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.     

Noise Trading and the Management of Operational Risk; Firms,Traders and Irrationality in Financial Markets*

abstract Efficient market models cannot explain the high level of trading in financial markets in terms of asset portfolio adjustment. It is presumed that much of this excessive trading is irrational ‘noise’ trading. A corollary is that there must either be irrational traders in the market or rational traders with irrational aberrations. The paper reviews the various attempts to explain noise trading in the finance literature, concluding that the persistence of irrationality is not well explained. Data from a study of 118 traders in four large investment banks are presented to advance reasons why traders might seek to trade more frequently than financial models predict. The argument is advanced that trades do not simply occur in order to generate profit, but it does not follow that such trading is irrational. Trading may generate information, accelerate learning, create commitments and enhance social capital, all of which sustain traders' long term survival in the market. The paper treats noise trading as a form of operational risk facing firms operating in financial markets and discusses approaches to the management of such risk.     

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.     

The amenity value of woodland in Great Britain: A comparison of economic estimates

Forests produce benefits over and above the revenue yielded from timber and other wood based products. Most important among these may be the recreational benefits for visitors, which have been examined in several studies. Total benefits for residents are perhaps more accurately captured in property values since, ceteris paribus, the price of a house reflects willingness to pay to live near an environmental amenity such as a forest to gain access to it, and also the amenity (non-use) value of the forest in so far as it creates a pleasant landscape. However, the total non-priced value of forestry is not the sum of HPM and ITCM benefit estimates. Recreational benefits will typically be less, and will be subsumed in the HPM estimates, since the hedonic price is partly induced by the value of recreational access.