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.     

Quality perceptions under evolving information conditions: Implications for diet,health and consumer satisfaction

Consumers’ perception of, and satisfaction with, fruit quality is an important issue for both public policy and commercial reasons. However, because of information problems, consumers cannot easily choose fruits of a quality most likely to satisfy their preferences and health needs. The research reported here employed an experimental auction method to test perceptions of fruit quality by evaluating the willingness to pay (WTP) of consumers for five different varieties of soft citrus under three different information conditions: visual inspection of the fruit before peeling; visual inspection after peeling; and after consumption. Significant differences were found in valuations of the different varieties as consumers gained information. Conclusions are drawn about the value of the methodology and the results themselves, and implications are inferred for policy and for growers and traders. It is argued that product information should be oriented not just towards nutritional education but also towards increasing the pleasure of healthy eating.     

Multi-party computation mechanism for anonymous equity block trading: A secure implementation of turquoise plato uncross

Dark pools are financial trading venues where orders are entered and matched in secret so that no order information is leaked. By preventing information leakage, dark pools offer the opportunity for large volume block traders to avoid the costly effects of market impact. However, dark pool operators have been known to abuse their privileged access to order information. To address this issue, we introduce a provably secure multi-party computation mechanism that prevents an operator from accessing and misusing order information. Specifically, we implement a secure emulation of Turquoise Plato Uncross, Europe's largest dark pool trading mechanism, and demonstrate that it can handle real world trading throughput, with guaranteed information integrity.