Research Articles (Actuarial Science)

Permanent URI for this collectionhttp://hdl.handle.net/2263/18599

This collection contains some of the full text peer-reviewed/ refereed articles published by researchers from the Department of Insurance and Actuarial Science

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Now showing 1 - 20 of 30

Static hedging of vanilla and exotic options in a South African context
(Operations Research Society of South Africa, 2024-07) Levendis, Alexis; Mare, Eben
In this paper, we test the performance of a static hedging strategy for a long-dated European call option and European spread call option in South Africa. The stochastic volatility double jump (SVJJ) model is calibrated to historical FTSE/JSE Top40 returns to generate real-world FTSE/JSE Top40 prices at future dates. The SVJJ model is also calibrated to the FTSE/JSE (Top40) implied volatility surface in order to value the options under the risk-neutral measure. Two static hedging programs are then implemented to test their effectiveness when replicating a long-dated European call option and European spread call option. Our results indicate that static hedging is a simple, yet effective, solution when hedging non-exchange-traded options with vanilla exchange-traded options.
Optimal monetary and fiscal policies to maximise non-parallel risk premia in sovereign bond markets
(MDPI, 2024-11) Hariparsad, Sanveer; Mare, Eben; eben.mare@up.ac.za
In this paper, we analysed several emerging market (EM) and developed market (DM) sovereign yield curves to identify the proportion of parallel and non-parallel shifts over time. We found that non-parallel shifts are more prevalent in EM due to higher political and economic risks. Key drivers include systemic risk events like wars, debt distress, and pandemics. By backtesting a long butterfly strategy to extract non-parallel risk premia from June 2007 to March 2024, we observed that steeper slopes and greater curvature result in higher returns. We also quantified monetary and fiscal regimes to determine what types of policies are required to extract non-parallel risk premia from these sovereign yield curves. Our research suggests that countries with opposing monetary and fiscal policies possess higher return opportunities whilst countries with complementing policies require tactical butterfly strategies to optimise returns.
A computable general equilibrium model of the monetary policy implications for financial stability in South Africa
(Wiley, 2024-12) Beyers, Conrad F.J.; Essel-Mensah, Kojo A.; Tsomocos, Dimitrios P.
The South African Reserve Bank (SARB) uses interest rates to control inflation. The Computable General Equilibrium (CGE) model can contribute to inflation targeting objective and also determine the effects on banks and the economy. We improved the accuracy of the results from previous work on the banking sector CGE model by estimating the elasticities of the reduced form equations of the model instead of arbitrarily choosing them. Our results conform with the established view that lower policy rates lead to an increase in inflation and a reduction in banks’ profits. However, because of the adverse supply shocks arising from the effects of the COVID-19 pandemic, the increase in the GDP is crowded out. The CGE model is a useful tool for the SARB for monetary policy implications on financial stability, informing and providing analysis on its repo rate decision, and determining the consequent effects on the economy.
Hybrid retirement strategy in South Africa
(AOSIS, 2024-09-17) Van Niekerk, Andries; Moutzouris, Vasili; Mare, Eben
BACKGROUND : Many retirees in South Africa face the challenge of either outliving their retirement savings or living below their means. Studies suggest a ‘safe’ withdrawal rate of between 4% and 5%, which is below the average fund size-weighted drawdown rate of approximately 6.66%. AIM : To provide a scientific basis for the success rate of a ‘hybrid’ retirement strategy, whereby a retiree invests a proportion of their savings in a life annuity and the remaining proportion in a living annuity, to increase the success rate for South African retirees. SETTING : Historical asset class returns (equities, bonds and inflation) for South Africa were sourced for the period 1900–2020. METHOD : Bootstrap sampling of historical asset returns was employed to simulate 10 000 random scenarios to investigate the success rate of various compositions of the ‘hybrid’ retirement strategy. RESULTS : The success rate of all ‘hybrid’ portfolio compositions is significantly greater than the success rate of a pure living annuity when the withdrawal rate is less than 8%. CONCLUSION : In a South African context, a ‘hybrid’ retirement portfolio increases the probability of success for retirees withdrawing less than 8% from their portfolio – which constitutes approximately 50% of the current annuatised population – and may increase the inheritance of a retiree’s heir. CONTRIBUTION : Where other studies have focussed solely on the success rate of a living annuity, we have shown that a ‘hybrid’ retirement strategy increases a South African retiree’s likelihood of retiring successfully when the withdrawal rate is less than 8%, which is approximately 50% of the annuatised population.
