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Browsing Research Articles (Mathematics and Applied Mathematics) by Author "Mare, Eben"
Now showing items 1-20 of 34
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Nteumagné, B.F.; Pindza, Edson; Mare, Eben (Scientific Research Publishing, 2014-01)The aim of this paper is to show how options with transaction costs under fractional, mixed Brownian-fractional, and subdiffusive fractional Black-Scholes models can be efficiently computed by using the barycentric Jacobi ...
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Khuzwayo, Bhekinkosi; Mare, Eben (Department of Economics, University of Pretoria, 2014)We consider so-called volatility targeting strategies in the South African equity market. These strategies are aimed at keeping the volatility of a portfolio consisting of a risky asset, typically an equity index, and ...
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Banking regulations : an examination of the failure of African Bank using Merton’s structural model Sanderson, Leon B.; Mare, Eben; De Jongh, Dawie C.J. (Academy of Science of South Africa, 2017-07)The business of banking involves the taking of deposits and the making of loans. Banking balance sheets are typically highly leveraged, with equity capital generally dwarfed by debt capital. Banks are regulated entities; ...
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Pindza, Edson; Youbi, Francis; Mare, Eben; Davison, Matt (American Institute of Mathematical Sciences, 2019-06)A new barycentric spectral domain decomposition methods algorithm for solving partial integro-differential models is described. The method is applied to European and butterfly call option pricing problems under a class of ...
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Venter, Pierre J.; Levendis, Alexis Jacques; Mare, Eben (Taylor and Francis, 2022)In this paper, the generalised autoregressive heteroskedasticity (GARCH) model is applied to the pricing of collateralised options in the South African equity market. Symmetric GARCH and nonlinear asymmetric GARCH (AGARCH) ...
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Taljaard, Byran Hugo; Mare, Eben (Actuarial Society of South Africa, 2019)We analyse and discuss the use of an equal-weighted index as an alternative to the market capitalisation weighted (cap-weighted) index as a benchmark for active equity portfolios in the South African equity market. Our ...
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Van Appel, Vaughan; Mare, Eben (Academy of Science of South Africa, 2022-03)An important topic for retirees is determining how much they can safely withdraw from their retirement savings: draw too much from their retirement fund and risk outliving their retirement savings, or draw too little and ...
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Levendis, Alexis Jacques; Mare, Eben (MDPI, 2022-11)Spread options are notoriously difficult to price without the use of Monte Carlo simulation. Some strides have been made in recent years through the application of Fourier transform methods; however, to date, these methods ...
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Flint, Emlyn James; Mare, Eben (Actuarial Society of South Africa, 2017)In this research we describe how forward-looking information on the statistical properties of an asset can be extracted directly from options market data and demonstrate how this can be practically applied to portfolio ...
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Flint, Emlyn James; Mare, Eben (University of Pretoria, Department of Economics, 2017-03-29)BACKGROUND : Contingent claims on underlying assets are typically priced under a framework that assumes, inter alia, that the log returns of the underlying asset are normally distributed. However, many researchers have ...
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Venter, Pierre Johan; Mare, Eben (Operations Research Society of South Africa, 2020)In this paper, different univariate GARCH option pricing models are applied to the FTSE/JSE Top 40 index to determine the best performing model when modelling the implied South African Volatility Index (SAVI). Three different ...
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Schoombie, S.W.; Mare, Eben (Society for Industrial and Applied Mathematics, 2008)In this paper several Nystrom methods for the van der Pol equation are considered. In an earlier study by Cai, Aoyagi, and Abe it was shown that the second order Nystrom, or leapfrog, method fails to approximate the limit ...
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Moutsinga, Claude Rodrigue Bambe; Pindza, Edson; Mare, Eben (Elsevier, 2018-01)Most existing multivariate models in finance are based on diffusion models. These models typically lead to the need of solving systems of Riccati differential equations. In this paper, we introduce an efficient method ...
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Mare, Eben (Investment Analysts Society of Southern Africa, 2009-12)Derivative securities are frequently priced within the Black-Scholes methodology. Theoretically this entails maintaining a hedge consisting of the underlying asset and cash which needs to be rebalanced continuously. In ...
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Taljaard, Byran Hugo; Mare, Eben (NISC Pty (Ltd) and Informa Limited (trading as Taylor and Francis Group), 2021)This paper considers the recent underperformance of the equal weighted portfolio of South African Top 40 stocks relative to the market capitalisation weighted portfolio. It highlights the impact of the increased concentration ...
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Du Preez, Paul F.; Mare, Eben (Department of Economics, University of Pretoria, 2013)This paper presents a method for interpolating yield curve data in a manner that ensures positive and continuous forward curves. As shown by Hagan and West (2006), traditional interpolation methods suffer from problems: ...
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Pindza, Edson; Mba, Jules Clement; Mare, Eben; Moubandjo, Desiree (De Gruyter, 2016)Evolution equations containing fractional derivatives can provide suitable mathematical models for describing important physical phenomena. In this paper, we propose an accurate method for numerical solutions of ...
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Holdsworth, Chris; Mare, Eben (Scientific Research Publishing, 2014)We provide a framework to ascertain the required equity risk premium (ERP) within the setting of Cumulative Prospect Theory (CPT) over arbitrary investment time periods. Once accounting for behavioral biases in ...
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Mare, Eben (Academy of Science of South Africa, 2018-07-30)On a historical basis, South African equity markets have outperformed inflation significantly. Using returns from the 2016 version of the Credit Suisse Global Investment Sourcebook1, I observe that over the period 1900 ...
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Venter, Pierre Johan; Mare, Eben; Pindza, Edson (Cogent OA, 2020)In this paper, two univariate generalised autoregressive conditional heteroskedasticity (GARCH) option pricing models are applied to Bitcoin and the Cryptocurrency Index (CRIX). The first model is symmetric and the other ...
Now showing items 1-20 of 34