Volatility and trading frequency in financial markets: modeling and inference.

Summary This thesis is composed of three independent chapters stemming from a common problem: to build econometric specifications of the dynamics of financial markets, integrating a structural modeling of informational aspects. The first chapter is devoted to the frequency of transactions on financial markets in the presence of asymmetric information. We consider a Kyle (1985) model, but where liquidity shocks do not always occur. We characterize the set of perfect Bayesian equilibria. In particular, we show that the insider does not systematically intervene in the market, which affects the trading frequencies. We then extend this analysis to the case where volumes are heterogeneous. The second chapter focuses on the temporal aggregation of volatility. We propose a class of models of conditional variance that includes most of the models existing in the literature where the variance is linear (Garch, linear factors). We show that this class is robust to temporal and individual aggregation and marginalization. We also show the superiority and relevance of this class compared to the so-called "weak arch" class in terms of financial and statistical interpretations. We establish the direct link between our class and the class of continuous time processes called "stochastic volatility". Finally, the last chapter is devoted to the estimation of models defined by their conditional mean and variance, in particular those of the arch type. We consider a large class of m-estimators and we show the optimal estimator, which depends crucially on the conditional skewness and kurtosis coefficients. We show that it is more efficient than the pmv estimator and that it is equivalent to the optimal gmm estimator. A Monte Carlo study confirms these results.