A Nonstandard Approach to Option Pricing

Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model.     

A New Test of Price Dispersion

In recent years considerable attention has been devoted to differences across countries in the institutional environments in which corporations operate, and the consequences of these institutional differences for corporate performance. In this paper we test for the presence of differences in corporate performance across 38 countries, and in particular whether these differences are related to the types of legal systems existing in each country. To measure corporate performance we estimate returns on investment relative to company costs of capital in each country. We find significant differences in the investment performance of corporations across our sample of countries. Companies in countries with English-origin, common law legal systems perform significantly better on average than do those in civil law systems.     

Integration for development — Hopes and problems

The following article deals with the conditions under which regional associations in the Third World can improve the economic situation of the developing countries and the question how suitable they are for this purpose.     

Search for relevant sets of variables in a high-dimensional setup keeping the familywise error rate

Two multiple procedures for the detection of relevant sets of variables in a high-dimensional problem are suggested. Multivariate tests for significance are combined with the search for interpretable multivariate structures. Thus, groups of highly correlated variables are investigated. The emphasis lies on managing the huge number of possible subsets, for example, in gene expression analysis. The first procedure is based on parametric spherical tests and an order relation of the subsets. The second procedure is a non-parametric method utilizing Westfall–Young principles.     

Regulation and efficiency in European insurance markets

With a series of directives completed in 1994 the European Commission tried to open and harmonize national European insurance markets. This has led to considerable deregulation in several countries. This paper surveys pre-1994 regulation in Germany and the UK and the Commission's policy. It argues that it is unlikely that the policy will have a significant impact on direct international competition between European insurance markets, until there is standardization of insurance law. However, the tightly regulated markets will become more like the loosely regulated UK market. The paper evaluates this outcome and concludes that the European Commission's policy may thereby have improved the welfare of insurance buyers in the previously highly regulated countries such as Germany. The paper also uses efficiency-frontier estimation to compare the dispersion of firm efficiencies in the German and British life insurance market. The results support the hypothesis that tighter solvency regulation allows the survival of a larger proportion of higher-cost firms.     

Are House Prices Responsible for Unemployment Persistence?

The paper analyses the ambiguous role of house prices and housing investment for unemployment dynamics. Whereas traditional models see an increase in house prices as a dynamic multiplier that contributes positively to business cycle swings, the paper considers additional transmission mechanisms via the competitiveness channel (wages) and productivity. As house prices rise, wages tend to follow in order to make up for the loss in real disposable income, which limits employment creation. In addition, with rising house prices, the relative size of the construction sector – a low-productivity industry – tends to increase, lowering aggregate productivity growth, further dampening competitiveness. The paper estimates a stylised dynamic general equilibrium model with unemployment flows. Introducing different transmission mechanisms through which the housing market influences labour and macroeconomic dynamics, the size and direction of the housing market channel is being analysed. The estimation results show that housing shocks can have long-lasting negative effects on employment even though a housing boom can generate a short-lived stimulus on growth and employment. The paper also offers some policy advice simulating housing shocks under different types of structural reforms and macro-prudential regulation.