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).

Native language, spoken language, translation and trade

We construct new series for common native language and common spoken language for 195 countries, which we use together with series for common official language and linguis-tic proximity in order to draw inferences about (1) the aggregate impact of all linguistic factors on bilateral trade, (2) whether the linguistic influences come from ethnicity and trust or ease of communication, and (3) in so far they come from ease of communication, to what extent trans-lation and interpreters play a role. The results show that the impact of linguistic factors, all together, is at least twice as great as the usual dummy variable for common language, resting on official language, would say. In addition, ease of communication is far more important than ethnicity and trust. Further, so far as ease of communication is at work, translation and inter-preters are extremely important. Finally, ethnicity and trust come into play largely because of immigrants and their influence is otherwise difficult to detect.

Native language, spoken language, translation and trade

We construct new series for common native language and common spoken language for 195 countries, which we use together with series for common official language and linguis-tic proximity in order to draw inferences about (1) the aggregate impact of all linguistic factors on bilateral trade, (2) whether the linguistic influences come from ethnicity and trust or ease of communication, and (3) in so far they come from ease of communication, to what extent trans-lation and interpreters play a role. The results show that the impact of linguistic factors, all together, is at least twice as great as the usual dummy variable for common language, resting on official language, would say. In addition, ease of communication is far more important than ethnicity and trust. Further, so far as ease of communication is at work, translation and inter-preters are extremely important. Finally, ethnicity and trust come into play largely because of immigrants and their influence is otherwise difficult to detect.