Exploiting non-parallel risk premia in the South African sovereign bond market
(AOSIS, 2024-05-31) Hariparsad, Sanveer; Mare, Eben
BACKGROUND : This study focuses on diversifying fixed income attribution beyond yield and duration by identifying new risk premia applicable to various investment strategies. AIM : To identify cross-sectional bond risk factors in the South African sovereign bond market, capitalising on non-parallel shifts during high-risk macroeconomic events, developing a strategy to extract persistent alpha from higher order interest rate risks and disproving the strong efficient market hypothesis. SETTING : This study finds that during high-risk macro events, non-parallel shifts increase in frequency. Empirical evidence suggests that post the 2008 financial crisis, there have been increased occurrences of risk-on/off events and researchers believe high risk macro events will increase in prominence. As such, most active US fixed income managers have reduced duration risk (from parallel shifts) in favour of alternative risk premia. METHOD : This study exploits slope and curvature risks, by utilising a butterfly strategy. Ten bond risk factors are back-tested and analysed during interest rate cycles, curve scenarios and risk-off periods from 1998 to 2023. RESULTS : The top-ranked strategies displayed strong and persistent outperformance over the bottom-ranked strategies for most of the bond factors especially during risk-on episodes. The Bond All-Factor Rank demonstrated improved diversification by balancing upside and downside risks. Trade costs are an important factor that requires pragmatic management. CONCLUSION : Geopolitical risks are increasing in frequency and developing a strategy to exploit non-parallel risk premia is an attractive proposition. CONTRIBUTION : This study identified new bond risk factors beyond the conventional spread factor to extract non-parallel risk premia.
Sustainable economic development in Kenya : influence of diaspora remittances, foreign direct investment and imports
(Emerald, 2024) Mutai, Noah Cheruiyot; Ibeh, Lawrence; Nguyen, Manh Cuong; Kiarie, Joyce Wangui; Ikamari, Cynthia
PURPOSE : Many African countries struggle to sustain steady economic growth. Specific macro-economic factors can influence a country’s economic growth. We investigated the trend and influence of diaspora remittances, foreign direct investment (FDI) and imports on Kenya’s economic growth. DESIGN/METHODOLOGY/APPROACH : We used panel data from the World Bank Indicators database from 1973 to 2021. By utilising the autoregressive distributed lag (ARDL) model for econometric analysis and performing computations using R software, we provide valuable insights into both short-term and long-term dynamics. FINDINGS : In the short term, we establish a non-significant negative impact of FDI and imports on economic growth, contrasting with the positive influence of diaspora remittances. However, in the long term, all three variables – FDI, imports and remittances – emerge as significant determinants of economic growth. RESEARCH LIMITATIONS/IMPLICATIONS : The availability and quality of data on diaspora remittances, FDI inflows, imports and economic indicators may vary, leading to potential data limitations, biases or gaps in the analysis. External factors such as global economic trends, political stability, COVID-19, regulatory changes and natural disasters may influence the study’s findings and should be considered when interpreting the results. PRACTICAL IMPLICATIONS : In the short term, the non-significant negative impact of FDI and imports on economic growth suggests that policies promoting FDI and imports may not yield immediate economic growth benefits. Policymakers might need to reassess the effectiveness of current strategies aimed at attracting FDI and managing imports in the short term. The positive influence of diaspora remittances on economic growth underscores the significance of these inflows in supporting economic development. Governments may need to focus on policies that encourage remittance inflows, such as facilitating remittance channels and providing incentives for diaspora investment in the home country. The shift in significance from non-significant in the short term to significant in the long term for FDI, imports and remittances highlights the importance of considering long-term effects in economic planning. Policymakers should adopt strategies that consider the cumulative impact of these factors over time. SOCIAL IMPLICATIONS : Diaspora remittances often play a crucial role in alleviating poverty and reducing inequality by providing direct financial support to families. Recognising the importance of remittances in improving living standards, policymakers should ensure that policies support the effective utilisation of remittance inflows to address poverty and inequality challenges. ORIGINALITY/VALUE : We therefore contribute original insights by examining the interplay between diaspora remittances, FDI, imports and economic growth over the study period. The emphasis on both short-term and long-term effects adds nicety to understanding their roles in shaping Kenya’s economic growth trail.
