The first essay analyzes the market microstructure of the European Climate Exchange (ECX), the largest European Union Emissions Trading Scheme trading venue. Spreads range from 2 to 6 times the minimum tick increment on European Union Allowances (EUA) futures. Market impact estimates imply that an average trade will move the EUA market by 1.08 euro centimes. Information shares imply that approximately 90% of price discovery is taking place in the ECX futures market. We find imbalances in the order book help predict returns for up to three days. A simple trading strategy that enters the market long or short when the order imbalance is strong is profitable even after accounting for spreads and market impact. The second essay provides a case that the Thompson-Waller (TW) estimator would have downward bias, which has not been carefully discussed in the literature. Such case is that (i) the buy (sell) order tends to follow buy (sell) order and (ii) the price changes associated to such orders are small. The upward bias of the TW estimator would be canceled out by the downward bias, and in such case the estimator would perform better than the other absolute price change methods. The application to the EUA futures contract trading implies that its trading pattern and the price change provide the conditions that reduce the bias of the TW estimator. The Madhavan, Richardson and Roomans model is applied to examine the spread component of the market. A dominance of asymmetric information component in the spread is found. The fraction of the spread attributable to that component increases gradually during the observation period. The final essay examines price discovery of Japanese companies' Tokyo-New York cross-listed shares. Kalman filter is utilized to estimate partial price adjustment model. By employing Kalman filter, the present research can deal with missing values problem researchers has to confront in order to analyze non-overlapping markets such as Tokyo and New York. I find that events with larger magnitude of efficient price change occur during Tokyo opening hours. Dynamic measure shows that New York Stock Exchange is more efficient in price discovery.