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.

Fear of model misspecifcation and the robustness premium

Robust decision making implies welfare costs or robustness premia when the approximating model is the true data generating process. To examine the importance of these premia at the aggregate level we employ a simple two-sector dynamic general equilibrium model with human capital and introduce an additional form of precautionary behavior. The latter arises from the robust decision maker s ability to reduce the effects of model misspecification through allocating time and existing human capital to this end. We find that the extent of the robustness premia critically depends on the productivity of time relative to that of human capital. When the relative efficiency of time is low, despite transitory welfare costs, there are gains from following robust policies in the long-run. In contrast, high relative productivity of time implies misallocation costs that remain even in the long-run. Finally, depending on the technology used to reduce model uncertainty, we fi nd that while increasing the fear of model misspecfi cation leads to a net increase in precautionary behavior, investment and output can fall.

Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities

Traditionally, it is assumed that the population size of cities in a country follows a Pareto distribution. This assumption is typically supported by nding evidence of Zipf's Law. Recent studies question this nding, highlighting that, while the Pareto distribution may t reasonably well when the data is truncated at the upper tail, i.e. for the largest cities of a country, the log-normal distribution may apply when all cities are considered. Moreover, conclusions may be sensitive to the choice of a particular truncation threshold, a yet overlooked issue in the literature. In this paper, then, we reassess the city size distribution in relation to its sensitivity to the choice of truncation point. In particular, we look at US Census data and apply a recursive-truncation approach to estimate Zipf's Law and a non-parametric alternative test where we consider each possible truncation point of the distribution of all cities. Results con rm the sensitivity of results to the truncation point. Moreover, repeating the analysis over simulated data con rms the di culty of distinguishing a Pareto tail from the tail of a log-normal and, in turn, identifying the city size distribution as a false or a weak Pareto law.

Rationalising ‘Irrational’ Support for Political Violence

This paper provides a rationale for group support for political violence when violence does not provide a material benefi t. A theory of fairness is adopted to demonstrate that although group violence may not be the equilibrium of a material game it may be a fairness equilibrium in a game containing psychological payoffs. For this to happen the material stakes must be perceived as low and psychological payoffs are expressive. Although the material stakes are actually high, members of each group may choose expressively to support the use of violence because the probability of being decisive is low. The paper also considers the possibility of peace emerging as a fairness equilibrium. This can only happen if each group perceives the other as making some sacrifi ce in choosing peace.

Domestic Violence and Football in Glasgow: Are Reference Points Relevant?

Much research suggests that sporting events can trigger domestic violence with recent evidence suggesting that pre-match expectations (which can be interpreted as reference points) play an especially important role in this relationship. In particular, unexpectedly disappointing results have been associated with large increases in domestic violence. This paper contributes to this literature using a new data set containing every domestic violence incident in Glasgow over a period of more than eight years. We find that Old Firm matches, where Glasgow rivals Celtic and Rangers play, are associated with large increases in domestic violence (regardless of the timing or the outcome of the match). Non-Old Firm matches tend to have little impact on domestic violence. Furthermore, we fi nd little evidence for the importance of reference points. Matches with disappointing outcomes, relative to pre-match expectations, are found to be associated with unusual increases in domestic violence only in a very limited set of matches.

Domestic Violence and Football in Glasgow: Are Reference Points Relevant?

Much research suggests that sporting events can trigger domestic violence with recent evidence suggesting that pre-match expectations (which can be interpreted as reference points) play an especially important role in this relationship. In particular, unexpectedly disappointing results have been associated with large increases in domestic violence. This paper contributes to this literature using a new data set containing every domestic violence incident in Glasgow over a period of more than eight years. We find that Old Firm matches, where Glasgow rivals Celtic and Rangers play, are associated with large increases in domestic violence (regardless of the timing or the outcome of the match). Non-Old Firm matches tend to have little impact on domestic violence. Furthermore, we find little evidence for the importance of reference points. Matches with disappointing outcomes, relative to pre-match expectations, are found to be associated with unusual increases in domestic violence only in a very limited set of matches.