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.

Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. 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. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.

[BSHM meetings] Topics in the history of financial mathematics: early commerce to chaos in modern stock markets

This account provides an overview of the study day, entitled 'Topics in the History of Financial Mathematics: Early commerce to chaos in modern stock markets,' held by the British Society for the History of Mathematics jointly with Gresham College, at Gresham College, London on 25th April 2008. The series of talks explored the development of mathematics and mathematical techniques in a commercial and financial context.

The financial crisis and nuclear power

An assessment of the impact of the financial crisis on the prospects for new nuclear power plant orders worldwide.

Private equity: financial investors, public services, and employment

The report surveys the activity of private equity and other financial investors in the water, waste and healthcare sectors in Europe. It includes the appraisal of a WEF study on employment effects.

The effect of ownership structure, country governance, and financial development on the capital structure of unlisted eastern European firms

This paper investigates the determinants of capital structure for a sample of 20,713 unlisted firms from 11 eastern European countries over the period 1994-2004. We employ usual firm-specific financial variables as well as country-specific variables that describe the degrees of governance structure and financial development of each country. Using regression analysis, our results indicate that firm ownership concentration and country governance structure are insignificant explanatory variables to the degree of leverage of the firms in our sample. On the other hand, indicators of country financial development are robust determinants of capital structure. However, the marginal explanatory power of country-specific variables is small. We conclude that firm-specific characteristics are decisive in capital structure.

Public sector pay in the UK: has the historic pattern of public/private sector pay movements been broken?

The historic pattern of public sector pay movements in the UK has been counter-cyclical with private sector pay growth. Periods of relative decline in public sector pay against private sector movements have been followed by periods of ‘catch-up’ as Government controls are eased to remedy skill shortages or deal with industrial unrest among public servants. Public sector ‘catch up’ increases have therefore come at awkward times for Government, often coinciding with economic downturn in the private sector (Trinder 1994, White 1996, Bach 2002). Several such epochs of public sector pay policy can be identified since the 1970s. The question is whether the current limits on public sector pay being imposed by the UK Government fit this historic pattern or whether the pattern has been broken and, if so, how and why? This paper takes a historical approach in considering the context to public sector pay determination in the UK. In particular the paper seeks to review the period since Labour came into office (White and Hatchett 2003) and the various pay ‘modernisation’ exercises that have been in process over the last decade (White 2004). The paper draws on national statistics on public sector employment and pay levels to chart changes in public sector pay policy and draws on secondary literature to consider both Government policy intentions and the impact of these policies for public servants.