OpenUCT :: Browsing by Subject "Actuarial Science"

Browsing by Subject "Actuarial Science"

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Open Access
Analysing the structure and nature of medical scheme benefit design in South Africa
(2015) Kaplan, Josh Tana; Ramjee, Shivani
This dissertation intends to shed light on open-membership medical scheme benefit design in South Africa. This will be done by analysing the benefit design of 118 benefit options, so as to provide an overview of the structure and nature of the benefit offerings available in the market in 2014. In addition, affordability of these benefit options was analysed in order to identify whether or not there exist connections between the benefits on offer and the price of cover. This paper will argue that at present, the large number of benefit options available in the market, the lack of standardisation between benefit options, together with the mosaic of confusing terminology employed in scheme brochures, creates a highly complex environment that hampers consumer decision making. However, this implicit complexity was found to be necessary owing to the incomplete regulatory environment surrounding medical schemes. The findings of this investigation show that benefit design requires significant attention in order to facilitate equitable access to cover in South Africa.
Open Access
Analysis of equity and interest rate returns in South Africa under the context of jump diffusion processes
(2015) Mongwe, Wilson Tsakane
Over the last few decades, there has been vast interest in the modelling of asset returns using jump diffusion processes. This was in part as a result of the realisation that the standard diffusion processes, which do not allow for jumps, were not able to capture the stylized facts that return distributions are leptokurtic and have heavy tails. Although jump diffusion models have been identified as being useful to capture these stylized facts, there has not been consensus as to how these jump diffusion models should be calibrated. This dissertation tackles this calibration issue by considering the basic jump diffusion model of Merton (197G) applied to South African equity and interest rate market data. As there is little access to frequently updated volatility surfaces and option price data in South Africa, the calibration methods that are used in this dissertation are those that require historical returns data only. The methods used are the standard Maximum Likelihood Estimation (MLE) approach, the likelihood profiling method of Honore (1998), the Method of Moments Estimation (MME) technique and the Expectation Maximisation (EM) algorithm. The calibration methods are applied to both simulated and empirical returns data. The simulation and empirical studies show that the standard MLE approach sometimes produces estimators which are not reliable as they are biased and have wide confidence intervals. This is because the likelihood function required for the implementation of the MLE method is not bounded. In the simulation studies, the MME approach produces results which do not make statistical sense, such as negative variances, and is thus not used in the empirical analysis. The best method for calibrating the jump diffusion model to the empirical data is chosen by comparing the width of the bootstrap confidence intervals of the estimators produced by the methods. The empirical analysis indicates that the best method for calibrating equity returns is the EM approach and the best method for calibrating interest rate returns is the likelihood profiling method of Honore (1998).
Open Access
Analysis of fertility estimates in Zimbabwe : A comparison of the census and DHS data
(2014) Madari, Zvikomborero T R; Moultrie, Tom
Analysis of census data is important to uncover new insights as well as highlight where improvements in future data collection are required. The study provides an assessment of the fertility estimates derived from census data in comparison to those derived from the Zimbabwe Demographic and Health Surveys. Robust methods are used to estimate fertility levels and to identify the trends in fertility in Zimbabwe. Fertility decline in Zimbabwe is observed to have started in the early 1980s. The greatest level of decline occurred between the 1980s and the mid-1990s. In more recent years fertility in Zimbabwe has stalled at roughly four children per woman. Using projected parity progression ratios fertility decline has been observed to be in part a result of parity limitation, as fewer women progress to higher parities. A comparison of the census and Zimbabwe Demographic and Health Survey fertility measures show that for the same cohort of women, the measures of fertility are strongly congruent. While there are problems with census data, it has been shown that using robust estimation the census fertility estimates are comparable to those from the Demographic and Health Surveys.
