Valuing American Derivatives by Least Squares Methods

Least Squares estimators are notoriously known to generate sub-optimal exercise decisions when determining the optimal stopping time. The consequence is that the price of the option is underestimated. We show how variance reduction methods can be implemented to obtain more accurate option prices. We also extend the Longsta¤ and Schwartz (2001) method to price American options under stochastic volatility. These are two important contributions that are particularly relevant for practitioners. Finally, we extend the Glasserman and Yu (2004b) methodology to price Asian options and basket options.

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).

The Fair Trade movement: an economic perspective

Fair Trade (FT) products such as coffee and textiles are becoming increasingly popular with altruistic consumers all over the world. This paper seeks to understand the economic effects of this grassroots movement which directly links ethically-minded consumers in industrialised countries with marginalised producers in developing economies. We extend the Ricardian trade model and introduce a FT sector in developing South that offers a fair wage – the FT premium. There are indeed positive welfare effects from FT but those come at the expense of rising inequalities within South which are in turn a rational by-product of FT. The degree of inequalities depends on the specifics of the cooperative structures in the FT sector. Given the rigidities and inequalities FT introduces and rests upon, this form of alternative trade appears to be only sustainable as niche movement.