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.

'Expanding Horizons': investigating the Glasgow 2014 legacy for young people in the East End of Glasgow

The recent staging of Glasgow 2014 drew universal praise as the ‘Best Games Ever’. Yet the substantial undertaking of hosting the Commonwealth Games (CWG) was sold to the nation as more than just eleven days of sporting spectacle and cultural entertainment. Indeed, the primary strategic justification offered by policymakers and city leaders was the delivery of a bundle of positive and enduring benefits, so-called ‘legacy’. This ubiquitous and amorphous concept has evolved over time to become the central focus of contemporary hosting bids, reflecting a general public policy shift towards using major sporting mega events as a catalyst to generate benefits across economic, environmental and social dimensions, on a scale intended to be truly transformative. At the same time, the academy has drawn attention to the absence of evidence in support of the prevailing legacy rhetoric and raised a number of sociological concerns, not least the socially unequitable distribution of purported benefits. This study investigated how young people living in the core hosting zone related to, and were impacted upon, by the CWG and its associated developments and activities with reference to their socio-spatial horizons, the primary outcome of interest. An ‘ideal world’ Logic Model hypothesised that four mechanisms, identified from official legacy documents and social theories, would alter young people’s subjective readings of the world by virtue of broadening their social networks, extending their spatial boundaries and altering their mind sets. A qualitative methodology facilitated the gathering of situated and contextualised accounts of young people’s attitudes, perceptions, beliefs and behaviours relating to Glasgow 2014. In-depth interviews and focus groups were conducted before and after the Games with 26 young people, aged 14-16 years, at two schools in the East End. This approach was instrumental in privileging the interests of people ‘on the ground’ over those of city-wide and national stakeholders. The findings showed that young people perceived the dominant legacy benefit to be an improved reputation and image for Glasgow and the East End. Primary beneficiaries were identified by them as those with vested business interests e.g. retailers, restaurateurs, and hoteliers, as well as national and local government, with low expectations of personal dividends or ‘trickle down’ benefits. Support for Glasgow 2014 did not necessarily translate into individual engagement with the various cultural and sporting activities leading up to the CWG, including the event itself. The study found that young people who engaged most were those who had the ability to ‘read’ the opportunities available to them and who had the social, cultural and economic capital necessary to grasp them, with the corollary that those who might have gained most were the least likely to have engaged with the CWG. Doubts articulated by research participants about the social sustainability of Glasgow 2014 underscored inherent tensions between the short-lived thrill of the spectacle and the anticipated longevity of its impacts. The headline message is that hosting sporting mega events might not be an effective means of delivering social change. Aspirant host cities should consider more socially equitable alternatives to sporting mega events prior to bidding; and future host cities should endeavour to engage more purposefully with more young people over longer time frames.

Dos prejuízos no regime de participation exemption: a relação entre estabelecimento estável e filial

Mestrado em Fiscalidade

Solvency considerations in the gamma-omega surplus model

Ce mémoire de maîtrise traite de la théorie de la ruine, et plus spécialement des modèles actuariels avec surplus dans lesquels sont versés des dividendes. Nous étudions en détail un modèle appelé modèle gamma-omega, qui permet de jouer sur les moments de paiement de dividendes ainsi que sur une ruine non-standard de la compagnie. Plusieurs extensions de la littérature sont faites, motivées par des considérations liées à la solvabilité. La première consiste à adapter des résultats d’un article de 2011 à un nouveau modèle modifié grâce à l’ajout d’une contrainte de solvabilité. La seconde, plus conséquente, consiste à démontrer l’optimalité d’une stratégie de barrière pour le paiement des dividendes dans le modèle gamma-omega. La troisième concerne l’adaptation d’un théorème de 2003 sur l’optimalité des barrières en cas de contrainte de solvabilité, qui n’était pas démontré dans le cas des dividendes périodiques. Nous donnons aussi les résultats analogues à l’article de 2011 en cas de barrière sous la contrainte de solvabilité. Enfin, la dernière concerne deux différentes approches à adopter en cas de passage sous le seuil de ruine. Une liquidation forcée du surplus est mise en place dans un premier cas, en parallèle d’une liquidation à la première opportunité en cas de mauvaises prévisions de dividendes. Un processus d’injection de capital est expérimenté dans le deuxième cas. Nous étudions l’impact de ces solutions sur le montant des dividendes espérés. Des illustrations numériques sont proposées pour chaque section, lorsque cela s’avère pertinent.

