Optimal Martingales and American Option Pricing

Pricing American options is an interesting research topic since there is no analytical solution to value these derivatives. Different numerical methods have been proposed in the literature with some, if not all, either limited to a specific payoff or not applicable to multidimensional cases. Applications of Monte Carlo methods to price American options is a relatively new area that started with Longstaff and Schwartz (2001). Since then, few variations of that methodology have been proposed. The general conclusion is that Monte Carlo estimators tend to underestimate the true option price. The present paper follows Glasserman and Yu (2004b) and proposes a novel Monte Carlo approach, based on designing "optimal martingales" to determine stopping times. We show that our martingale approach can also be used to compute the dual as described in Rogers (2002).

Bargaining and Conflict with Incomplete Information

This paper studies bargaining and conflict under incomplete information, provides an overview and a critical account of the literature on the topic and contributes with original research. We first revise models of mechanism design and sequential bargaining that take confrontation as final. Conflict and inefficiencies are to be expected in these models whenever parties have optimistic prospects on the outcome of the all-out conflict. After examining the causes and reasons for this optimism, we move to the analysis of the recent literature that considers the existence of limited confrontations that allow bargaining to resume. In the presence of private information, these limited conflicts convey information and thus become a bargaining instrument. The paper closes with a discussion on the related empirical literature, the challenges that it faces and some potential avenues for further research.