Time domain decomposition for European options in financial modelling

Finance is one of the fastest growing areas in modern applied mathematics with real world applications. The interest of this branch of applied mathematics is best described by an example involving shares. Shareholders of a company receive dividends which come from the profit made by the company. The proceeds of the company, once it is taken over or wound up, will also be distributed to shareholders. Therefore shares have a value that reflects the views of investors about the likely dividend payments and capital growth of the company. Obviously such value will be quantified by the share price on stock exchanges. Therefore financial modelling serves to understand the correlations between asset and movements of buy/sell in order to reduce risk. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. There are other financial activities and it is not an intention of this paper to discuss all of these activities. The main concern of this paper is to propose a parallel algorithm for the numerical solution of an European option. This paper is organised as follows. First, a brief introduction is given of a simple mathematical model for European options and possible numerical schemes of solving such mathematical model. Second, Laplace transform is applied to the mathematical model which leads to a set of parametric equations where solutions of different parametric equations may be found concurrently. Numerical inverse Laplace transform is done by means of an inversion algorithm developed by Stehfast. The scalability of the algorithm in a distributed environment is demonstrated. Third, a performance analysis of the present algorithm is compared with a spatial domain decomposition developed particularly for time-dependent heat equation. Finally, a number of issues are discussed and future work suggested.

The parallel solution of early-exercise Asian options with stochastic volatility

This paper describes an parallel semi-Lagrangian finite difference approach to the pricing of early exercise Asian Options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices. Asian options are contingent claims with payoffs that depend on the average price of an asset over some time interval. The payoff may depend on this average and a fixed strike price (Fixed Strike Asians) or it may depend on the average and the asset price (Floating Strike Asians). The option may also permit early exercise (American contract) or confine the holder to a fixed exercise date (European contract). The Fixed Strike Asian with early exercise is considered here where continuous arithmetic averaging has been used. Pricing such an option where the asset price has a stochastic volatility leads to the requirement to solve a tri-variate partial differential inequation in the three state variables of asset price, average price and volatility (or equivalently, variance). The similarity transformations [6] used with Floating Strike Asian options to reduce the dimensionality of the problem are not applicable to Fixed Strikes and so the numerical solution of a tri-variate problem is necessary. The computational challenge is to provide accurate solutions sufficiently quickly to support realtime trading activities at a reasonable cost in terms of hardware requirements.

Real options as an alternative methodology to assess investment projects

This paper aims to broaden the applicability of the assessment methodology of investment projects through real options as a key element for investment decision making -- Traditional project valuation methodologies are described and their gaps, which special characteristic is uncertainty, are presented -- A parallel between financial and real options that could be used for valuation is made, using the binomial tree method -- Finally, a case study in the construction sector shows a project valuation using expand and waiting options

Governance and effectiveness in regional planning: an analysis of North American, European, and Australasian practice

Over the past several years, there has been resurgent interest in regional planning in North America, Europe and Australasia. Spurred by issues such as metropolitan growth, transportation infrastructure, environmental management and economic development, many states and metropolitan regions are undertaking new planning initiatives. These regional efforts have also raised significant question about governance structures, accountability and measures of effectiveness.n this paper, the authors conducted an international review of ten case studies from the United States, Canada, England, Belgium, New Zealand and Australia to explore several critical questions. Using qualitative data template, the research team reviewed plans, documents, web sites and published literature to address three questions. First, what are the governance arrangements for delivering regional planning? Second, what are the mechanisms linking regional plans with state plans (when relevant) and local plans? Third, what means and mechanisms do these regional plans use to evaluate and measure effectiveness? The case study analysis revealed several common themes. First, there is an increasing focus on goverance at the regional level, which is being driven by a range of trends, including regional spatial development initiatives in Europe, regional transportation issues in the US, and the growth of metropolitan regions generally. However, there is considerable variation in how regional governance arrangements are being played out. Similarly, there is a range of processes being used at the regional level to guide planning that range from broad ranging (thick) processes to narrow and limited (thin) approaches. Finally, evaluation and monitoring of regional planning efforts are compiling data on inputs, processes, outputs and outcomes. Although there is increased attention being paid to indicators and monitoring, most of it falls into outcome evaluations such as Agenda 21 or sustainability reporting. Based on our review we suggest there is a need for increased attention on input, process and output indicators and clearer linkages of these indicators in monitoring and evaluation frameworks. The focus on outcome indicators, such as sustainability indicators, creates feedback systems that are too long-term and remote for effective monitoring and feedback. Although we found some examples of where these kinds of monitoring frameworks are linked into a system of governance, there is a need for clearer conceptual development for both theory and practice.