Open Access
Avoiding data mining bias when testing technical analysis strategies - a methodological study
(2020) Douglas, Rowan; Gilbert, Evan; Maritz, Erich
When seeking to identify a profitable technical analysis (TA) strategy, a na¨ıve investigation will compare a large number of possible strategies using the same set of historical market data. This process can give rise to a significant data mining bias, which can cause spurious results. There are various methods which account for this bias, with each one providing a different set of advantages and disadvantages. This dissertation compares three of these methods, the step wise Superior Predictive Ability (step-SPA) method of P.-H. Hsu, Y.-C. Hsu and Kuan (2010), the False Discovery Rate (FDR) method of Benjamini and Hochberg (1995) and the Monte Carlo Permutations (MCP) method of Masters (2006). The MCP method is also extended, using a step wise algorithm, to allow it to identify multiple profitable strategies. The results of the comparison show that while both the FDR and extended MCP methods can be useful under certain circumstances, the stepSPA method is ultimately the most robust, making it the best choice in spite of its significant computational requirements and stricter set of assumptions.
Open Access
Compositional observations and their role in regression
(2018) Spracklen, Callum
This dissertation examines the properties and some of the uses of compositional data. It gives a brief history of the distinction between 'normal' data and compositions, as well as the various methods of analysing compositional data. It is mainly concerned with performing regression analysis including compositions. In order to model a composition it is necessary to understand the nature of compositions and how to use standard statistical tools with them. This dissertation describes the simplex and several functions which can be performed in it, as well as introducing several useful covariate structures for compositional samples after transformation. It also introduces the transformations between the simplex and unconstrained real space. The dissertation concludes with four examples of regression analyses involving compositions.
Open Access
Deriving traditional reproductive regimes to explain subnational fertility differentials in Zambia
(2008) Wotela, Kambidima; Moultrie, Tom
This thesis applies multivariate statistical techniques to six data sets to account for past and present-day features underlying ethnic fertility differentials in Zambia.
Open Access
Estimating adult mortality in South Africa using information on the year-of-death of parents from the 2016 Community Survey
Mambwe, Chibwe; Dorrington, Rob
In developing countries, systems that collect vital statistics are usually inadequate to facilitate the direct estimation of adult mortality. This has necessitated the development of indirect methods such as the orphanhood method. These methods are however limited, i.e., the single-survey approach produces out of date estimates of mortality and the two-survey approach is affected by the differential reporting of orphanhood between two surveys. To avoid these limitations, this research considers an extension of the orphanhood approach pioneered by Chackiel and Orellana (1985) to estimate adult mortality using year-of-death data rather than the conventional form of the orphanhood data. This is because the year-of- death data can be used to produce accurate time locations to which estimates of mortality apply but more important, one can create a synthetic survey from a single survey and hence obtain more recent and accurate estimates of mortality. The single-survey orphanhood method is applied to survey data to obtain estimates of adult mortality and time location. A variation of the two-survey orphanhood method (Timæus 1991b) is also applied to survey data and the synthetic survey that is created from year-of-death data in order to derive estimates of adult mortality. In addition, the age range of respondents is extended down to age O to include year-of-death data from younger respondents on the assumption that underestimating orphanhood due to the adoption effect is minimal. This is done to investigate if the estimates derived from the two-survey method can be improved. Further, a cohort survival method that involves the calculation of a survival ratio for each age group at the first survey and the equivalent older ages groups at the second survey is applied to investigate the possibility of producing useful estimates of adult mortality based on cohort survival. The level and trend in mortality estimates calculated from the single-survey, two - survey and the cohort survival approaches are discussed and compared to the estimates from the Rapid Mortality Surveillance (RMS) which are used as a benchmark for the trend and level of adult mortality in South Africa. The estimates produced using the single-survey method appear too low, while those from the two-survey method appear to be reasonable for the conventional from of the orphanhood data. Extending the two-survey method to include younger respondents produces estimates that are too low indicating that both the conventional form of the orphanhood data and the year-of-death data suffer from the adoption effect. The cohort survival approach produces reasonable estimates that are consistent with the RMS benchmark for both the conventional form of the orphanhood data and year-of-death data.
