Stochastic volatility models: arbitrage, equilibrium and statistical inference.

Summary This work consists of six independent chapters. The first chapter exploits the characterization of the set of admissible prices by the no-arbitrage principle to examine the bias on hedging by the classical model of Black and Sholes (1973). The second chapter generalizes a result of A Rochet and Bajeux (1992) and shows that any option, European or American, completes the market in the presence of a correlation between the asset price and its volatility. The third chapter presents recent developments in portfolio choice and consumption theory. The next chapter gives a necessary and sufficient condition on a given price system (or risk premium pair) to be consistent with an additive multi-agent intertemporal equilibrium model. These statistical inference problems are addressed in the last part of the thesis. The fifth chapter introduces a method for estimating the parameters of the volatility process of the e. The convergence of the proposed estimators is proved and their asymptotic distribution is characterized. The last chapter compares, by Monte Carlo methods, this estimation method to indirect inference.