Discrete Closed-Form Solutions for Barrier Options
Working Paper (Interest) 29
Publication date: May 2003
Pricing barrier options in discrete-time using lattice techniques is not a straightforward exercise. While the use of larger numbers of time steps may produce more accurate values for standard options, the value of a barrier option is extremely sensitive to the number of time steps used. Merely using more time steps will often produce erroneous option values while simultaneously increasing computation time. There is a consequential necessity for closed-form solutions for this class of derivative. This paper outlines how a reformulation of a simple random walk and an application of the reflection principle may be used to find a binomial coefficient that counts the number of ways a sample path will cross a constant barrier. In this way a general discrete closed-form solution, analogous to Cox, Ross and Rubinstein’s result, may be found for some barrier options. The case of a down-and-in call option is examined in detail. In addition, we prove the convergence of this discrete solution to its continuous-time counterpart.
Total downloads: 1 218
Just How Sub-Optimal is Robert Mugabe? Optimizing Candidates Seeking Elected Office
Working Paper (Interest) 30
Publication date: May 2003
We consider the optimal choice set of candidates standing for elected office. The decision dimensions are in the number of candidates standing for election, and the experiential base of the candidates standing for election as measured by the length of prior experience held by the candidates and the proportion of candidates with such prior experience. We find that while there are benefits that accrue to having a larger choice, the optimal number of candidates is strictly finite. Second, to justify an increase in the optimal length of prior experience requires strong increases in the ratio of benefits that accrue from additional experience to the cost of abuse of the priviledge. The conditions under which an increase in the length of prior experience can be justified is where the cost associated with abuse of privilege is negligible. This would require the development of appropriate formal (legal and constitutional) and informal (civil society) institutions that ensure that abuse of office remain negligible. Finally, we allow the number of electoral candidates, the length of their prior experience, as well as the proportion of candidates with experience to vary. Strong non-linearities ensure that even very small changes in the parameters that characterize a society can generate strong changes in the optimal experiential base of the political class. Where political systems are slow to change, and do so by means of small incremental changes, severe dissatisfaction with political systems is readily explained in the current model as the result of very small social changes. Moreover, optimal pairings of length of experience and the proportion of candidates with prior experience may not exist. Hence societies may be condemned to suboptimality even should the political system prove to be amenable to change, rendering disaffection endemic to the political system.
Total downloads: 357
An examination of the Impact of Economic Policy on long-run Economic Growth: An application of a VECM structure to a middle-income context
Working Paper (Interest) 25
Publication date: January 2002
This paper examines the impact of two indicators of government policy, government consumption expenditure and inflation, on per capita GDP in South Africa over the period 1935-1992. The paper draws from both the theoretical literature on growth as well as the international empirical findings. We highlight two possible effects of government consumption expenditure: government consumption expenditure may potentially have an optimal level with respect to the growth rate of output; and there may be both direct and indirect impacts from government spending through the introduction of an investment equation. We employ the Johansen VECM structure in order to show that policy does indeed have an impact on GDP, consistent with the international literature. In a replication of specifications employed in international growth studies, we find that the direct impact on GDP is indeed negative. However, we also find evidence in favour of a non-linearity in the relation between policy and GDP.
Total downloads: 1 032
Unemployment and labour force participation in South Africa: A focus on the supply-side
Working Paper (Interest) 28
Publication date: January 2002
We provide an analytical framework for explaining how individuals without jobs end up in different labour market states. We extend a simple search model to explain why some unemployed individuals choose to search and others choose not to search. We use this descriptive model to identify factors that could influence an individual’s rational decision to be in a particular labour market state. It further highlights the idea of different degrees of labour force attachment. Different degrees of labour force attachment may imply both different intensities of searching and different degrees of responsiveness to given changes in the labour market environment.
Total downloads: 3 633
An examination of the impact of financial deepening on long-run economic growth: An application of a VECM structure to a middle-income country context
Working Paper (Interest) 24
Publication date: December 2001
This paper examines the impact of financial deepening on long run economic growth in South Africa over the period 1954-92. Two models are developed using the Johansen VECM structure. The first model investigates whether the financial system has a direct or indirect effect on per capital output via the investment rate. The second model attempts to investigate the possibility of feedback effects between the financial and real sectors. We find that both dimensions of the financial system - financial intermediation and securities - affect economic growth in both models. Furthermore, both models reveal that the financial system has an indirect effect on GDP via the investment rate.