Open Access
Estimating the risks in defined benefit pension funds under the constraints of PF117
(2017) Mahmood, Ra'ees; Kendal, Shannon; Dorrington, Rob
With the issuing of Pension Funds circular PF117 in 2004 in South Africa, regulation required valuation assumptions for defined benefit pension funds to be on a best-estimate basis. Allowance for prudence was to be made through explicit contingency reserves, in order to increase reporting transparency. These reserves for prudence, however, were not permitted to put the fund into deficit (the no-deficit clause). Analysis is conducted to understand the risk that PF117 poses to pension fund sponsors and members under two key measures: contribution rate risk and solvency risk. A stochastic model of a typical South African defined benefit fund is constructed with simulations run to determine the impact of the PF117 requirements. Findings show that a best-estimate funding basis, coupled with the no-deficit clause, results in significant risk under both contribution rate and solvency risk measures, particularly in the short-term. To mitigate these risks, alternative ways of introducing conservatism into the funding basis are required, with possible options including incorporating margins into investment return assumptions or the removal of the no-deficit clause.
Open Access
Evaluating the adequacy of the method of using vital registration and census data in estimating adult mortality when applied sub-provincially
(2017) Chinogurei, Chido; Dorrington, Rob
In developing countries, vital registration is the best source of death data that can be used to estimate adult mortality provided they are sufficiently complete. However, they are usually insufficient for estimating mortality sub-nationally due to incomplete registration. This research adapts a method used by Dorrington, Moultrie and Timæus at the provincial level to determine whether it is adequate for estimating adult mortality at the district municipality level in the year prior to the 2001 census. The method uses registration data adjusted for completeness of registration to scale (up or down) the deaths reported by households in the census by age group for each sex. The process of correcting the registered deaths in the year prior to the 2001 census involves estimating intercensal completeness for each population group and each sex between 1996 and 2001 using the average of results from the GGB and the SEG+δ methods. Thereafter, the results are used to estimate the completeness in each of the years within the intercensal period. Thus, an estimate of completeness is obtained in the year prior to the 2001 census for correcting the registered deaths at the population group level. These registered deaths are then used to obtain population group specific adjustment factors to correct the deaths reported by households at the district level, and thereafter to estimate adult mortality rates. Most districts in Kwa-Zulu-Natal have amongst the highest rates of adult mortality, while most districts in the Western Cape have amongst the lowest rates. Results show the Buffalo metropolitan municipality to have higher mortality than that expected for most of the district metropolitan municipalities for both sexes. The same is true for women in Mangaung metropolitan district. It is suspected that HIV prevalence had a significant impact on different levels of adult mortality in the districts, although some adults in the more urban provinces may have died in other provinces. At the provincial level, the method produces marginally higher estimates of adult mortality than the other sources. Provinces that reflect a higher level of mortality appear to deviate more from other research findings than those reflecting lower mortality. In conclusion, the method produces district estimates of ₄₅q₁₅ that are consistent with provincial estimates from other sources and with estimates of HIV prevalence at the district level.
Open Access
The evaluation of case-mix adjusted efficiency scores the case of the South African private hospital industry
(2013) Dreyer, Kathryn Ann; Ramjee, Shivani
There is little existing South African literature relating to hospital efficiency that allows for differences in case mix across hospitals. One of the primary motivations for this dissertation is to help fill this gap in the literature by examining the impact that adjusting for differences in case mix has on efficiency scores. Data Envelopment Analysis (DEA) is chosen as the efficiency measurement method because of its exibility and ease of handling multiple inputs and outputs. A number of DEA models are applied to a sample of South African private hospitals for the years 2008 to 2011 inclusive. Three different case-mix adjustment techniques are investigated and their ability to capture differences in case mix is assessed. The three techniques investigated are: a case-mix adjustment factor (constructed using Diagnosis-Related Groups (DRGs)) to adjust outputs; including the case-mix adjustment factor as an additional output; and disaggregating hospital admissions into broad categories which are used as outputs. A comparison of the unadjusted model with the case-mix adjusted model reveals that omitting the adjustment can have a considerable impact on efficiency scores. Whilst little difference is noted in average efficiency scores for the group of hospitals, 90% for the unadjusted model and 92% for the adjusted model in 2011, there are substantial differences between the adjusted and unadjusted efficiency scores of individual hospitals. On comparison of the three different techniques investigated, it is evident that if there is sufficient data to construct a case-mix adjustment factor, case-mix adjusted admissions should be used, rather than using the factor as an additional output variable. In the case where insufficient data is available, disaggregating admissions does capture some of the differences in case mix but a substantial amount of power is lost as a result of increasing the number of output variables.
