Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

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.

Financial Decisions via Methods of Guaranteed Control Theory

AMS subject classification: 93C95, 90A09.

Practice briefing : Is BOT the best financing model to procure infrastructure projects? A case study of the Hong Kong-Shuhai-Macau Bridge

Abstract: Purpose – Several major infrastructure projects in the Hong Kong Special Administrative Region (HKSAR) have been delivered by the build-operate-transfer (BOT) model since the 1960s. Although the benefits of using BOT have been reported abundantly in the contemporary literature, some BOT projects were less successful than the others. This paper aims to find out why this is so and to explore whether BOT is the best financing model to procure major infrastructure projects. Design/methodology/approach – The benefits of BOT will first be reviewed. Some completed BOT projects in Hong Kong will be examined to ascertain how far the perceived benefits of BOT have been materialized in these projects. A highly profiled project, the Hong Kong-Zhuhai-Macau Bridge, which has long been promoted by the governments of the People's Republic of China, Macau Special Administrative Region and the HKSAR that BOT is the preferred financing model, but suddenly reverted back to the traditional financing model to be funded primarily by the three governments with public money instead, will be studied to explore the true value of the BOT financial model. Findings – Six main reasons for this radical change are derived from the analysis: shorter take-off time for the project; difference in legal systems causing difficulties in drafting BOT agreements; more government control on tolls; private sector uninterested due to unattractive economic package; avoid allegation of collusion between business and the governments; and a comfortable financial reserve possessed by the host governments. Originality/value – The findings from this paper are believed to provide a better understanding to the real benefits of BOT and the governments' main decision criteria in delivering major infrastructure projects.

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.

Option pricing in market models driven by telegraph processes with jumps

Esta tesis está dividida en dos partes: en la primera parte se presentan y estudian los procesos telegráficos, los procesos de Poisson con compensador telegráfico y los procesos telegráficos con saltos. El estudio presentado en esta primera parte incluye el cálculo de las distribuciones de cada proceso, las medias y varianzas, así como las funciones generadoras de momentos entre otras propiedades. Utilizando estas propiedades en la segunda parte se estudian los modelos de valoración de opciones basados en procesos telegráficos con saltos. En esta parte se da una descripción de cómo calcular las medidas neutrales al riesgo, se encuentra la condición de no arbitraje en este tipo de modelos y por último se calcula el precio de las opciones Europeas de compra y venta.

An evidence-based review on the likely economic and environmental impact of genetically modified cereals and oilseeds for UK agriculture

An evidence-based review of the potential impact that the introduction of genetically-modified (GM) cereal and oilseed crops could have for the UK was carried out. The inter-disciplinary research project addressed the key research questions using scenarios for the uptake, or not, of GM technologies. This was followed by an extensive literature review, stakeholder consultation and financial modelling. The world area of canola, oilseed rape (OSR) low in both erucic acid in the oil and glucosinolates in the meal, was 34M ha in 2012 of which 27% was GM; Canada is the lead producer but it is also grown in the USA, Australia and Chile. Farm level effects of adopting GM OSR include: lower production costs; higher yields and profits; and ease of farm management. Growing GM OSR instead of conventional OSR reduces both herbicide usage and environmental impact. Some 170M ha of maize was grown in the world in 2011 of which 28% was GM; the main producers are the USA, China and Brazil. Spain is the main EU producer of GM maize although it is also grown widely in Portugal. Insect resistant (IR) and herbicide tolerant (HT) are the GM maize traits currently available commercially. Farm level benefits of adopting GM maize are lower costs of production through reduced use of pesticides and higher profits. GM maize adoption results in less pesticide usage than on conventional counterpart crops leading to less residues in food and animal feed and allowing increasing diversity of bees and other pollinators. In the EU, well-tried coexistence measures for growing GM crops in the proximity of conventional crops have avoided gene flow issues. Scientific evidence so far seems to indicate that there has been no environmental damage from growing GM crops. They may possibly even be beneficial to the environment as they result in less pesticides and herbicides being applied and improved carbon sequestration from less tillage. A review of work on GM cereals relevant for the UK found input trait work on: herbicide and pathogen tolerance; abiotic stress such as from drought or salinity; and yield traits under different field conditions. For output traits, work has mainly focussed on modifying the nutritional components of cereals and in connection with various enzymes, diagnostics and vaccines. Scrutiny of applications submitted for field trial testing of GM cereals found around 9000 applications in the USA, 15 in Australia and 10 in the EU since 1996. There have also been many patent applications and granted patents for GM cereals in the USA for both input and output traits;an indication of the scale of such work is the fact that in a 6 week period in the spring of 2013, 12 patents were granted relating to GM cereals. A dynamic financial model has enabled us to better understand and examine the likely performance of Bt maize and HT OSR for the south of the UK, if cultivation is permitted in the future. It was found that for continuous growing of Bt maize and HT OSR, unless there was pest pressure for the former and weed pressure for the latter, the seed premia and likely coexistence costs for a buffer zone between other crops would reduce the financial returns for the GM crops compared with their conventional counterparts. When modelling HT OSR in a four crop rotation, it was found that gross margins increased significantly at the higher levels of such pest or weed pressure, particularly for farm businesses with larger fields where coexistence costs would be scaled down. The impact of the supply of UK-produced GM crops on the wider supply chain was examined through an extensive literature review and widespread stakeholder consultation with the feed supply chain. The animal feed sector would benefit from cheaper supplies of raw materials if GM crops were grown and, in the future, they might also benefit from crops with enhanced nutritional profile (such as having higher protein levels) becoming available. This would also be beneficial to livestock producers enabling lower production costs and higher margins. Whilst coexistence measures would result in increased costs, it is unlikely that these would cause substantial changes in the feed chain structure. Retailers were not concerned about a future increase in the amount of animal feed coming from GM crops. To conclude, we (the project team) feel that the adoption of currently available and appropriate GM crops in the UK in the years ahead would benefit farmers, consumers and the feed chain without causing environmental damage. Furthermore, unless British farmers are allowed to grow GM crops in the future, the competitiveness of farming in the UK is likely to decline relative to that globally.

