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).

Improving Students’ Learning Aspirations Beyond Post-Primary Education: A First Account of Two Non-Formal Education Programmes in Middle-Income

Non-formal education programmes are active in a number of developing countries. These programmes offer vulnerable students an opportunity to pursue their education although they were excluded for various reasons from the formal education systems. This paper examines the impact of two programmes (one in Mauritius, and one in Thailand) on their participants’ aspirations towards learning. We develop a methodology to measure the perception of students regarding their learning experience. More than a third of them, for example, believe that there is no barrier to their education. Most acknowledge the role of their teachers in raising their aspirations towards their educational achievement. When compared to male students, female students seem to value more the role of their education.

Monetary policy strategies, financial institutions and financial markets in the Middle East and North Africa: an overview

Three polar types of monetary architecture are identified together with the institutional and market infrastructure required for each type and the kinds of monetary policy feasible in each case: a ‘basic’ architecture where there is little or no financial system as such but an elementary central bank which is able to fix the exchange rate, as a substitute for a proper monetary policy; a ‘modern’ monetary architecture with developed banks, financial markets and central bank where policy choices include types of inflation targeting; and an ‘intermediate’ monetary architecture where less market-based monetary policies involving less discretion are feasible. A range of data is used to locate the various MENA countries with respect to these polar types. Five countries (Iran, Libya, Sudan, Syria and Yemen) are identified as those with the least developed monetary architecture, while Bahrain and Jordan are identified as the group at the other end of the spectrum, reaching beyond the intermediate polar type in some dimensions but not others. The countries in between vary on different dimensions but all lie between basic and intermediate architectures. The key general findings are that the MENA countries are both less differentiated and less ‘developed’ than might have been expected. The paper ends by calling for research on the costs and benefits of different types of monetary architecture.