Feedback effects are also found to exist between the real and financial sectors. One interpretation of the evidence is that credit rationing is prevalent in South Africa with firms extensively relying on internal finance to meet their financing requirements.
Total downloads: 948
Arbitrage, Cointegration and Efficiency in Financial Markets in the Presence of Financial Crisis
Working Paper (Interest) 13
Publication date: May 2001
The authors gratefully acknowledge the assistance of Genesis Analytics in providing both financial and above all data support to the present project. The results were obtained for the South African Financial Services Board. The views expressed in this paper are those of the authors alone, and should not be taken to necessarily reflect those of either Genesis Analytics or the Financial Services Board in any form.
The present paper examines the link between South African stock index futures markets and the underlying stock market index over the 1960-98 period. Analysis proceeds by means of Johansen VECM and ARDL co-integration analysis. The paper finds strong evidence of the cost-of-carry arbitrage relationship between the two markets. We conclude that the futures market in South Africa is zero-arbitrage efficient even across the period of financial instability that characterised the 1997-98 period.
Total downloads: 1 057
Capstone or Deadweight? Inefficiency, Duplication and Inequity in South Africa’s Tertiary Education System, 1910-93
Working Paper (Interest) 14
Publication date: June 2001
The present paper examines the patterns of inequality to emerge in South Africa’s tertiary education system. We find that the three parts of the tertiary educational system had different forms of inequality attached to them. In the university sector, education in the universities designated for the “Black”, “Coloured” and “Asian” (BCA) population groups under Apartheid legislation were not under-resourced relative to “White” universities in financial or lecturing staff dimensions. However, in terms of output generated, the BCA universities show a lower capacity of preparing their student bodies for the labour market, and a considerably lower research capacity than their “White” counterparts. The Apartheid university system was therefore not only a poor educational vehicle, but it was also expensive. By contrast, in technical education inequality is revealed by differential access to tertiary education between the BCA and white race groups. Finally, in teachers colleges, the patterns of inequality are much as for South Africa’s schooling system: poor resourcing in terms of real per student expenditure and student-lecturer ratios leading to poorer training in the BCA institutions relative to their “White” counterparts.
Total downloads: 760
Economic Growth and Social Capital: a critical reflection
Working Paper (Interest) 08
Publication date: April 2001
The literature on economic growth has increasingly come to emphasise the importance of social capital as a potential determinant of long run economic performance. This paper provides a conceptual examination of the concept of social capital, and the functions it can be assumed to perform in relation to economic growth. We point out that the concept as it has been advanced thus far in the literature is subject to some ambiguity - leaving unaddressed the questions of how much social capital is optimal, of whether all forms of social capital are equally desirable, and of whether all stages of economic development require the same forms of social capital. We argue that in order to provide answers to such questions, it is important to understand a number of distinct functions of social capital - and discuss two, transparency and rationalisation, in some detail. In doing so, we come to reflect on the linkage between social capital and other social institutions such as the state, as well as the role of human capital in economic development. Finally, we suggest that the functional characterisation of social capital, serves to explain the dynamic in terms of which the social capital of a society comes to evolve over time. The authors gratefully acknowledge financial support from the South African Network for Economic Research, and the University of Natal for financial support which made work on this project possible. We express our thanks to D. Herwitz, R.E. Klitgaard, S. Schirmer, C. Torr, M. Woolcock, H. Zarenda and anonymous referees for useful comments on earlier drafts. Responsibility for the contents of this paper remains ours.
Total downloads: 1 232
Growth and Institutions II
Working Paper (Interest) 06
Publication date: March 2001
A number of new political rights and property rights measures are used to explore the link between institutions and economic activity for South Africa over the 1935-97 period. The study uses cointegration analysis to establish the importance of property rights and political instability both as determinants of the level of the desired per capita capital stock, and of investment expenditure. Political freedoms are established as an outcome variable, in a perverse modernization link with per capita output. Some conclusions on the nature of the investment function for South Africa also follow. The financial support of the South African Network of Economic Research is gratefully acknowledged. Responsibility for views expressed remains ours alone.
