Option Pricing: Real and Risk-Neutral Distributions

The central premise of the Black and Scholes [Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–659] and Merton [Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141–184] option pricing theory is that there exists a self-financing dynamic trading policy of the stock and risk free accounts that renders the market dynamically complete. This requires that the market be complete and perfect. In this essay, we are concerned with cases in which dynamic trading breaks down either because the market is incomplete or because it is imperfect due to the presence of trading costs, or both. Market incompleteness renders the risk-neutral probability measure non unique and allows us to determine the option price only within a range. Recognition of trading costs requires a refinement in the definition and usage of the concept of a risk-neutral probability measure. Under these market conditions, a replicating dynamic trading policy does not exist. Nevertheless, we are able to impose restrictions on the pricing kernel and derive testable restrictions on the prices of options.We illustrate the theory in a series of market setups, beginning with the single period model, the two-period model and, finally, the general multiperiod model, with or without transaction costs.We also review related empirical results that document widespread violations of these restrictions.Option; Pricing

Financial innovations and bank performance in Kenya: evidence from branchless banking models

PhD (Finance), School of Economic and Business Sciences, UNIVERSITY OF THE WITWATERSRAND, JOHANNESBURG 8th June, 2016This study examines the relationship between financial innovation and financial performance of commercial banks in Kenya, as well as the drivers of financial innovations at both firm and macro levels. The financial innovations covered are the branchless banking models, which represent a departure from the traditional branch-based banking. More specifically, the financial innovations covered are: Mobile banking, agency banking, internet banking and Automated Teller Machines (ATMs). The study uses 10-year panel (secondary) data for the period spanning year 2004 to 2013. The study conducts an empirical analysis of the four types of financial innovations using three econometric models. The models have been specified using Koyck distributed lag models and estimated using dynamic panel estimation with System Generalised Method of Moments (GMM). The speed of adjustment of bank financial performance to financial innovation as well as the speed of adjustment of financial innovation to the financial innovation drivers has been tested using Koyck mean and median lags. The empirical results provide strong evidence of the link between financial innovations and bank financial performance with respect to Kenyan commercial banks. The study makes a number of other findings. Firstly, financial innovations significantly contribute to firm financial performance and that firm-specific factors are more important to the firm’s current financial performance than industry factors. Secondly, firm-specific variables significantly drive financial innovations at firm level with firm size being the most significant driver of financial innovation at firm level. The firm specific factors include firm size, transaction costs, agency costs, and technological infrastructure at firm level. Thirdly, macro level variables significantly drive financial innovation at firm level with regulation being the most important driver at macro level. The macro level drivers reviewed include: Regulation and taxes, incompleteness in financial markets, technological infrastructure at macro level and globalisation. Lastly, the existence of reverse causation between firm financial performance and firm financial innovation is established. The speed of adjustment of firm financial performance to financial innovation has been determined. The results show that it takes on average 1.179 years for bank financial performance to adjust to the four financial innovations studied. Secondly, it takes less than a year (0.368 years) to accomplish 50% of the total change in firm performance following a unit-sustained change in the financial innovations. Moreover, mobile banking has the shortest mean lag (2.849) while ATMs have the longest mean lag (4.926). Therefore, it takes approximately three years for mobile banking to adjust to financial innovation drivers at firm level and on average five years for ATMs to adjust to the financial innovation drivers. By and large, the speed of adjustment of financial innovations to macro level drivers is higher than the speed of adjustment of financial innovations to firm level drivers. This study has made significant contribution to the body of knowledge in the field of financial innovations. The study has developed an econometric model which captures four financial innovations in a single study and empirically used the model to test their link to firm financial performance. The second and third econometric models have also captured the drivers of financial innovations at firm and macro levels. The reviewed literature observes that previous studies have largely focused on financial products in developed countries at the expense of emerging financial innovations in developing countries. In addition, previous studies have also largely ignored empirical approaches to the study of financial innovations. This study has empirically established the link between financial innovations and firm performance by modelling the four innovations in single model in a developing country (Kenya) context. One of the major contributions of this study is the establishment of the speed of adjustment of firm performance to financial innovations and the speed of adjustment of financial innovations to financial innovation drivers at both firm and macro levels. Lastly, the study has developed an original conceptual financial innovation value model (Fig. 6.1), which will be used in future financial innovation studies. This study has a number of managerial and policy implications which have been reviewed in the study.MT201

Why Social Enterprises Are Asking to Be Multi-stakeholder and Deliberative: An Explanation around the Costs of Exclusion.

