Three essays in asset pricing theory

Since there is clearly much more uncertainty in the economy than what is spanned by existing securities, asset pricing with incomplete markets is a key issue in finance both from a theoretical and a practical perspective. In this dissertation, we consider three specific situations where some form of market incompleteness arises, and discuss a number of implications for contingent claim pricing and hedging.;In a first essay, we discuss the problem of pricing and hedging a random cash-flow received at a random date. Our main contribution is a detailed theoretical inspection of the market price for timing risk, a point that has been little examined in the literature. A related question is the market price for default risk. We address this latter question in both a static and a dynamic, continuous-time, equilibrium setups, and conclude that correlation between default risk and market risk is a key ingredient of the equilibrium price for default risk. Independence between these two risks is not, however, a sufficient condition for a trivial price for default risk.;In a second essay, we discuss the question of option replication in the presence of transaction costs. In this context, we show how to expand the set of all possible time-based strategies through the introduction of a multi-scale class of strategies, which consist in re-balancing different fractions of an option portfolio at different time frequencies. This method, based on time-scale diversification, is to dynamic replication what investment in diversified portfolios is to static portfolio selection.;In a third essay, we address the question of option hedging when the underlying asset is not available for dynamic trading, and some other asset is used as a substitute. We derive the optimal hedging and also provide a quantitative measure of the residual risk over the life of the option. This result allows us to conclude that correlation risk is more significant than other risk factors typically considered in the literature, e.g. the risk induced by a discrete versus continuous dynamic hedging strategy. In a second part of the essay, the analysis is extended to encompass the question of volatility risk hedging.