Generalised Geske--Johnson Interpolation of Option Prices

Abstract:  This paper describes four separate option types as special cases of Bermudans with general inter–exercise and time to final maturity. This produces a surface with European, finite American, infinite Bermudan and infinite American options as special cases. This allows Geske–Johnson (1984) two–point pricing to be extended to consider time–to–maturity as well as time–between–exercise opportunities. Due to their position on this 'map', infinite Bermudans are christened Arctic options and their pricing solution is presented. Numerical comparisons to benchmark methods are made for call prices under GBM although the results here hold for other processes and for both puts and calls when symmetry arguments are invoked.     

Closed-form transformations from risk-neutral to real-world distributions

Risk-neutral and real-world densities are derived from option prices and risk assumptions, and are compared with historical densities obtained from time series. Two parametric risk-transformations are used to convert risk-neutral densities into real-world densities. Both transformations are estimated by maximizing the likelihood of observed index levels, for two parametric density families. Results for the FTSE-100 index show that parametric densities derived from option prices have more explanatory power than historical densities and higher likelihoods than densities estimated by spline methods. A combination of parametric real-world and historical densities provides the preferred predictive densities.     

Production of and trade in African indigenous vegetables in the urban and peri-urban areas of Durban,South Africa

This paper reports on the farming and trade of lesser known crops, here termed African indigenous vegetables (AIVs), in the Durban metropole. Most households grow AIVs, and collect them from the wild, primarily for home consumption. Modal income from sale was approximately R30 per month per farmer, most of whom were middle-aged to elderly females, with limited education, who had been cultivating AIVs here for many years. The main constraints to greater sales were deemed to be low market demand and adverse climate. The commonest AIVs grown were pumpkin leaves, taro and amaranth. Although most farmers sold very little, there is a thriving retail trade in AIVs. Generally, retailers were females, but younger and more educated than the farmers. The majority viewed retailing as a full-time occupation. Modal income for retailers was R450 per month, but included non-AIV produce. Most of the traders thought there was insufficient market demand for AIVs.     

A multi-horizon comparison of density forecasts for the S&P 500 using index returns and option prices

We compare density forecasts of the S&P 500 index from 1991 to 2004, obtained from option prices and daily and 5-min index returns. Risk-neutral densities are given by using option prices to estimate diffusion and jump-diffusion processes which incorporate stochastic volatility. Three transformations are then used to obtain real-world densities. These densities are compared with historical densities defined by ARCH models. For horizons of two and four weeks the best forecasts are obtained from risk-transformations of the risk-neutral densities, while the historical forecasts are superior for the one-day horizon; our ranking criterion is the out-of-sample likelihood of observed index levels. Mixtures of the real-world and historical densities have higher likelihoods than both components for short forecast horizons.     

On the errors and comparison of Vega estimation methods

This article discusses convergence problems when calculating Vega (option sensitivity to volatility) that arise from discretization errors embedded in the lattice approach. Four alternative improvements to the traditional binomial method are discussed and investigated for performance. We also propose a new Modified Binomial (MB) Method to calculate Vegas. Numerical results show that although the MB is not the most price accurate of the models, due to its error structure as a function of volatility, it produces the most accurate and fastest Vega estimates. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:21–38, 2005     

Skills and unemployment

This article attempts to spell out the links which are assumed to exist between skills and unemployment. It is argued that the claims made for the beneficial effects of raising the skill levels of the workforce have been exaggerated. The author then goes on to indicate some of the other factors which influence unemployment levels, and sketches the relevance of this to local economic initiatives.     

training in germany: a dissident view

The German system of training is often seen as an example for Britain. Len Shackleton and David Lange, of Westminster University, argue that, in fact, it handicaps the German economy.     

Dirigisme in Higher Education

The Government's proposals for higher education run contrary to its emphasis on individual choice J R Shackleton (right), Lecturer in Economics at the Polytechnic of Central London, calls for privatisation to encourage innovation in provision extend individual choice, and remove a sizable burden from the taxpayer