This thesis consists of three chapters. The first chapter, co-authored with Marcelo Fernandes, is published at Econometric Reviews 29 (3), 2010. In this chapter, we introduce a test for independence between two time series, and a test for serial independence as a corollary. The idea behind the test is that the distance between the joint distribution and the product of the marginal distributions should not be too large if the two stochastic processes are independent. We define a family of entropy-based test statistics that measure such distance, and we develop asymptotic normality of these test statistics. We compare the size and the power of these tests to some competing tests both by a Monte Carlo experiment and by an empirical exercise. The tests work very well.

The second chapter, co-authored with Luiz Lima, won the award Best Third year Paper, given by the Department of Economics, New York University (NYU), in 2009. In this chapter, we introduce a test for strict stationarity based on the fluctuations of the conditional quantiles of the time series, and we show that this test has power not only against the alternative hypothesis of unconditional heteroskedasticity, but also against the alternative hypotheses of time-varying skewness or kurtosis. Again, both via a Monte Carlo experiment and via an empirical exercise, we show that this test performs very well when compared to other tests known in the literature.

The third chapter, co-authored with Robert Engle, is on the microstructure of the options market. We show that, besides the three main kinds of cost (order processing cost, inventory cost, and asymmetric information cost) that the stock market maker faces, the options market maker has hedging costs. The hedging costs can be further decomposed in the cost of setting up the hedge position (proportional to the percentage delta and to the bid and ask spread of the underlying stock), and the cost of rebalancing the hedge position (proportional to gamma and to the volatility of the underlying stock). We show that these hedging costs are an important component of the bid and ask spread in the options market.