The viability of commercial tomato production in the Autopot system

An investigation of the viability of commercial tomato production using the Autopot growing system in Australia. The Autopot system is a relatively new hydroponic production system technology that is being introduced onto the market in competition with traditional systems. Although commercial tomato production was found to be significantly more water and nutrient efficient in the Autopot system than in a traditional open system, yields were significantly lower. Financial modelling shows that tomato production in this system would not be commercially viable in Australia for a typical tomato growing venture under current conditions.

Causality detection on US mutual fund movements using evolutionary subset time-series

In this paper we develop an evolutionary kernel-based time update algorithm to recursively estimate subset discrete lag models (including fullorder models) with a forgetting factor and a constant term, using the exactwindowed case. The algorithm applies to causality detection when the true relationship occurs with a continuous or a random delay. We then demonstrate the use of the proposed evolutionary algorithm to study the monthly mutual fund data, which come from the 'CRSP Survivor-bias free US Mutual Fund Database'. The results show that the NAV is an influential player on the international stage of global bond and stock markets.

Project financing 8th edition

The eighth edition is a fundamental and essential update to the seventh edition published in 2000. This new edition examines a comprehensive range of existing and newer topics that are relevant to project financing in 2012 and explores current trends in the project finance and leasing industries. Contributors are experienced academics and practitioners. Since the first edition was published, the financial markets have undergone tremendous upheavals and many new structures and instruments have been created to meet the financing needs of business. This edition considers the wider world of project finance, applicable to such diverse situations as venture capital and leveraged buyouts, and using new approaches such as Islamic finance techniques. The eighth edition is an essential and over-due update to the previous edition published in 2000. The eighth edition updates a comprehensive review of financial and related topics which are relevant to project financing in 2012 and explores current trends in financial modelling of a project, risk management and the private finance initiatives. This is a comprehensive and practical book full of advice and tips for successful project financing, including leasing, offering a clear, easy to understand guide to a complex area with examples. The topic coverage is well organized and complete moving from the fundamentals to the more complex issues. There is an extensive glossary to support readers. Finally the use of 12 practitioner case studies brings many of these complex issues to life. This is the new edition of the clear, easy-to-understand industry-standard text on project financing. With a good overview of a broad area and using principles of project financing to explain complex structures, this book includes lots of examples and case studies (including Eurotunnel, Dabhol, multiple Paiton deals and other recent deals along with subsequent developments) to show the concepts in use, examine outcomes and to ensure you understand important issues such as effective project structuring and financing, financial modelling for project valuation, and risk management. Substantially updated and expanded to provide the latest developments in all aspects of project financing. An important manual reference, this book is a must-have for every project financier's desk. The text unites the domain of project financing with a wealth of project management techniques, supported by diagrams and charts and other pictorial features, where appropriate. All these supporting features facilitate a better understanding of the accompanying text for the reader. In many chapters there are diagrams to clarify the specific transaction structure discussed in the accompanying text. These diagrams enable the reader to get a very clear idea of the transaction structure, which is particularly useful where it is complex or unusual. There are also a number of checklists to assist stakeholders in the project and resource management of complex project financings. The new financial modelling chapters allow exploration of some of the pitfalls project models encounter, challenging the accurate replication of the project cash flows for stakeholders to evaluate. In the later new risk management chapters, worked examples are included to illustrate the techniques in practice. The new public private partnership/private finance initiatives chapter introduces readers to this new approach to public projects. References are made to useful websites throughout the text. Cases are included at the end of the main text to encourage examination of real-life examples of project financing in practice and also highlight specific issues of current interest. The book will be helpful to project finance sponsors, lawyers, host governments, bankers and providers of capital

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.