The study of multi-stakeholdership (and multi-stakeholder social enterprises in particular) is only at the start. Entrepreneurial choices which have emerged spontaneously, as well as the first legal frameworks approved in this direction, lack an adequate theoretical support. The debate itself is underdeveloped, as the existing understanding of organisations and their aims resist an inclusive, public interest view of enterprise. Our contribution aims at enriching the thin theoretical reflections on multi-stakeholdership, in a context where they are already established, i.e. that of social and personal services. The aim is to provide an economic justification on why the governance structure and decision-making praxis of the firm needs to account for multiple stakeholders. In particular with our analysis we want: a) to consider production and the role of firms in the context of the “public interest” which may or may not coincide with the non-profit objective; b) to ground the explanation of firm governance and processes upon the nature of production and the interconnections between demand and supply side; c) to explain that the costs associated with multi-stakeholder governance and deliberation in decision-making can increase internal efficiency and be “productive” since they lower internal costs and utilise resources that otherwise would go astray. The key insight of this work is that, differently from major interpretations, property costs should be compared with a more comprehensive range of costs, such as the social costs that emerge when the supply of social and personal services is insufficient or when the identification of aims and means is not shared amongst stakeholders. Our model highlights that when social costs derived from exclusion are high, even an enterprise with costly decisional processes, such as the multistakeholder, can be the most efficient solution amongst other possible alternatives

Computability and Evolutionary Complexity: Markets As Complex Adaptive Systems (CAS)

The purpose of this Feature is to critically examine and to contribute to the burgeoning multi disciplinary literature on markets as complex adaptive systems (CAS). Three economists, Robert Axtell, Steven Durlauf and Arthur Robson who have distinguished themselves as pioneers in different aspects of how the thesis of evolutionary complexity pertains to market environments have contributed to this special issue. Axtell is concerned about the procedural aspects of attaining market equilibria in a decentralized setting and argues that principles on the complexity of feasible computation should rule in or out widely held models such as the Walrasian one. Robson puts forward the hypothesis called the Red Queen principle, well known from evolutionary biology, as a possible explanation for the evolution of complexity itself. Durlauf examines some of the claims that have been made in the name of complex systems theory to see whether these present testable hypothesis for economic models. My overview aims to use the wider literature on complex systems to provide a conceptual framework within which to discuss the issues raised for Economics in the above contributions and elsewhere. In particular, some assessment will be made on the extent to which modern complex systems theory and its application to markets as CAS constitutes a paradigm shift from more mainstream economic analysis

Inclusive governance in non-profit organisations

The study of private non-profit enterprises that offer general interest services is only at the start. The understanding of existing organisations resists an inclusive, public interest view of governance. This contribution aims at providing a reflection on specific features that non-profit enterprises should have, and outlines four main justifications for including stakeholders in production governance: 1) access to knowledge and other resources, 2) trust creation, 3) internal efficiency, 4) external efficiency. Conclusions elaborate on Hansmann’s classic theory of the firm to suggest that governance solutions need to be assessed on the basis of total costs, considering also the lower level of social costs that is created when governance includes relevant stakeholders. Our model highlights that when social costs are high, even an enterprise with costly decisional processes, such as the multi-stakeholder, can be the most efficient solution amongst other possible alternatives

On jump-diffusion processes with regime switching: martingale approach

We study jump-diffusion processes with parameters switching at random times. Being motivated by possible applications, we characterise equivalent martingale measures for these processes by means of the relative entropy. The minimal entropy approach is also developed. It is shown that in contrast to the case of L\'evy processes, for this model an Esscher transformation does not produce the minimal relative entropy.Comment: 23 pages, 2 figure