Theses and Dissertations (Actuarial Science)

Permanent URI for this collectionhttp://hdl.handle.net/2263/32487

Browse

Now showing 1 - 20 of 20

Fraud detection using operational risk modelling with incomplete data
Muzerengwa, Kudzai Calvin (University of Pretoria, 2019-02)
Systems and processes may fail and employees can engage in fraudulent ac-tivities that can go unnoticed for a very long time and the resulting losses can be very high and catastrophic to an institution. Setting a minimum threshold or a level of completeness will not guarantee that all losses above this point will be reported. In order to model operational risk data, a method that does not depend on the level of completeness is suggested. This can be done by introducing a de-tection probability that is combined with the underlying loss distribution to give a 3-parameter gamma distribution and fitted to a simulated dataset. It is found that the methodology is able to accurately estimate parameters when the data is incomplete.
Examining non-parallel interest rate risk premia with a focus on South African markets
Hariparsad, Sanveer (University of Pretoria, 2025-03)
In this thesis we analysed sovereign yield curves for emerging and developed markets to identify the proportion of parallel and non-parallel shifts over time. We found that non-parallel shifts were more prevalent in emerging markets due to relatively higher political and economic risks. Key drivers included systemic risk events like wars, debt distress, and pandemics. Geopolitical risks were seen to increase in frequency in the modern era and developing a strategy to exploit non-parallel risk premia is an attractive proposition. We determined which policy regimes are appropriate to extract non-parallel risk premia. Our research suggests that countries with opposing monetary and fiscal policies possess greater non-parallel return opportunities whilst countries with complementing policies require tactical non-parallel strategies to optimise returns. We identified the South African (SA) swap and bond interest rate markets as suitable candidate for maximising non-parallel risk premia via a long butterfly strategy (which is immune to parallel curve shifts but exposed to non-parallel curve shifts). Various butterfly weighting methodologies were analysed with a cash and duration neutral methodology being the preferred option due to its conservatism and practicality. Ten swap and bond butterfly risk factors were defined using monthly SA data from 2001-2024. We back-tested and analysed these factors during interest rate cycles, curve scenarios and risk-off periods. Most of the top ranked swap and bond butterfly factors displayed strong and persistent outperformance over their corresponding bottom ranked factors, resulting in improved risk-adjusted and absolute returns especially during positive and steep twists, and bull and bear flattening curve scenarios. The All-Factor Rank which combined all the factors demonstrated improved diversification by balancing upside and downside risks. By demonstrating this outperformance our results contradict the strong efficient market hypothesis of not being able to consistently outperform the market on a risk-adjusted basis. Trade costs were an important factor that required pragmatic management, we compared monthly and quarterly rebalancing frequencies which resulted in monthly rebalancing producing greater gross returns but due to high trade costs, less frequent rebalancing as in the quarterly frequency reduced trade costs and improved net returns. Trade costs can be significant so having a pragmatic rebalancing strategy with efficient market makers that limit trade costs to one basis point of spread duration make these butterfly risk factors an effective and successful portable alpha strategy.
An analytical examination of retirement strategies in South Africa
Van Niekerk, Andries Jacobus (University of Pretoria, 2025-03)
A typical retirement strategy requires a multifaceted approach, considering various products like annuities and a well-structured investment portfolio. Balancing risks like mortality and longevity, along with factors such as healthcare costs, inflation, and tax implications, is essential for ensuring a secure retirement. Most retirees in South Africa face the challenge of either outliving their retirement savings or living below their means. Studies suggest a ‘safe’ withdrawal/spending rate of between 4% and 5%, which is below the average fund size-weighted drawdown rate of approximately 6.7% experienced in South Africa. The success rates of hybrid retirement strategies are evaluated, and the primary aim of these strategies is to enhance the overall success rate and sustainability of retirement portfolios. We assess the success rates of retirement strategies that incorporate foreign exposure by converting any gains in the S&P 500 back to South African Rand (ZAR), factoring in the exchange rate, which is modelled stochastically to simulate real-world currency fluctuations. Both US and South African inflation rates (CPI) are incorporated to ensure that success rates are evaluated in real terms, capturing the impact of inflation on retirees’ income. A core aspect of this study is the incorporation of stochastic correlation and volatility modelling. Using the hyperbolic tangent Ornstein-Uhlenbeck process, we capture the dynamic, complex relationships between relevant asset classes, enabling realistic simulations of asset behaviour under varied market conditions. We analyse the success rates and fugits1of living annuities and various retirement strategies, within a South African context.