The contribution of insurers to systemic risk : a practical framework for regulators
(Actuarial Society of South Africa, 2023-12) Rusconi, Rob; Beyers, Frederik Johannes Conradie; Walters, Nadine; robert.rusconi@up.ac.za
While insurers are not typically the most significant contributors to systemic risk, their actions and behaviour may materially contribute to such risk. This study considers the models that may be used to detect systemic risk originating in the insurance market and proposes a framework for identifying and classifying the sources of systemic risk attributable to insurers. It applies this framework to the insurance market in South Africa, in the process providing practical recommendations for consideration by all regulators.
Pricing two-asset rainbow options with the fast Fourier transform
(South African Statistical Association (SASA), 2023) Levendis, Alexis Jacques; Mare, Eben
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 for the underlying assets: two-factor geometric Brownian motion and three-factor stochastic volatility. We show that the FFT can achieve a certain level of convergence by carefully choosing the number of terms and truncation width in the FFT algorithm. Furthermore, the FFT converges at an exponential rate and the pricing results are closely aligned with the results obtained from a Monte Carlo simulation for complex models that incorporate stochastic volatility.
An economic scenario generator for embedded derivatives in South Africa
(Actuarial Society of South Africa, 2022) Levendis, Alexis Jacques; Mare, Eben; eben.mare@up.ac.za
It is well known that interest rate risk is a dominating factor when pricing long-dated contingent claims. The Heston stochastic volatility model fails to capture this risk as the model assumes a constant interest rate throughout the life of the claim. To overcome this, the risk-free interest rate can be modelled by a Hull-White short rate process and can be combined with the Heston stochastic volatility model to form the so-called Heston-Hull-White model. The Heston-Hull-White model allows for correlation between the equity and interest rate processes, a component that is important when pricing long-dated contingent claims. In this paper, we apply the Heston-Hull-White model to price Guaranteed Minimum Maturity Benefits (GMMBs) and Guaranteed Minimum Death Benefits (GMDBs) offered in the life insurance industry in South Africa. We propose a further extension by including stochastic mortality rates based on either a continuous-time Cox-Ingersoll-Ross short rate process or a discrete-time AR(1)-ARCH(1) model. Our findings suggest that stochastic interest rates are the dominating factor when reserving for GMMB and GMDB products. Furthermore, a delta-hedging strategy can help reduce the variability of embedded derivative liabilities.
Collateralised option pricing in a South African context : a univariate GARCH approach
(Taylor and Francis, 2022) Venter, Pierre J.; Levendis, Alexis Jacques; Mare, Eben; eben.mare@up.ac.za
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) models are considered. The models are used to price fully collateralised and zero collateral options (European, Asian, and lookback options). The effect of collateral is illustrated by the difference between zero collateral and fully collateralised option price surfaces. Finally, the effect of asymmetry is shown by the difference between the symmetric and asymmetric GARCH option price surfaces.
Efficient pricing of spread options with stochastic rates and stochastic volatility
(MDPI, 2022-11) Levendis, Alexis Jacques; Mare, Eben
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 have only been applied to specific underlying processes including two-factor geometric Brownian motion (gBm) and three-factor stochastic volatility models. In this paper, we derive the characteristic function for the two-asset Heston–Hull–White model with a full correlation matrix and apply the two-dimensional fast Fourier transform (FFT) method to price equity spread options. Our findings suggest that the FFT is up to 50 times faster than Monte Carlo and yields similar accuracy. Furthermore, stochastic interest rates can have a material impact on long-dated out-of-the-money spread options.