Open Access
Inflation modelling for long-term liability driven investments
(2014) De Kock, Justin; Mollentz, Greg; McWalter, Tom
A regime-switching model allows a process to switch randomly between different regimes which have different parameter estimates. This study investigates the use of a two regime-switching model for inflation in South Africa as a means of determining a hedging strategy for inflation linked liabilities of a financial institution. Each regime is modeled using an autoregressive process with different parameters and the change in regimes is governed by a two state Markov chain. Once the parameters have been estimated, the predictive validity of the regime-switching process as a model for inflation in South Africa is tested and a hedging strategy is outlined for a set of inflation linked cash flows. The hedging strategy is to invest in inflation linked bonds, the number of which is determined through the use of a Rand-per-point methodology that is applied to the inflation linked cash flows and inflation linked bonds. Over the period from January 2008 to June 2013 this hedging strategy was shown to be profitable.
Open Access
The interaction between HIV and other sexually transmitted infections in South Africa: a model-based evaluation
(2008) Johnson, Leigh F; Dorrington, Rob; Bradshaw, Debbie
Sexually transmitted infections (STIs) have been shown to increase the probability of HIV transmission, but there remains much uncertainty regarding the role of STI treatment in HIV prevention. This thesis aims to develop a mathematical model to estimate the prevalence of STIs in South Africa, the contribution of STIs to the spread of HIV, and the effects of changes in sexual behaviour and changes in STI treatment. A deterministic model is developed to simulate the transmission of HIV and six other STIs (syphilis, genital herpes, chancroid, gonorrhoea, chlamydial infection and trichomoniasis), as well as the incidence of bacterial vaginosis and vaginal candidiasis in women. The model is fitted to national HIV prevalence survey data, STI prevalence data from sentinel surveys and data from sexual behaviour surveys, using Bayesian techniques. Model results suggest that South Africa has some of the highest STI prevalence levels in the world, but that certain STIs â€“ notably syphilis, chancroid, gonorrhoea and trichomoniasis â€“ have declined in prevalence since the mid-1990s, following the introduction of syndromic management programmes and increases in condom use. STIs account for more than half of new HIV infections, and genital herpes is the most significant STI promoting the transmission of HIV. Syndromic management programmes reduced HIV incidence in South Africa by 3-10% over the decade following their introduction (1994-2004). Further reductions in HIV incidence could be achieved by promoting patient-initiated treatment of genital herpes, by addressing rising levels of drug resistance in gonococcal isolates, and by encouraging prompt health seeking for STIs. Concurrent partnerships are a major factor driving HIV transmission, accounting for 74-87% of new HIV infections over the 1990-2000 period. Halving unprotected sex in non-spousal relationships would reduce HIV incidence over the 2010 -2020 period by 32-43%. This thesis contributes to the understanding of HIV/AIDS epidemiology in South Africa by quantifying the contribution of various behavioural and biological factors to HIV transmission. This thesis also high lights several opportunities for reducing the future incidence of HIV. In addition, this thesis advances the assessment of uncertainty in STI models by proposing a Bayesian approach to incorporating sexual behaviour data and STI prevalence data into the parameter estimation process
Open Access
An investigation into the effect of information on decision-making for members of defined contribution pension funds
(2012) Tagwira, Ruvimbo; Strugnell, Dave
On retirement individuals are expected to live on what they have saved over their working life-times if they are not to be dependent on the state or family. However, investments made over the working life-time may be inadequate to provide fully for retirement. Whilst it is obvious that one must save enough to retire on, it is not always clear how much is enough, or how best to save this. This can, and usually does, result in individuals retiring with less income than they need or expect (Masilela, 2011a), and in many cases, causes them to become dependent on their families or the state.