Application of machine learning to retirement fund preservation : identifying significant variables in retirement fund preservation decisions
Oberholzer, Liezel (University of Pretoria, 2024-09)
This study aims to understand the retirement fund preservation field and determine which factors lead to low preservation of retirement funds. In addition, the study aims to build a machine learning model that classifies the retirement fund preservation data. The study applied feature engineering to the preservation of retirement fund data from a large insurer in South Africa. The three feature-engineering methods applied were Ordinal Encoding, Dummy Encoding and Target Encoding. These methods were applied to build the three models: Logistic Regression, Random Forest and a Support Vector Machine (SVM). All three models can accurately predict whether an individual will preserve or not. The random forest overall performed best but had the lowest precision. The SVM produces the highest precision of the three models. The results from the logistic regression and the random forest showed that individuals who preserve part of the amount paid to them and take the other part in cash have better preservation rate than those who preserved their full amount or did not preserve at all. This is a strong indicator because it shows that if individuals can preserve more and still take a part of their funds in cash the overall preservation of their retirement funds is good. This study could benefit the industry through identifying variables to focus on to improve the individual’s preservation of their retirement funds.
Applying stochastic volatility models in the risk-neutral and real-world probability measures
Levendis, Alexis Jacques (University of Pretoria, 2023)
Stochastic volatility models have become immensely popular since their introduction in 1993 by Heston. This is because their dynamics are more consistent with market behaviour compared to the standard Black-Scholes model. More specifically, stochastic volatility models can somewhat capture the asymmetric distribution often observed in daily equity returns. Numerous extensions to the stochastic volatility model of Heston have since been proposed, including jumps and stochastic interest rates. Due to their complex dynamics, numerical methods such as Monte Carlo simulation, the fast Fourier transform (FFT), and the efficient method of moments (EMM) are often required to calibrate and implement stochastic volatility models. In this thesis, we explore the application of stochastic volatility models to a variety of problems for which research is still in its infancy phase. We consider the pricing of embedded derivatives in the South African life insurance industry given the illiquid derivatives market; the pricing of rainbow and spread options that depend on two underlying assets; the calibration of stochastic volatility models with jumps to historical equity returns; and the use of stochastic volatility models in static hedging. Our findings suggest that stochastic interest rates are the dominant risk driver when pricing long-dated contingent claims; the FFT significantly outperforms Monte Carlo simulation in terms of efficiency; jumps are an important factor required to explain daily equity returns; and static hedging is a simple and effective way to replicate vanilla and exotic options.