Regulating South Africa’s retirement funds : the case for clearer objectives
(Juta Law, 2021-11-30) Rusconi, Rob; robert.rusconi@up.ac.za
The rationale for the regulation of participants in financial markets, like retirement funds, is sound. It would be strengthened, however, by a clear statement of the objectives of such regulation. In this article the position is taken that the objectives underpinning the regulation of South African privately-managed retirement funds should be enhanced. It presents this argument with reference to international principles concerning systems of old-age provision, and to the examples of regulations in other jurisdictions. It recommends a set of practical regulatory objectives in the pursuit of efficiency, sustainability, coverage, adequacy and security of provision for old age.
Simulation-based optimisation of the timing of loan recovery across different portfolios
(Elsevier, 2021-09) Botha, Arno; Beyers, Conrad F.J.; De Villiers, Johan Pieter; conrad.beyers@up.ac.za
A novel procedure is presented for the objective comparison and evaluation of a bank’s decision rules in optimising the timing of loan recovery. This procedure is based on finding a delinquency threshold at which the financial loss of a loan portfolio (or segment therein) is minimised. Our procedure is an expert system that incorporates the time value of money, costs, and the fundamental trade-off between accumulating arrears versus forsaking future interest revenue. Moreover, the procedure can be used with different delinquency measures (other than payments in arrears), thereby allowing an indirect comparison of these measures. We demonstrate the system across a range of credit risk scenarios and portfolio compositions. The computational results show that threshold optima can exist across all reasonable values of both the payment probability (default risk) and the loss rate (loan collateral). In addition, the procedure reacts positively to portfolios afflicted by either systematic defaults (such as during an economic downturn) or episodic delinquency (i.e., cycles of curing and re-defaulting). In optimising a portfolio’s recovery decision, our procedure can better inform the quantitative aspects of a bank’s collection policy than relying on arbitrary discretion alone.
If the equal weighted portfolio is so great, why isn’t it working in South Africa?
(NISC Pty (Ltd) and Informa Limited (trading as Taylor and Francis Group), 2021) Taljaard, Byran Hugo; Mare, Eben
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 of market capitalisation weights in the Top 40, which is currently at extreme levels. Furthermore, lower levels in the benefits of diversification, through higher average correlations, has reduced the positive impact of rebalancing. Finally, the turnover in index constituents has been higher than average in recent years and this has caused a further drag on performance. The combination of these effects has had a negative impact on the equal weighted portfolio’s relative performance. A rudimentary linear model, with these factors as inputs, that highlights the importance of monitoring these drivers to improve the equal weighted portfolio’s relative performance is presented.
Univariate and multivariate GARCH models applied to bitcoin futures option pricing
(MDPI, 2021-06-10) Venter, Pierre Johan; Mare, Eben; eben.mare@up.ac.za
In this paper, the Heston–Nandi futures option pricing model is applied to Bitcoin futures options. The model prices are compared to market prices to give an indication of the pricing performance. In addition, a multivariate Bitcoin futures option pricing methodology based on a multivatiate GARCH model is developed. The empirical results show that a symmetric model is a better fit when applied to Bitcoin futures returns, and also produces more accurate option prices compared to market prices for two out of three expiry dates considered.
Determining safe retirement withdrawal rates using forward-looking distributions
(Academy of Science of South Africa, 2022-03) Van Appel, Vaughan; Mare, Eben; eben.mare@up.ac.za
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 live below their means. For retirees to decide on the appropriate withdrawal rate, retirees need to have the tools available to decide on their spending rates. There are many factors that influence withdrawal rates, such as initial wealth, asset allocations, age, life expectancy, and risk tolerances. The topic of safe withdrawal rates aims to optimise spending rates while minimising the risk of running out of retirement savings. The focus of this study was on using forward-looking moments of the risk-neutral and real-world asset distributions in determining safe withdrawal rates for South African retirees. The use of forward-looking information, typically derived from traded derivative securities (rather than historical data), is essential in optimising safe withdrawal rates for retirees. In particular, we extracted the forwardlooking risk-neutral and real-world distributions from option prices on the South African Top 40 index, and used the moments of the distributions as a signal in a simple tactical asset allocation framework. That is, when we expect the growth asset to decrease in value, we hold cash (or short the asset) and, alternatively, when we expect the growth asset to increase in value, we hold the growth asset for the period. Using this approach, we found that we can sustain withdrawal rates of up to 7% compared to the commonly quoted 4% safe withdrawal rate obtained by historical simulations. Significance: • Through this paper, we aim to create further awareness on safe retirement spending rates. It is important that retirees are guided through this process with the correct knowledge of the risk and return of asset classes. • Using forward-looking information allows for a more realistic modelling of portfolio returns, which allows for the possibility of better modelling of safe withdrawal rates. • We show that using the moments of the forward-looking distributions in a simple tactical asset allocation framework yielded superior portfolio returns to a fixed asset allocation structure.