Open Access
An investigation into the use of the Black-Scholes model for pricing long term options, for the purpose of costing maturity guarantees
(1995) Gamerov, Steven; Dorrington, Rob
This thesis investigates the use of the Black-Scholes option pricing model for long term options for the purposes of costing long term maturity guarantees. The maturity guarantees concerned are typically given on endowment policies issued by life offices. These endowment policies have terms usually in excess of five years. The thesis investigates whether the assumptions underlying the Black-Scholes model, which was developed for pricing short term traded options, are still acceptable when applied to long term options, and if not, what adjustments need to be made. The paper focuses on the pricing of European put options which are equivalent to the payoff of a maturity guarantee.
Open Access
Measuring child mortality in resource limited settings using alternative approaches: South African case study
(2018) Nannan, Nadine; Dorrington, Rob; Bradshaw, Debbie
Post the Millennium Development Goal project a significant number of countries are still faced with the challenge of monitoring child mortality. Despite numerous enquiries since 1996 to provide this basic health indicator, South Africa has experienced prolonged periods of uncertainty regarding the level and trend of infant and under-5 mortality. The thesis develops an analytical framework to review all available data sources and methods of analysis and presents the results of the four approaches adopted to measure child mortality trends. Reviewing the demographic indicators produced from seven census and survey enquiries, the overall performance and the strengths and limitations of each approach is evaluated. Poor and extremely poor quality of data for child mortality emerges as a pervasive challenge to census and survey data. The thesis presents the remarkable improvement in the completeness of birth and death registration through South Africa's CRVS system, particularly since 2000, illustrating the possibility of using CRVS data to monitor provincial child mortality in the future and highlighting statistical challenges arising from the movement of children. In conclusion, South Africa should focus on improving CRVS for purposes of monitoring childhood mortality provincially and the comprehensive evaluation of available data is a useful lesson for other upper-middle-income countries.
Open Access
Measuring hospital efficiency using DEA an investigation into the relationship between scale and efficiency within the South African private hospital environment
(2013) Linden, Andrew
This paper investigates the relationship between scale and efficiency through the application of Data Envelopment Analysis (DEA) to a set of South African private hospitals over the three year period from 2007 to 2009. As part of the investigation, this paper provides a description of the current research into scale and efficiency with a focus on definition and measurement. It also provides an introduction to DEA as a tool for measuring the relationship between hospital scale and efficiency. Based on the underlying set of private hospitals, this investigation found that scale efficiency improvements are likely to be possible.
Open Access
New perspectives in the modelling of alpha
(2012) Flint, Emlyn James; Polakow, Daniel
This dissertation presents an eclectic mix around a central theme of alpha, or value-add. It comprises four essays that are concerned with various theoretical and empirical aspects of alpha. The primary objective is to provide new perspectives in the major areas of modelling alpha; namely, performance measurement, opportunity forecasting and tradability.
Open Access
News media, asset prices and capital flows: evidence from a small open economy
(2017) Sher, Galen; Strugnell, Dave
Objectives: This work investigates the role for the content of print news media in determining asset prices and capital flows in a small open economy (South Africa). Specifically, it examines how much of the daily variation in stock prices, bond prices, trading volume and capital flows can be explained by phrases in the print news media. Furthermore, this work links such evidence to the existing theoretical and empirical literature. Methods: This work employs natural language processing techniques for counting words and phrases within articles published in national newspapers. Variance decompositions of the resulting word and phrase counts summarise the information extracted from national newspapers in this way. Following previous studies of the United States, least squares regression relates stock returns to single positive or negative 'sentiment' factors. New in this study, support vector regression relates South African stock returns, bond returns and capital flows to the high-dimensional word and phrase counts from national newspapers. Results: I find that domestic asset prices and capital flows between residents and non-residents reflect the content of domestic print news media. In particular, I find that the contents of national newspapers can predict 9 percent of the variation in daily stock returns one day ahead and 7 percent of the variation in the daily excess return of long-term bonds over short-term bonds three days ahead. This predictability in stocks and bonds coincides with predictability of the content of domestic print news media for net equity and debt portfolio capital inflows, suggesting that the domestic print news media affects foreign residents' demand for domestic assets. Moreover, predictability of domestic print news media for near future stock returns is driven by emotive language, suggesting a role for 'sentiment', while such predictability for stock returns further ahead and the premium on long-term bonds is driven by non-emotive language, suggesting a role for other media factors in determining asset prices. These results do not seem to reflect a purely historical phenomenon, finite-sample biases, reverse causality, serial correlation, volatility or day-of-the-week effects. The results support models where foreign agents' short-run beliefs or preferences respond to the content of domestic print news media heterogeneously from those of domestic agents, while becoming more homogeneous in the medium term.