Time-varying volatility models and indices : a GARCH option pricing approach
Venter, Pierre Johan (University of Pretoria, 2022)
In this thesis, the generalised autoregressive conditional heteroskedasticity (GARCH) option pricing model is applied to illiquid markets, volatility indices and in a modern derivative pricing framework. Chapter 2 provides empirical support for the use of a volatility index to obtain a more accurate GARCH option pricing model (applied to the South African equity market). In Chapter 3, the analysis (GARCH option pricing and volatility indices) is extended to FX markets. Empirical results show that asymmetry is an important factor to consider when modelling FX volatility indices. The aim of Chapter 4 is to quantify the effect of asymmetry in the cryptocurrency market. Furthermore, the accuracy of the GARCH option pricing model applied to cryptocurrencies is also considered. Results indicate that the GARCH option pricing model produces reasonable price discovery, and that asymmetric effects are not significant when pricing cryptocurrency options. Chapter 5 focuses on the construction of a cryptocurrency volatility index, the models in Chapter 4 are used as a basis. The term structure of the GARCH generated volatility indices are consistent with expectations. Furthermore, short term volatility tends to increase when large jumps occur in the underlying asset. In Chapter 6, the Heston–Nandi futures option pricing model is applied to Bitcoin (BTC) 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. Chapter 7 focuses on the pricing of volatility index options respectively. In Chapter 7, the GARCH option pricing model is applied to the Standard and Poor's 500 (S&P500) Volatility Index (VIX) option pricing. The different GARCH models are fitted to VIX futures returns. The results show that the symmetric GARCH model with skewed Student-t errors is the best performing model, and that the GARCH option pricing model provides reasonable price discovery when applied to the VIX. In Chapter 8, the standard Black model and Heston-Nandi futures options pricing model are applied to the hedging of VIX futures options. The hedge performance is compared based on the stability of the profit and loss distribution (P&L) of the hedged portfolio. Empirical results show that the Heston-Nandi futures option pricing model is more reliable when applied to hedging of VIX futures options. The focus of Chapter 9 is the application of the GARCH model 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. Finally, a closed-form expression for a collateralised European option in the presence of counterparty credit risk and stochastic volatility is derived in Chapter 10. The model is applied to S&P500 index options. The option prices obtained are consistent with expectations, default risky options are cheaper than options with no counterparty credit risk, and fully collateralised options are more expensive when compared to zero collateral options. The effect of correlation is tested by plotting the default risky at-the-money (ATM) option price for different levels of correlation. The results indicate that correlation has an insignificant impact when pricing using the calibrated parameters.
Modelling of financial risk using forward-looking distributions derived from contingent claims
Van Appel, Vaughan (University of Pretoria, 2022)
