Browsing Research Articles (Mathematics and Applied Mathematics) by Author "Mare, Eben"

Browsing Research Articles (Mathematics and Applied Mathematics) by Author "Mare, Eben"

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  • Pricing two-asset rainbow options with the fast Fourier transform 
    Levendis, Alexis; Mare, Eben (South African Statistical Association (SASA), 2023)
    In this paper, we present a numerical method based on the fast Fourier transform (FFT) to price call options on the minimum of two assets, otherwise known as two-asset rainbow options. We consider two stochastic processes ...
  • Pricing variable annuity guarantees in South Africa under a Variance-Gamma model 
    Ngugi, A.M. (Alvin Macharia); Mare, Eben; Kufakunesu, Rodwell (Actuarial Society of South Africa, 2015)
    The purpose of this study is to investigate the pricing of variable annuity embedded derivatives using a suitably refined model for the underlying assets, in this case the Johannesburg Securities Exchange FTSE/JSE All ...
  • A proposed best practice model validation framework for banks 
    De Jongh, Pieter J. (Riaan); Larney, Janette; Mare, Eben; Van Vuuren, Gary W.; Verster, Tanja (University of Pretoria, Department of Economics, 2017-06-23)
    BACKGROUND : With the increasing use of complex quantitative models in applications throughout the financial world, model risk has become a major concern. The credit crisis of 2008–2009 provoked added concern about the ...
  • Quantitative guidelines for retiring (more safely) in South Africa 
    Van Appel, Vaughan; Mare, Eben; Van Niekerk, Andries (Actuarial Society of South Africa, 2021-01-01)
    In this paper we present guidelines for safe withdrawal rates from a living annuity (income drawdown accounts), periodically, to cover living expenses. In essence, a retiree is faced with the risk management problem of ...
  • The recovery theorem with application to risk management 
    Van Appel, Vaughan; Mare, Eben (South African Statistical Association, 2020)
    The forward-looking nature of option prices provides an appealing way to extract risk measures. In this paper, we extract forecast densities from option prices that can be used in forecasting risk measures. More specifically, ...
  • Regime-based tactical allocation for equity factors and balanced portfolios 
    Flint, Emlyn James; Mare, Eben (Actuarial Society of South Africa, 2019)
    It is now an accepted fact that the majority of financial markets worldwide are neither normal nor constant, and South Africa is no exception. One idea that can be used to understand such markets and has been gaining ...
  • A robust spectral integral method for solving chaotic finance systems 
    Moutsinga, Claude Rodrigue Bambe; Pindza, Edson; Mare, Eben (Elsevier, 2020-03)
    Nonlinear chaotic finance systems are represented by nonlinear ordinary differential equations and play a significant role in micro-and macroeconomics. In general, these systems do not have exact solutions. As a result, ...
  • The Ross recovery theorem with a regularised multivariate Markov chain 
    Van Appel, Vaughan; Mare, Eben (Operations Research Society of South Africa, 2018-11-04)
    Recently, Ross derived a theorem, namely the “Recovery Theorem”, that allows for the recovery of the pricing kernel and real-world asset distribution, under particular assumptions, from a forward-looking risk neutral ...
  • Safe spending rates for South African retirees 
    Mare, Eben (AOSIS Open Journals, 2016-01)
    Retirees face a difficult financial choice. They need to decide on an appropriate amount to withdraw from their retirement investment and they need to ‘optimise’ between outliving their money and living below their means. ...
  • Sinc collocation method for solving the Benjamin-Ono equation 
    Pindza, Edson; Mare, Eben; Benim, Ali Cemal (Hindawi Publishing, 2014-07-23)
    We propose a simple, though powerful, technique for numerical solutions of the Benjamin-Ono equation. This approach is based on a global collocation method using Sinc basis functions. Some properties of the Sinc collocation ...
  • Solving the generalized regularized long wave equation using a distributed approximating functional method 
    Pindza, Edson; Mare, Eben; Preusser, Tobias (Hindawi Publishing, 2014-04-12)
    The generalized regularized long wave (GRLW) equation is solved numerically by using a distributed approximating functional (DAF) method realized by the regularized Hermite local spectral kernel. Test problems including ...
  • Value at risk in the South African equity market : a view from the tails 
    Milwidsky, C.; Mare, Eben (Juta, 2010-09)
    Traditional parametric Value at Risk (VaR) estimates assume normality in financial returns data. However, it is well known that this distribution, while convenient and simple to implement, underestimates the kurtosis ...
  • Volatility – ubiquitous, yet evasive? 
    Mare, Eben (Treasury Management International, 2014)
    In this article we discuss aspects of asset class volatility. We look specifically at the VIX index and some of its properties – VIX has become very popular in the media of late, especially with low historical levels being ...
  • Why has the equal weight portfolio underperformed and what can we do about it? 
    Taljaard, Byran Hugo; Mare, Eben (Routledge, 2021)
    It is widely noted that market capitalisation weighted portfolios are inefficient and underperform an equal weighted portfolio over the long-term. However, at least since 2016, an equal weighted portfolio of stocks in the ...