Open Access
Old age mortality in South Africa, 1985-2011
(2017) Richman, Ronald David; Dorrington, Rob
Estimating the level and trend in population mortality rates at advanced ages in South Africa is complicated by problems with both the population and death data. Population and death data, particularly in developing countries, often suffer from age misreporting - age exaggeration and digit preference. Also, censuses may under- or overestimate the population and registration of deaths is usually incomplete in developing countries (Dorrington, Moultrie and Timæus 2004). To avoid these problems, the research in this dissertation relies on the method of extinct generations and its extensions (Thatcher, Kannisto and Andreev 2002) to re-estimate the population using only the death data, which is often recorded more accurately than the population data. Since deaths are not reported completely in South Africa, the death data must be corrected before use. Death Distribution Methods (Moultrie, Dorrington, Hill et al. 2013) are used to correct the death data for incomplete registration of deaths. After correction, Near Extinct Generation methods (NEG) are used to re-estimate the population by projecting future deaths of nearly extinct cohorts. After showing that mortality rates produced using the original NEG methods are biased because of age and year of birth heaping present in the South African death data, the NEG methods are adapted to the South African context. The adapted NEG model smooths the age and year of birth heaping in the death data and produces mortality rates that are less biased than the original NEG methods. This model - referred to as the NEG-GAM model in this research - is used to re-estimate the population at each age from 70 and above and to calculate mortality rates since 1985. The population estimates aged 70+ produced using the NEG-GAM model match those from the 2011 census well. It is found that both the population and death data suffer from the same pattern of heaping, that the population and death data are affected by age exaggeration and that the death data are less affected by age exaggeration than the population data. The level and trend in mortality rates calculated using the NEG-GAM model are discussed and compared to the mortality rates in the Human Mortality Database and other studies of South African mortality. The mortality rates produced for the African and Coloured population groups appear too low at the older ages due to age exaggeration in the death data, while those for the Indian and White population groups appear to be reasonable over the entire age range. Mortality appears to be improving in the age range 70-79 for the Coloured, Indian and White population groups and deteriorating slowly for the African population group.
Open Access
On improving the forecast accuracy of the hidden Markov model
(2016) Rooney, Thomas J A; MacDonald, Iain L
The forecast accuracy of a hidden Markov model (HMM) may be low due first, to the measure of forecast accuracy being ignored in the parameterestimation method and, second, to overfitting caused by the large number of parameters that must be estimated. A general approach to forecasting is described which aims to resolve these two problems and so improve the forecast accuracy of the HMM. First, the application of extremum estimators to the HMM is proposed. Extremum estimators aim to improve the forecast accuracy of the HMM by minimising an estimate of the forecast error on the observed data. The forecast accuracy is measured by a score function and the use of some general classes of score functions is proposed. This approach contrasts with the standard use of a minus log-likelihood score function. Second, penalised estimation for the HMM is described. The aim of penalised estimation is to reduce overfitting and so increase the forecast accuracy of the HMM. Penalties on both the state-dependent distribution parameters and transition probability matrix are proposed. In addition, a number of cross-validation approaches for tuning the penalty function are investigated. Empirical assessment of the proposed approach on both simulated and real data demonstrated that, in terms of forecast accuracy, penalised HMMs fitted using extremum estimators generally outperformed unpenalised HMMs fitted using maximum likelihood.