price categories are denoted by x.xxx1, x.xxx5, and x.xxx0, where the first category has 8 elements. Standard errors are not reported in the tables, but are zero rounded to three decimal places. Panel A: S&P 500 Futures Contract
Panel B: Currency Futures Contracts DM Yen SF
Table VII Price Clustering: Stationary State Probabilities This table contains estimates of stationary price category probabilities obtained from maximum likelihood estimation of the transition matrix of a first-order Markov chain. Prices in the S&P 500 are written to two decimal places, e.g., 470.05. The five price clustering categories are denoted by xxx.05 (8 possible prices), xxx.10 (8 possible prices), xxx.25 (2 possible prices), xxx.50, and xxx.00. For example, the stationary probability reported in panel A for the xxx.05 category is 0.037, representing the probability of price being in any one of the eight possible subcategories divided by 8. Prices in the currency futures are written to four decimal places, e.g., 0.7651. The price categories are denoted by x.xxx1, x.xxx5, and x.xxx0, where the first category has 8 elements. Standard errors are not reported in the tables, but are zero rounded to three decimal places. Panel A: S&P 500 Futures Contract
Panel B: Currency Futures Contracts DM Yen SF
Table VIII Price Resolution: Intensity Effects in a Static Framework This table contains estimates of the derivatives of the price category, or state, probabilities,  , with respect to the frequency of transactions per 15-minute period of trading, T at time t-1. The derivatives are evaluated at sample means of the data, and are based on parameter estimates of a static linear probability model, augmented by time of day effects.
Panel A: S&P 500 Futures Contract, 
a x 10-3 b x 10-5 Panel B: Currency Futures Contracts,
DM Yen SF
a x 10-3 b x 10-5 Table IX Market State and Intensity Effects in a Dynamic Model of Price Clustering This table contains estimates of the derivatives of the diagonal elements of a Markov chain transition matrix at time t, with respect to price category, or state, probabilities, , and the frequency of transactions per 15-minute period of trading, T, both at time t-1. The derivatives are evaluated at sample means of the data, and are based on parameter estimates of a time-varying interactive Markov chain model.
Panel A: S&P 500 Futures Contract Market State Market Intensity  
a x 10-2 Panel B: DM Futures Contracts Market State Market Intensity
a x 10-2 (Table IX, continued) Panel C: Yen Futures Contracts Market State Market Intensity
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