Comparison of numerical methods to price zero coupon bonds in a two-factor CIR model

In this paper we price a zero coupon bond under a Cox–Ingersoll–Ross (CIR) two-factor model using various numerical schemes. To the best of our knowledge, a closed-form or explicit price functional is not trivial and has been less studied. The use and comparison of several numerical methods to determine the bond price is one contribution of this paper. Ordinary differential equations (ODEs) , finite difference schemes and simulation are the three classes of numerical methods considered. These are compared on the basis of computational efficiency and accuracy, with the second aim of this paper being to identify the most efficient numerical method. The numerical ODE methods used to solve the system of ODEs arising as a result of the affine structure of the CIR model are more accurate and efficient than the other classes of methods considered, with the Runge–Kutta ODE method being the most efficient. The Alternating Direction Implicit (ADI) method is the most efficient of the finite difference scheme methods considered, while the simulation methods are shown to be inefficient. Our choice of considering these methods instead of the other known and apparently new numerical methods (eg Fast Fourier Transform (FFT) method, Cosine (COS) method, etc.) is motivated by their popularity in handling interest rate instruments. Keywords: Cox–Ingersoll–Ross model; numerical methods; Runge–Kutta method; zero-coupon bonds; Alternating Direction Implicit method

A stochastic investment model for actuarial use in South Africa

In this paper, we propose a stochastic investment model for actuarial use in South Africa by modelling price inflation rates, share dividends, long-term and short-term interest rates for the period 1960–2018 and inflation-linked bonds for the period 2000–2018. Possible bi-directional relations between the economic series have been considered, the parameters and their confidence intervals have been estimated recursively to examine their stability, and the model validation has been tested. The model is designed to provide long-term forecasts that should find application in long-term modelling for institutions such as pension funds and life insurance companies in South Africa Keywords: Stochastic investment models; price inflation; share dividend yields; share dividends; share prices; long-term interest rates; short-term interest rates; inflation-linked bonds; South Africa

An investigation of an overlap in penalty calculations: profit commission in reinsurance treaties versus profit commission in binder agreements for underwriting managers

Reinsurance treaties and binder agreements regulate penalty calculations in the event the insurer and underwriting manager is unprofitable and/or profitable. The formulae and different premium terminologies are investigated to calculate loss ratios and whether there is an overlap in sliding scale penalty calculations/formulae relevant to loss ratios of treaties and binder agreements. Treaties and binder agreements generally use sliding scale penalties to calculate reinsurance commission or sharing in the insurer’s profits by an underwriting manager and is in conflict with the Conventional Penalties Act 15 of 1962 of South Africa. The Conventional Penalties Act 15 of 1962 must guide reinsurers and insurers in their profit calculations formulae to prevent any form of sliding scale penalties relevant to loss ratios. It is therefore suggested that a standard template of profit calculations and terminologies should be used in binder agreements to prevent different calculations of loss ratios in the short term insurance landscape. This will guide the Financial Conduct Authority Services (previously the Financial Services Board) to understand loss ratios of affordable short term financial products when compared to loss ratios of other short term financial products in South Africa. Keywords: Reinsurance commission; loss ratio; risk premium; penalties; underwriting manager

Sustaining the life insurance industry in the Fourth Industrial Revolution

As the Fourth Industrial Revolution (4IR) continues to change the ways of doing business across industries, organisations around the world are grappling with the unprecedented challenges imposed by radical and widespread technological change. In the face of this dilemma, the South African life insurance industry has remained remarkably resilient, exhibiting very little adaptation in terms of structural, cultural, or business model innovation. However, the stable environmental conditions that once enabled this position for incumbent organisations are weakening. Transformational change, like that in the adjacent financial services industry, is imminent and adaptation on the part of incumbent insurers will be vital to sustaining relevance. This research examines the organisational beliefs and capabilities of South African insurance companies regarding the 4IR in order to gauge the current challenges within the broader industry. Semi-structured interviews were conducted with 12 senior leaders and decisionmakers from across the industry. A qualitative inductive analysis shows the inhibitors and enablers of digital innovation within the organisations. The pervasive lack of trust, agility, and urgency within the sector are cited as inhibitors of digital innovation. Enablers include a continuous learning mindset within the organisation, partnerships within the broader ecosystem, and the role of senior leaders for shaping cultural attitudes and structures. Overall, these findings show a disparity between what insurers know they must do to proactively lead change, enact digital innovation, and remain relevant, and what they are actually executing. Recommendations are provided for addressing this gap. Keywords: Fourth Industrial Revolution; life insurance; strategy; leadership; agility

Defining and measuring portfolio diversification

It is often said that diversification is the only ‘free lunch’ available to investors; meaning that a properly diversified portfolio reduces total risk without necessarily sacrificing expected return. However, achieving true diversification is easier said than done, especially when we do not fully know what we mean when we are talking about diversification. While the qualitative purpose of diversification is well known, a satisfactory quantitative definition of portfolio diversification remains elusive. In this research, we summarise a wide range of diversification measures, focusing our efforts on those most commonly used in practice. We categorise each measure based on which portfolio aspect it focuses on: cardinality, weights, returns, risk or higher moments. We then apply these measures to a range of South African equity indices, thus giving a diagnostic review of historical local equity diversification and, perhaps more importantly, providing a description of the investable opportunity set available tofund managers in this space. Finally, we introduce the idea of diversification profiles. These regimedependent profiles give a much richer description of portfolio diversification than their single-value counterparts and also allow one to manage diversification proactively based on one’s view of future market conditions. Keywords: Portfolio diversification; index concentration; weight-based diversification; risk-based diversification; correlation; covariance; market regimes

The contribution of South Africa’s insurers to systemic risk: thoughts for policymakers

The rationale for regulating financial markets is strong. First, these markets have a critical role to play in the well-being of economies of all sizes. Second, the consequences of failure of these markets is frequently felt well outside of the markets themselves. This regulation should be based on the foundation of a clearly-written publicly-stated set of objectives. One of these objectives ought to be the mitigation of systemic risk, that is the risk that the actions of a financial-sector entity could trigger widespread damage to large parts of the financial markets and to the real economy. Establishing and utilising an appropriate mix of regulatory methods, however, is rendered extraordinarily challenging by the intrinsic complexity, delicacy even, of these markets. This paper explores these issues, applies them to insurance markets, in general and then in South Africa, and asks whether more could be done by South Africa’s insurance regulators to mitigate the systemic risk attributable to the country’s insurers. At heart is the concern that increasingly sophisticated efforts to measure and manage entity-specific risk may have the consequence of adding materially to systemic risk. Keywords: Financial markets, insurance, systemic risk, regulation