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.     

The unpredicted rise of motorcycles: A cost benefit analysis

This article examines the consequences, for Paris, of the increase in two-wheel motor vehicle (2WMV) traffic (measured in vehicle/km). Our study reveals that, between 2000 and 2007, the subway's (Métro) share in total inner-Paris travel increased by 13.6%, the RER's share by 10.3% and the SNCF's share by 20.5%. These three means of transport account for 58% of daily travel. On the other hand, the bus share has decreased by 16% and that of cars by 23.7%. Private motor vehicles represent 37.3% of total travel. Looking at road traffic, where public transport (buses) and private motor transport compete for the use of limited road space, private motor vehicles account for 91.5% and public transport 8.5% of total travel.The 2WMV share in Paris traffic increased by 36% between 2000 and 2007, with 2WMVs now accounting for a share twice as large as that of buses. A survey has shown that 100 million additional passenger kilometres were made by 2WMV in 2007 compared to 2000. 53% of this increase comes from people shifting to 2WMV from public transport and 26.5% from private cars. The remaining 20% is attributable to the increased use of 2WMVs by those already owning such vehicles in 2000.Is the growth in the share of 2WMV traffic in Paris beneficial to the community? This shift in the means of transport generates time savings of €293 million and increases owners' vehicle usage costs by €49 million. The cost of accidents is increased by €49 million and the negative consequences in terms of pollution are estimated at €22.6 million. The welfare impact of the government revenue change is negative and equal to €4.7 million. In total, the gain for the community is therefore around €168 million. Accident costs are the key issue. The fact that there are on average 21 2WMV fatalities in Paris (average 2006–2007) for a means of transport accounting for 16% of passenger/km made every day in Paris offers a striking contrast to the 6 (average 2006–2007) fatalities concerning cyclists which account for a mere 0.1% of trips. The massive shift to 2WMV has taken place without any public policy support. Public policy could easily further improve the 2WMV cost-benefit balance by taking measures that would decrease the number of accidents.     

Produktinnovationen und Produktmodifikationen in der Versicherungswirtschaft: Rolle und Bedeutung nach der Deregulierung

One consequence of the deregulation of the insurance industry in 1994 is a considerably improved scope for insurance companies to design products. Therefore, the question should be raised if there is an observable effect on the insurer’s behaviour with regard to the development of new products. This paper embodies results of an empirical study that collected data of 650 products that were launched in the German insurance industry between 1996 and 2005 and that could be categorised as product innovations or as product modifications. On the basis of the study, it was possible for the first time to provide quantitative evidence that in the whole industry the amount of product innovations (in average 2,4 per year) as well as of product modifications (in average 63 per year) stayed on a modest level after the deregulation and that the evaluated impact of the deregulation on the development of new products is relatively small. This is also demonstrated by the fact that 27% of all German insurers developed only one new product in ten years. In addition, it became evident that there is no significant change in the extent of the (small) impact in the last ten years. Thus, the deregulation itself only sent limited impulses for renewing products in the German insurance industry. Apparently, the theoretical considerations are supported that while considering a high entrepreneurial risk and the absence of a monopoly rent at the same time the Value Based Management imposes a high hurdle for the insurance industry to develop new products. The role of renewing products is therefore determined by their value contribution to companies and customers, whereas the deregulation itself marginally changed this role.     

Ist der Fahrplan der Energiewende noch einzuhalten?

The German energy transition represents a policy-driven, sustainability-oriented restructuring of both supply- and demand-side components of the entire energy system by 2050. Whereas the development of renewable energies in the electricity sector is right on track, due to the feed-in tariffs of the German Renewable Energy Sources Act, many other crucial requirements for a successful transition are not, amongst others the improvement of energy effi ciency and the decarbonisation of the transport sector. Contrary to the public discussion, the primary future challenges do not consist in limiting electricity prices or abandoning feed-in support schemes, but rather in coordinating the variety of actors as well as appropriately matching the different system elements (grids, technologies, energy sectors, demand and supply side, etc.). Much remains to be done. By highlighting some examples like the need to take into account future implications of climate change for the energy sector, the consequences of the current crisis in the European Union’s emissions trading scheme and the need for a cautious adjustment of the EEG, the paper argues that the major challenges regarding the German energy transition mainly go beyond the current policy-driven and short-term discussion of energy prices. Germany’s pioneering attempt to integrate steadily increasing share of non-dispatchable electricity from renewable sources is challenging the stability of the system. Several characteristics in the current selfregulating system are identifi ed and analysed, which reveal themselves as potential weaknesses or shortcomings in the upcoming system.     

The economic situation in Russia and Belorussia - the reform process at the crossroads

The economic situation in Russia and Belorussia - the reform process at the crossroadsSummary of the first report, September 1992     

Input substitution,aggregation, and engineering descriptions of production activities

This paper presents experimental evidence on the effects of aggregation over micro units on the Allen partial elasticities of substitution between factor inputs. In contrast to all past work on aggregation, the micro technologies are described with engineering, process analysis models.     

International human resource policies and practices in japanese,european, and united states multinationals

This article presents the results of a survey comparing international human resource policies and practices in Japanese, European, and United States multinational companies. The survey focused on the use of expatriates over local nationals in overseas management positions, adoption of nonethnocentric policies, and incidence of international human resource management problems. Regression analysis using the entire sample indicated that ethnocentric staffing and policies are associated with higher incidence of international human resource management problems. Also, Japanese companies as a group are shown to have more ethnocentric staffing practices and policies, and they experience more international human resource management problems than do American and European firms.