In rational, efficiently functioning and complete markets, returns on derivative and underlying securities should be perfectly contemporaneously correlated. Due to market imperfections, one of these markets may reflect information faster. The use of high-frequency data and the choice for a small unit time interval to measure these lead-lag relations comes at the cost of some or many missing observations, causing traditional estimators to either under- or overestimate covariances and correlations. We use a new estimator to estimate lead-lag relationships between the cash AEX index, options and futures. We find that futures returns lead both options and cash index returns by approximately 10 minutes. The relationship between options and the cash market is not completely unidirectional.

We empirically compare Libor and Swap Market Models for the pricing of interest rate derivatives, using panel data on prices of US caplets and swaptions. A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices. For both models we analyze how well they price caplets and swaptions that were not used for calibration. We show that the Libor Market Model in general leads to better prediction of derivative prices that were not used for calibration than the Swap Market Model. Also, we find that Market Models with a declining volatility function give much better pricing results than a specification with a constant volatility function. Finally, we find that models that arechosen to exactly match certain derivative prices are overfitted; more parsimonious models lead to better predictions for derivative prices that were not used for calibration.

Two important characteristics of current equity markets are the large number of competing trading venues with publicly displayed order books and the substantial fraction of dark trading, which takes place outside such visible order books. This article evaluates the impact on liquidity of dark trading and fragmentation in visible order books. Dark trading has a detrimental effect on liquidity. Visible fragmentation improves liquidity aggregated over all visible trading venues but lowers liquidity at the traditional market, meaning that the benefits of fragmentation are not enjoyed by investors who choose to send orders only to the traditional market.

We analyze the resiliency of a pure limit order market by investigating the limit order book (bid and ask prices, spreads, depth and duration), order flow and transaction prices in a window of best limit updates and transactions around aggressive orders (orders that move prices). We find strong persistence in the submission of aggressive orders. Aggressive orders take place when spreads and depths are relatively low, and they induce bid and ask prices to be persistently different after the shock. Depth and spread remain also higher than just before the order, but do return to their initial level within 20 best limit updates after the shock. Relative to the sample average, depths stay around their mean before and after aggressive orders, whereas spreads return to their mean after about twenty best limit updates. The initial price impact of the aggressive order is partly reversed in the subsequent transactions. However, the aggressive order produces a long-term effect as prices show a tendency to return slowly to the price of the aggressive order.