English: In this thesis, we investigate several methods for extracting the forecast distribution from historical asset returns and market-quoted option prices. Typically, risk-neutral distributions, extracted from market quoted option prices, are considered biased estimates of the forecast distribution, and therefore need to be transformed into a real-world distribution. Transformation processes often require the use of historical data and restrictive assumptions on a representative investor. Alternatively, the recovery theorem provides a theoretically appealing method to recover the real-world distribution from the risk-neutral transition probability matrix without the use of historical returns. However, estimating the risk-neutral transition probability matrix has proven to be a challenging task, as it involves solving an ill-posed problem. Therefore, we propose a regularised multivariate Markov chain in the estimation of the risk-neutral transition probability matrix to obtain a more accurate real-world forecast distribution than obtained using the univariate model. Comparative studies on the accuracy of real-world forecast distributions are scarce in the literature. Therefore, we further backtested and compared the accuracy of the extracted distributions on the South African Top 40 index, where we found that the forward-looking real-world distribution improved forecasting in certain situations. We also proposed a forward-looking mixture model of historical and option-implied distributions to improve forecasting. Furthermore, we implemented the extracted forecast distributions in determining safe retirement withdrawal rates. In our empirical study, we showed that the use of forward-looking distributions drastically improved the success in retirement withdrawal rates. Sepedi: Mo theseseng ye, re nyakišiša mekgwa ye mmalwa ya go ntšha kabo ya ponelopele go tšwa dipoelong tša matlotlo tša histori le ditheko tša dikgetho tšeo di tsopotšwego mmarakeng. Ka tlwaelo, dikabo tše di hlokago dikotsi, tšeo di ntšhitšwego dithekong tša dikgetho tše di tsopotšwego mmarakeng, di tšewa bjalo ka dikakanyetšo tše sekametšego kabong ya ponelopele, ka fao di swanetše go fetošetšwa kabong ya lefase la kgonthe. Ditshepetšo tša phetogo, gantši di nyaka tšhomišo ya datha ya histori le dikakanyo tše di iletšago moemedi wa mmeeletši. Ka mo go fapanego, teorema ya go tsošološa e fana ka mokgwa wa theory wo o ipiletšago teoring wa go bušetša kabo ya lefase la kgonthe go tšwa go matrix wa kgonagalo ya phetogo woo o sa sekamelago kotsing ntle le tšhomišo ya dipoelo tša histori. Le ge go le bjale, go akanyetša mathrikse ya kgonagalo ya phetogo yeo e sa sekamelago kotsing go ipontšhitše e le mošomo wo boima, ka ge go akaretša go rarolla bothata bjo bo sa bewago gabotse. Ka fao, re šišinya molokoloko wo o beakantšwego wa go fetoga wa Markov wa mehutahuta wa kotsi ya magareng ya kgonego ya mathrikse wa go hwetša kabo ya ponelopele ya lefase la nnete ye e nepagetšego kudu go feta yeo e hweditšwego ka go šomiša mohlala wa wa papetšo o tee. Dinyakišišo tša go bapetša tša go nepagala ga dikabo tša ponelopele ya lefase la kgonthe di a hlaelela ka dingwalweng. Ka fao, re ile ra tšwela pele go dira diteko tša pušetšomorago le go bapetša go nepagala ga dikabo tše di ntšhitšwego go Dipalopalo tša Maemo a Godimo Aa bo 40 ka Afrika Borwa, moo re hweditšego gore kabo ya lefase ya kgonthe ya tebelelopele e kaonafaditše ponelopele maemong a itšego. Re ile ra šišinya gape mohlala wa mohlakanelwa wa tebelelopele ya dikabo tša histori le tšeo di akaretšwago ke kgetho go kaonafatša ponelopele. Godimo ga fao, re phethagaditše dikabo tša ponelopele tše di ntšhitšwego go laetša ditekanyo tša go ntšha tšhelete ka go rola modiro ka polokego. Ka dinyakišišong tša rena tša bohlatse, re bontšhitše gore tšhomišo ya dikabo tša tebelelopele di kaonafaditše kudu katlego ya ditekanyo tša go ntšha tšhelete ge go rolwa modiro. Afrikaans: In hierdie proefskrif ondersoek ons verskeie metodes om die voorspelde verdeling uit historiese bate-opbrengste en markgekwoteerde opsiepryse te onttrek. Tipies word risiko-neutrale verdelings, onttrek uit markgekwoteerde opsiepryse, as bevooroordeelde ramings van die voorspelde verdeling beskou en moet dus in 