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.     

Hymer and Uneven Development Revisited: Foreign Direct Investment and Regional Inequalities

Picking up on one of Hymer's key contributions, this paper examinesthe impact that inward foreign direct investment (FDI) intothe UK has on the patterns of development, both within and acrossregions. Using a panel of data for the manufacturing sector,the paper illustrates that even where one isolates the effecton the domestic sector alone, inward investment acts to increasethe demand for skilled, relative to unskilled labour, and alsogenerates the expected agglomeration effects in terms of thedemand for capital investment. The paper then goes on to drawcertain policy comparisons between these findings and the desiredaim of attracting FDI, notably to increase demand for labourin those regions suffering structural unemployment, and secondlyto reduce the disparities between regions.     

Cross-national differences in trade union membership in OECD countries

This article examines how trade union membership varies across 16 OECD countries in the 1980s. Higher density of membership is found to be associated with a higher degree of centralisation of wage bargaining, higher percentage of employees covered by collective bargaining, a larger public sector and a more leftist party of government.     

Commentary: Some Further Evidence on Discount Rate Selection in the Context of Goodwill Impairment Testing

In an earlier edition of this journal, we published evidence relating to the nature of discount rates chosen by a sample of large Australian‐listed firms in the context of their goodwill impairment testing ( Carlin and Finch 2009 ). We argued that our evidence suggested that the rigour of the International Financial Reporting Standards (IFRS) goodwill impairment testing process was being undermined by inappropriate choice of discount rates on the part of many firms. In a commentary published alongside our article, questions were raised as to the validity of our conclusions and the methodology we applied in our study ( Gallery 2009 ). Subsequently, Bradbury has also contributed to the debate, raising similar concerns to those voiced by Gallery ( Bradbury 2010 ). In this brief paper, we provide further and better particulars in relation to our original dataset in a bid to assist those who have taken an interest in this debate to further inform their view of the merits (or otherwise) of the case we made in our original article.     

A note on the Robust Trend and ARARMA methodologies used in the M3 Competition

This brief note describes two of the forecasting methods used in the M3 Competition, Robust Trend and ARARMA. The origins of these methods are very different. Robust Trend was introduced to model the special features of some telecommunications time series. It was subsequently found to be competitive with Holt’s linear model for the more varied set of time series used in the M1 Competition. The ARARMA methodology was proposed by Parzen as a general time series modelling procedure, and can be thought of as an alternative to the ARIMA methodology of Box and Jenkins. This method was used in the M1 Competition and achieved the lowest mean absolute percentage error for longer forecasting horizons. These methods will be described in more detail and some comments on their use in the M3 Competition conclude this note.     

Health effects on labour market exits and entries

This paper analyses the role of health on exits out of and entries into employment using data from the first twelve waves of the British Household Panel Survey (1991–2002). We use discrete-time duration models to estimate the effect of health on the hazard of becoming non-employed and on the hazard of becoming employed. The results show that general health, measured by a variable that captures health limitations and by a constructed latent health index, affects entries into and exits out of employment; the effects being higher for men than for women. The results are robust to different definitions of employment, and to the exclusion of older workers from the analysis.