A study on the effect of functional distribution of income on aggregate demand

In this thesis, we study the causal relationship between functional distribution of income and economic growth. In particular, we focus on some of the aspects that might alter the effect of the profit share on growth. After a brief introduction and literature review, the empirical contributions will be presented in Chapters 3,4 and 5. Chapter 3 analyses the effect of a contemporaneous decrease in the wage share among countries that are major trade partners. Falling wage share and wage moderation are a global phenomenon which are hardly opposed by governments. This is because lower wages are associated with lower export prices and, therefore, have a positive effect on net-exports. There is, however, a fallacy of composition problem: not all countries can improve their balance of payments contemporaneously. Studying the country members of the North America Free Trade Agreement, we find that the effect on export of a contemporaneous decrease in the wage share in Mexico, Canada and the United States, is negative in all countries. In other words, the competitive advantage that each country gains because of a reduction in its wage share (to which is associated a decrease in export prices), is offset by a contemporaneous increase in competitiveness in the other two countries. Moreover, we find that NAFTA is overall wage-led: the profit share has a negative effect on aggregate demand. Chapter 4 tests whether it is possible that the effect of the profit share on growth is different in the long run and in the short run. Following Blecker (2014) our hypothesis is that in the short run the growth regime is less wage-led than it is in the long run. The results of our empirical investigation support this hypothesis, at least for the United States over the period 1950-2014. The effect of wages on consumption increases more than proportionally compared to the effect of profits on consumption from the short to the long run. Moreover, consumer debt seem to have only a short-run effect on consumption indicating that in the long run, when debt has to be repaid, consumption depends more on the level of income and on how it is distributed. Regarding investment, the effect of capacity utilization is always larger than the effect of the profit share and that the difference between the two effects is higher in the long run than in the short run. This confirms the hypothesis that in the long run, unless there is an increase in demand, it is likely that firms are not going to increase investments even in the presence of high profits. In addition, the rentier share of profits – that comprises dividends and interest payments – has a long-run negative effect on investment. In the long run rentiers divert firms’ profits from investment and, therefore, it weakens the effect of profits on investment. Finally, Chapter 5 studies the possibility of structural breaks in the relationship between functional distribution of income and growth. We argue that, from the 1980s, financialization and the European exchange rate agreements weakened the positive effect of the profit share on growth in Italy. The growth regime is therefore becoming less profit-led and more wage-led. Our results confirm this hypothesis and also shed light on the concept of cooperative and conflictual regimes as defined by Bhaduri and Marglin (1990).

Three essays on liquidity

Doutoramento em Gestão.

The meaning of implied volatility in pricing stock options traded in options markets

Ph.D. in the Faculty of Business Administration

De la captación ilegal de dinero en Colombia. Análisis de la política y protección de la Superintendencia Financiera

45 p.

The impact of culture and corporate governance in dividend policy: evidence from emerging and developed countries

The present research aims to analyse the impact of corporate governance and cultural dimensions in dividend policy. The corporate governance and dividend policy have a close relationship, in that both are evidenced in literature to mitigate agency problems. Cultural factors are also related to agency problems. The existence of agency problems and their solutions differs across countries and it is related to the implementation of the mechanisms of governance. So, cultural factors may have influence on corporate governance and dividend policy. Our sample consists in 1 232 companies belonging to the main indices of 38 countries classified as emerging or developed. To measure the quality of firm level corporate governance, we use the ASSET4 Corporate Governance Performance Index, developed by Thomson Reuters, and as proxy of culture we use three cultural dimensions developed by Geert Hofstede, namely uncertainty avoidance, masculinity and indulgence. We obtained significant empirical evidence that firms with high quality of corporate governance pay higher dividends. With regard to cultural factors, we confirm that in countries with high levels of masculinity and uncertainty avoidance, the dividend payout ratio is lower. On the other hand, countries with high level of indulgence have higher dividend payout ratio. However, we verify that the impact of cultural effects is minimized when the firms have a high quality level of corporate governance. Additionally, we found that the impact of corporate governance and cultural factors in dividend policy differs when dealing with emerging or developed countries.

Determinants Of Firm Terminal Value: The Perspective Of North American And European Financial Analysts

Company valuation models attempt to estimate the value of a company in two stages: (1) comprising of a period of explicit analysis and (2) based on unlimited production period of cash flows obtained through a mathematical approach of perpetuity, which is the terminal value. In general, these models, whether they belong to the Dividend Discount Model (DDM), the Discount Cash Flow (DCF), or RIM (Residual Income Models) group, discount one attribute (dividends, free cash flow, or results) to a given discount rate. This discount rate, obtained in most cases by the CAPM (Capital asset pricing model) or APT (Arbitrage pricing theory) allows including in the analysis the cost of invested capital based on the risk taking of the attributes. However, one cannot ignore that the second stage of valuation that is usually 53-80% of the company value (Berkman et al., 1998) and is loaded with uncertainties. In this context, particular attention is needed to estimate the value of this portion of the company, under penalty of the assessment producing a high level of error. Mindful of this concern, this study sought to collect the perception of European and North American financial analysts on the key features of the company that they believe contribute most to its value. For this feat, we used a survey with closed answers. From the analysis of 123 valid responses using factor analysis, the authors conclude that there is great importance attached (1) to the life expectancy of the company, (2) to liquidity and operating performance, (3) to innovation and ability to allocate resources to R&D, and (4) to management capacity and capital structure, in determining the value of a company or business in long term. These results contribute to our belief that we can formulate a model for valuating companies and businesses where the results to be obtained in the evaluations are as close as possible to those found in the stock market

Determinants of Terminal Value in the Evaluation of Companies: A Panel Data Approach to the Context of European Companies.

The uncertainty of the future of a firm has to be modelled and incorporated into the evaluation of companies outside their explicit period of analysis, i.e., in the continuing or terminal value considered within valuation models. However, there is a multiplicity of factors that influence the continuing value of businesses which are not currently being considered within valuation models. In fact, ignoring these factors may cause significant errors of judgment, which can lead models to values of goodwill or badwill, far from the substantial value of the inherent assets. Consequently, these results provided will be markedly different from market values. So, why not consider alternative models incorporating life expectancy of companies, as well as the influence of other attributes of the company in order to get a smoother adjustment between market price and valuation methods? This study aims to provide a contribution towards this area, having as its main objective the analysis of potential determinants of firm value in the long term. Using a sample of 714 listed companies, belonging to 15 European countries, and a panel data for the period between 1992 and 2011, our results show that continuing value cannot be regarded as the current value of a constant or growth perpetuity of a particular attribute of the company, but instead be according to a set of attributes such as free cash flow, net income, the average life expectancy of the company, investment in R&D, capabilities and quality of management, liquidity and financing structure.