'n werklike verdeling omskep word. Transformasieprosesse vereis dikwels die gebruik van historiese data en beperkende aannames oor 'n verteenwoordigende belegger. Alternatiewelik bied die herwinnigstelling 'n teoreties aantreklike metode om die werklike verspreiding uit die risiko-neutrale oorgangswaarskynlikheidsmatriks te herwin sonder die gebruik van historiese opbrengste. Die beraming van die risiko-neutrale oorgangswaarskynlikheidsmatriks het egter uitdagend geblyk, aangesien dit die oplossing van 'n swak geformuleerde probleem behels. Daarom stel ons 'n gereguleerde meerveranderlike Markov-ketting voor in die beraming van die risiko-neutrale oorgangswaarskynlikheidsmatriks om 'n meer akkurate werklike voorspellingsverspreiding te verkry as wat verkry word met behulp van die eenveranderlike model. Vergelykende studies oor die akkuraatheid van werklike voorspellingsverspreidings is skaars in die literatuur. Daarom het ons die akkuraatheid van die onttrekte verspreidings op die Suid-Afrikaanse Top 40-indeks verder teruggetoets en vergelyk, waar ons gevind het dat die vooruitskouende werklike verspreiding voorspelling in sekere situasies verbeter het. Ons het ook 'n vooruitskouende gemengde model van historiese en opsie-geïmpliseerde verspreidings voorgestel om voorspelling te verbeter. Verder het ons die onttrekte voorspellingsverspreidings geïmplementeer in die bepaling van veilige aftree-onttrekkingsyfers. In ons empiriese studie het ons getoon dat die gebruik van toekomsgerigte verspreidings die sukses in aftree-onttrekkingsyfers drasties verbeter het. IsiZulu: Kulolu cwaningo, siphenya izindlela ezimbalwa zokukhipha isibikezelo sokusatshalaliswa okuvela ekubuyekezweni kwenzuzo yempahla yomlando kanye nezintengo zokukhetha ezibizwe emakethe. Ngokuvamile, ukusatshalaliswa okungenangozi nokungagqamisi uhlobo, okukhishwe kukukhetha okubizwe emakethe, kuthathwa njengezilinganiso ezichemile zokubikezela ukusatshalaliswa , ngakho-ke kudingeka ukuthi kuguqulelwe kukusatshalaliswa komhlaba wangempela. Kule thesisi, siphenya izindlela ezimbalwa zokukhipha isibikezelo sokusatshalaliswa okuvela ekubuyekezweni kwenzuzo yempahla yomlando kanye nezintengo zokukhetha ezibizwe emakethe. Okunye ukuthi, ithiyoremu yokubuyisa ihlinzeka ngendlela ekhangayo ngokomqondo ukuze kubuyiselwe ukusatshalaliswa komhlaba wangempela ukusuka ku-mathiksi yamathuba angabakhona enguquko engenangozi nokugqamisa uhlobo ngaphandle kokusetshenziswa kwezinzuzo zomlando. Kodwa-ke, ukulinganisa imethriksi yamathuba angabakhona enguquko engenangozi nokugqamisa uhlobo kufakazela ukuthi kuwumsebenzi oyinselelo, njengoba kubandakanya ukuxazulula inkinga ebekwe kabi. Ngakho-ke, siphakamisa iketanga elijwayelekile le-Markov elinhloboningi futhi elenziwe ngokomthetho ekulinganisweni kwemethriksi yamathuba angabakhona enguquko engenangozi nokugqamisa uhlobo ukuze kutholwe isibikezelo sokusatshalaliswa komhlaba wempela okunemba kakhudlwana kunaloko okutholwa kusetshenziswa izifanekiso eziwuhlobo olulodwa. Izifundo Eziqhathanisa ngokunemba kwesibikezelo sokusatshalaliswa komhlaba wangempela ziyingcosana emibhalweni. Ngakho-ke, siqhubekile nokuhlola saqhathanisa ukunemba kokusatshalaliswa okutholakele ku-Top 40 index yaseNingizimu Afrika, lapho sithole khona ukuthi ukusatshalaliswa okubheke phambili kwangempela kuthuthukise ukubikezela kwezinye izimo. Siphinde saphakamisa umfanekiso oyinhlanganisela obikezela ukusabalalisa okungokomlando kanye nokukhetha okuqondayo ukwenza ngcono ukubikezela. Ngaphezu kwalokho, sisebenzise isibikezelo sokusatshalaliswa esikhishwe ekunqumeni izilinganiso eziphephile zokudonsa umhlalaphansi. Ocwaningweni lwethu lwendlela yesayensi, sibonise ukuthi ukusetshenziswa kokubikezela ukusatshalaliswa kuyenza kangcono kakhulu impumelelo kuzilinganiso zokudonsa umhlalaphansi.