Why has the equal weight portfolio underperformed and what can we do about it?
(Routledge, 2021) Taljaard, Byran Hugo; Mare, Eben
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 S&P500 has significantly underperformed the market capitalisation weighted portfolio. In this paper, we analyse this underperformance using stochastic portfolio theory. We show that the equal weighted portfolio does appear to outperform the market capitalisation weighted portfolio over the long-term but with periods of significant short-term underperformance. In addition, we find that concentration in the market capitalisation weighted portfolio has increased in recent years and has contributed to the recent underperformance together with a significantly lower level of diversification benefits. Furthermore, we highlight an approach to improve the performance of a portfolio by dynamically selecting a market cap or an equal weighting using a rudimentary linear regression model.
A computable general equilibrium model as a banking sector regulatory tool in South Africa
(Wiley, 2022-03) Beyers, Frederik Johannes Conradie; De Freitas, Allan; Essel-Mensah, Kojo Amonkwandoh; Seymore, Reyno; Tsomocos, Dimitrios P.; conrad.beyers@up.ac.za
A computable general equilibrium (CGE) model is used as a regulatory tool for the banking sector in South Africa. The model is used to determine the effects of regulatory penalties, capital adequacy requirements (CAR) and the monetary policy on the economy. Our results indicate that there is a trade-off between the default and the CAR regulation. For example, when reducing the default penalty, the banks' profits increase, whereas reducing the CAR violation penalty, banks' profits decrease. Changes to the default penalty have a stronger impact than changes in the CAR violation penalty (i.e. when both penalties are reduced, the banks' profits increase). Moreover, regulatory policies that are targeted at different banks produce asymmetric results, as well capitalised banks with richer portfolios swiftly readjust their balance sheet and transfer the default externality to the more constrained banks and/or the private sector agents.
A computable general equilibrium model for banking sector risk assessment in South Africa
(Springer, 2020-06) Beyers, Conrad F.J.; De Freitas, Allan; Essel-Mensah, Kojo Amonkwandoh; Seymore, Reyno; Tsomocos, Dimitrios P.
In this article a banking sector Computable general equilibrium (CGE) model for South Africa is developed. The model is used to estimate the potential effect of regulatory policy on the economy and as a risk assessment tool to assess how changes in regulation affect the economy. The model provides a methodology for regulators of the banking sector and policy makers in South Africa to deal with risk assessment and future regulatory planning. The CGE model allows interactions amongst various entities of the economy so that policy makers could detect the risks in the banking sector. The CGE model used in this paper performed well as a risk assessment tool for the South African banking sector. The results of the various shocks from the model are consistent with the results obtained from similar shocks done in the UK. We establish that default penalty has a higher effect on the banks’ profits and the interest rates than capital requirement infringement penalty. Our results also suggest that interest rate targeting has more controlled effects than monetary base targeting since pecuniary externalities are reduced.
The recovery theorem with application to risk management
(South African Statistical Association, 2020) Van Appel, Vaughan; Mare, Eben; eben.mare@up.ac.za
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, we extract a real-world return density forecast, implied from option prices, using the recovery theorem. In addition, we backtest and compare the predictive power of this real-world return density forecast with a risk-neutral return density forecast, implied from option prices, and a simple historical simulation approach. In an empirical study, using the South African FTSE/JSE Top 40 index, we found that the extracted real-world density forecasts, using the recovery theorem, yield satisfying forecasts of risk measures.

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