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).

Marx: From Hegel and Feuerbach to Adam Smith

This paper discusses the development of Marx’s thought over a period of something like fifteen months, between the spring of 1843 and the autumn of 1844. The focus of the paper is Marx’s first encounter with classical political economy as he found it in the Wealth of Nations. The outcome of this encounter was presented by Marx in his Economic and Philosophical Manuscripts of 1844. It is argued here that in the classical theory, with which he had hitherto been largely unfamiliar, Marx found all the elements he needed to synthesise the philosophical standpoint he had developed in the preceding months with political economy. The Manuscripts represent the first crucial stage in the development of this synthesis. This first encounter of Marx with classical political economy, and his first steps in the development of his synthesis, have received hardly any attention in the literature. The present paper seeks to fill this gap.

Marx: From Hegel and Feuerbach to Adam Smith

This paper discusses the development of Marx’s thought over a period of something like fifteen months, between the spring of 1843 and the autumn of 1844. The focus of the paper is Marx’s first encounter with classical political economy as he found it in the Wealth of Nations. The outcome of this encounter was presented by Marx in his Economic and Philosophical Manuscripts of 1844. It is argued here that in the classical theory, with which he had hitherto been largely unfamiliar, Marx found all the elements he needed to synthesise the philosophical standpoint he had developed in the preceding months with political economy. The Manuscripts represent the first crucial stage in the development of this synthesis. This first encounter of Marx with classical political economy, and his first steps in the development of his synthesis, have received hardly any attention in the literature. The present paper seeks to fill this gap.

Nearer to Sraffa than Marx: Adam Smith on Productive and Unproductive Labour

This paper supercedes an earlier attempt I made to pin down the meaning and significance of Adam Smith’s theory of productive and unproductive labour. (Strathclyde Discussion Papers in Economics, No.08-05) My conclusion then was that while Smith’s understanding of what was needed to achieve economic growth was sound, his discussion was marred by apparently conflicting definitions of productive labour. That (essentially conventional) interpretation does not, I now believe, do justice to Smith. Revision is therefore called for: hence the present paper.