Improving our understanding of the equal weighted portfolio
Taljaard, Byran H. (University of Pretoria, 2022)
English: This thesis analyses the performance of the equal weighted portfolio using an approach from stochastic portfolio theory. This framework allows for the decomposition of the relative performance of the equal weighted portfolio into four main parts; the change in the concentration of the cap weighted portfolio, the excess return generated by a diversification benefit, the difference in dividend rates, and a term called the leakage effect. In general equal weighted portfolios do outperform their cap weighted portfolio counterparts, although with varying degrees across different countries. In South Africa, for example, high levels of leakage over the past ten years and increasing concentration have led to poor relative performance of the equal weighted portfolio. In other countries such as the United Kingdom and Japan, equal weighted portfolios have done very well, with high levels of diversification benefits and low levels of leakage. Two models are presented in an attempt to reduce the relative drawdowns of the equal weighted portfolio and to blend the two weights (equal and cap) in an optimal manner. These models appear to do well in markets where the equal weighted portfolio has poor performance and large relative drawdowns. Sepedi: Thesese ye e sekaseka phethagatšo ya photefolio ya boima bjo bo lekanago ka go šomiša mokgwa go tšwa teoring ya pothefolio ya setokhastiki. Tlhako ye e dumelela karoganyo ya go šoma fao go lekanyeditšwego ga photefolio ya boima bjo bo lekanago ka dikarolo tše nne tše kgolo; phetogo ya teteana ga photefolio ya boima bjo lekanyeditšwego, poelo ye e fetišago yeo e tšweleditšwego ke mohola wa go fapantšha, phapano ya ditekanyo tša dikabo, le lereo leo le bitšwago khuetšo ya go dutla. Ka go diphotefolio tša boima bjo bo lekanago tša kakaretšo di šoma go feta balekane ba tšona ba diphotefolio tše di nago le boima bja go lekanetšwa, le ge e le gore di fapana ka dikelo tše di fapanego go ralala le dinaga tše di fapanego. Ka Afrika Borwa, go fa mohlala, maemo a godimo a go dutla mo mengwageng ye lesome ye e fetilego le go oketšega ga teteano di lebišitše go tshepedišo ye mpe ya go lekana ya potefolio ya boima bjo bo lekanago. Dinageng tše dingwe tša go swana le United Kingdom le Japane, diphotefolio tša boima bjo bo lekanago di dirile gabotse kudu, ka maemo a godimo a mehola ya go fapafapana le maemo a fase a go dutla. Mehlala ye mebedi e tšweletšwa ka maitekelo a go fokotša tekano ya kgogelofase ya photefolio ya boima bjo bo lekanago le go kopanya boima bjo bobedi (go lekana lele peelo) ka mokgwa wo o loketšego. Mehlala ye e bonala e dira gabotse mebarakeng yeo potefolio ye e nago le boima bjo bo lekanago e nago le tshepedišo ye mpe le tekanyo ye kgolo ya phokotšego. Afrikaans: Hierdie proefskrif ontleed die prestasie van die gebalanseerde portefeulje deur gebruik te maak van 'n benadering uit stogastiese portefeuljeteorie. Hierdie raamwerk maak voorsiening vir die ontbinding van die relatiewe prestasie van die gebalanseerde portefeulje in vier hoofdele: die verandering in die konsentrasie van die kapitalisasiegeweegde portefeulje, die oortollige opbrengs wat gegenereer word deur 'n diversifikasievoordeel, die verskil in dividendkoerse, en 'n term genaamd die lekkasie-effek. Oor die algemeen presteer gebalanseerde portefeuljes beter as hul gekapitaliseerde portefeulje-eweknieë, hoewel met wisselende grade oor verskillende lande. In Suid-Afrika, byvoorbeeld, het hoë vlakke van lekkasie oor die afgelope tien jaar en toenemende konsentrasie gelei tot swak relatiewe prestasie van die gebalanseerde portefeulje. In ander lande soos die Verenigde Koninkryk en Japan het gebalanseerde portefeuljes baie goed gevaar, met hoë vlakke van diversifikasievoordele en lae vlakke van lekkasie. Twee modelle word aangebied in 'n poging om die relatiewe afnames van die gebalanseerde portefeulje te verminder en die twee gewigte (gebalanseerd en gekapitaliseerd) op 'n optimale manier te meng. Hierdie modelle blyk goed te vaar in markte waar die gebalanseerde portefeulje swak prestasie en