Attitudes towards American brands and brand America

A study of 556 students at colleges and universities in Australia, Hong Kong and Singapore explored the relationship between attitude towards the United States and brand attitudes and preferences. Singaporean student attitudes towards both the US Government and US people were higher than were those of the Australian and Hong Kong students. Coke, Nike and McDonald's were among both the most-liked and disliked US brands among the international students, a finding suggesting that brands may possess both a 'lovemark' status, as described in the literature, and its opposite — 'loathemark' status — within the same demographic group. US brand preference scores did not offer support for the belief that international consumers 'vote with their pocketbooks' by refusing to purchase US brands if they have a negative attitude towards the United States. Among Hong Kong and Singaporean students, favourable attitudes towards the purchase of US brands was found to be positively related to favourability towards the US Government.

The Euro-American psyche and the imaging of Samoa in the early 20th century

Drawing on English language sources and material from Western Samoa (now Samoa), this examination of photographically illustrated serial encyclopaedia and magazines proposes an alternative historical analysis of the colonial photographs of Samoa, the most extensively covered field in Oceanic photographic studies. Photographs published between the 1890s and World War II were not necessarily from that era, and despite claims in the text of illustrated publications of an unchanged, enduring, archaic tradition in Samoa, the amazing variety of content and subject matter often offered contradictory evidence, depicting a modern, adaptive and progressive Samoa. Contrary to orthodox historical analysis, the images of Samoa in illustrated magazines and encyclopaedia were not limited to a small, repetitive gallery of partially clothed women and costumed chiefs.

Investment decision-making under risk (reliability) and uncertainty for infrastructure asset management

Risks and uncertainties are inevitable in engineering projects and infrastructure investments. Decisions about investment in infrastructure such as for maintenance, rehabilitation and construction works can pose risks, and may generate significant impacts on social, cultural, environmental and other related issues. This report presents the results of a literature review of current practice in identifying, quantifying and managing risks and predicting impacts as part of the planning and assessment process for infrastructure investment proposals. In assessing proposals for investment in infrastructure, it is necessary to consider social, cultural and environmental risks and impacts to the overall community, as well as financial risks to the investor. The report defines and explains the concept of risk and uncertainty, and describes the three main methodology approaches to the analysis of risk and uncertainty in investment planning for infrastructure, viz examining a range of scenarios or options, sensitivity analysis, and a statistical probability approach, listed here in order of increasing merit and complexity. Forecasts of costs, benefits and community impacts of infrastructure are recognised as central aspects of developing and assessing investment proposals. Increasingly complex modelling techniques are being used for investment evaluation. The literature review identified forecasting errors as the major cause of risk. The report contains a summary of the broad nature of decision-making tools used by governments and other organisations in Australia, New Zealand, Europe and North America, and shows their overall approach to risk assessment in assessing public infrastructure proposals. While there are established techniques to quantify financial and economic risks, quantification is far less developed for political, social and environmental risks and impacts. The report contains a summary of the broad nature of decision-making tools used by governments and other organisations in Australia, New Zealand, Europe and North America, and shows their overall approach to risk assessment in assessing public infrastructure proposals. While there are established techniques to quantify financial and economic risks, quantification is far less developed for political, social and environmental risks and impacts. For risks that cannot be readily quantified, assessment techniques commonly include classification or rating systems for likelihood and consequence. The report outlines the system used by the Australian Defence Organisation and in the Australian Standard on risk management. After each risk is identified and quantified or rated, consideration can be given to reducing the risk, and managing any remaining risk as part of the scope of the project. The literature review identified use of risk mapping techniques by a North American chemical company and by the Australian Defence Organisation. This literature review has enabled a risk assessment strategy to be developed, and will underpin an examination of the feasibility of developing a risk assessment capability using a probability approach.

Conference Report of the First Meeting of the Native American and Indigenous Studies Association, 21-23 May 2009, Department of American Indian Studies, University of Minneapolis, Minesota, United States of America

Report provided back by Bronwyn Fredericks on her participation at the First Native American and Indigenous Studies Association Meeting held 21-23 May 2009 in Minnesota, United States of America.