Total downloads: 348
Indicators of Political Liberty, Property Rights and Political Instability in South Africa: 1935-97
Working Paper (Interest) 04
Publication date: February 2001
This paper presents a number of new indicators of political institutions in South Africa, over the 1935-1997 period. The indicators presented include indicators of political freedom, political instability, immovable and intellectual property rights, and the efficiency of institutions through which rights claims can be enforced in
South Africa. We present the methodology employed to construct each of the indexes, and explore the patterns of association that are present between the indicators.
Total downloads: 1 442
Investment in Fixed Capital Stock: testing for the impact of sectoral and systemic uncertainty
Working Paper (Interest) 16
Publication date: July 2001
This paper applies current theory concerning the impact of irreversibility of investment, in order to test for the impact of uncertainty on investment expenditure for a middle income country. The contribution of the paper is unique in two respects. First, it employs dynamic heterogeneous panel estimation techniques not previously applied to investment functions. Second, it explicitly tests for the impact of both sectoral and systemic uncertainty on investment expenditure. We find that both sectoral (as measured by output volatility around potential output) and systemic uncertainty impacts negatively on investment rates in a middle income country context. However, sectoral uncertainty is more important for resource intensive manufacturing sectors, while systemic uncertainty has a generalized impact across all manufacturing sectors. Standard proxies for expected return on capital stock, and the user cost of capital perform in accordance with theoretical priors.
Total downloads: 498
Job search in South Africa: A nonparametric analysis
Working Paper (Interest) 03
Publication date: January 2001
An approach to South African unemployment based on the perspectives of search theory suggests that labour market flows are very important. We present some evidence on what these flows might look like, based on three cross-sectional surveys. We use changes between age cohorts as proxies for the intertemporal changes involved. Our analysis suggests that there are two types of unemployment: a large spike of youth unemployment and a much longer term labour absorption problem. We also suggest that the education system does not provide effective signals to employers and that search and screening costs of employers may explain some of the dynamics of South African unemployment.
Total downloads: 893
Justifiable Preferences for Freedom of Choice
Working Paper (Interest) 20
Publication date: September 2001
In this paper we say that a preference for freedom of choice is justifiable if there exists a reflexive and complete binary relation on the set of alternatives, such that one opportunity set is at least as good as a second, if and only if the there is at least one alternative from the first set which is no worse than any alternative of the two sets combined together, with respect to the binary relation on the alternatives. In keeping with the revered tradition set by von Neumann and Morgenstern we call a reflexive and complete binary relation, an abstract game ( note : strictly speaking von Neumann and Morgenstern refer to the asymmetric part of a reflexive and complete binary relation as an abstract game; hence our terminology though analytically equivalent, leads to a harmless corruption of the original meaning).In this paper we obtain necessary and sufficient conditions for the justifiability of transitive and quasi transitive preferences for freedom of choice.
Total downloads: 345
Modeling Initiation in South Africa: A Multivariate Cointegration Analysis
Working Paper (Interest) 17
Publication date: July 2001
We employ an expectations augmented Phillips curve framework to investigate the link between inflation, unit labour costs, the output gap, the real exchange rate and inflation expectations. Using multivariate co-integration techniques, we find robust evidence for mark-up behaviour of output prices over unit labour costs. Most importantly, we find that the mark-up in the South African economy is much higher than in the U.S. For South Africa we find a mark-up of about 30 percent; three times a high as the 10 percent mark-up found for the U.S.
Total downloads: 444
Predatory equilibria: Systematic theft and its effects on output, inequality and long-run growth
Working Paper (Interest) 18
Publication date: August 2001
We present a model in which agents can devote energies to production or to appropriating the fruits of other people’s labour. We investigate the situations under which such transfers are equilibria, i.e. will reproduce themselves over time. We note that many of worst outcomes can be observed when players are relatively evenly matched and when the social environment makes predatory activity very successful. In these situations we may even see economic collapse. The introduction of property rights has many of the expected effects, with rewards to productive activity increasing. Nevertheless these gains materialise only if the protection is stronger in areas where the more productive player has a comparative advantage. It is possible to achieve more cooperative outcomes in the repeated game, but paradoxically this might lead to higher levels of income transfers.
Total downloads: 654