groot relatiewe afnames toon. IsiZulu: Lolu cwaningo luhlaziya ukusebenza kwephothifoliyo enesisindo esilinganayo isebenzisa isu elivela kwinjulalwazi ye-stochastic kuphothifoliyo. Lolu hlaka luvumela ukuhlukaniswa kokusebenza okuhlobene kwephothifoliyo enesisindo esilinganayo ibe izingxenye ezine eziyinhloko; ushintsho ekugxileni kuphothifoliyo enesisindo eyinhloko, imbuyiselo eyeqile ekhiqizwa inzuzo yokuhlukahlukaniswa, umehluko kuzilinganiso zezabelo, kanye negama elibizwa ngokuthi umphumela wokuvuza. Ngokuvamile amaphothifoliyo anesisindo esilinganayo enza kangcono kunozakwabo bephothifoliyo enesisindo esinhloko, nanoma enamazinga ahlukahlukene ngokuphambanisa amazwe ahlukene. ENingizimu Afrika, ngokwesibonelo amazinga okuvuza kule minyaka eyishumi edlule aphezulu futhi ukwanda kokugxilisa ingqondo kuye kwaholela ekusebenzeni kabi okulinganiselwe kwephothifoliyo enesisindo esilinganayo. Kwamanye amazwe anjenge-United Kingdom ne-Japani, amaphothifoliyo anesisindo esilinganayo enze kahle kakhulu, ngamazinga aphezulu ezinzuzo zokuhlukahlukana kanye namazinga aphansi okuvuza. Imifanekiso emibili eyethulwe ngomzamo wokunciphisa ukucekelwa phansi okusimeme kwephothifoliyo enesisindo esilinganayo kanye nokuhlanganisa izisindo ezimbili (ezilinganayo neziyinhloko) ngendlela enhle kakhulu. Le mifanekiso ibonakala yenza kahle ezimakethe lapho iphothifoliyo enesisindo esilinganayo inokusebenza okungalungile kanye nokudonselwa phansi okusimeme okukhulu .
The effect of observation errors on parameter estimates applied to seismic hazard and insurance risk modelling
Pretorius, Samantha (University of Pretoria, 2014-04-30)
The research attempts to resolve which method of estimation is the most consistent for the parameters of the earthquake model, and how these different methods of estimation, as well as other changes, in the earthquake model parameters affect the damage estimates for a specific area. The research also investigates different methods of parameter estimation in the context of the log-linear relationship characterised by the Gutenberg-Richter relation. Traditional methods are compared to those methods that take uncertainty in the underlying data into account. Alternative methods based on Bayesian statistics are investigated briefly. The efficiency of the feasible methods is investigated by comparing the results for a large number of synthetic earthquake catalogues for which the parameters are known and errors have been incorporated into each observation. In the second part of the study, the effects of changes in key parameters of the earthquake model on damage estimates are investigated. This includes an investigation of the different methods of estimation and their effect on the damage estimates. It is found that parameter estimates are affected by observation errors. If errors are not included in the method of estimation, the estimate is subject to bias. The nature of the errors determines the level of bias. It is concluded that uncertainty in the data used in earthquake parameter estimates is largely a function of the quality of the data that is available. The inaccuracy of parameter estimates depends on the nature of the errors that are present in the data. In turn, the nature of the errors in an earthquake catalogue depends on the method of compilation of the catalogue and can vary from being negligible, for single source catalogues for an area with a sophisticated seismograph network, to fairly impactful, for historical earthquake catalogues that predate seismograph networks. Probabilistic seismic risk assessment is used as a catastrophe modelling tool to circumvent the problem of scarce loss data in areas of low seismicity and is applied in this study for the greater Cape Town region in South Africa. The results of the risk assessment demonstrate that seemingly small changes in underlying earthquake parameters as a result of the incorporation of errors can lead to significant changes in loss estimates for buildings in an area of low seismicity.
Investigating the threshold of event detection with application to earthquake and operational risk theory
De Witt, Corn e Juan (University of Pretoria, 2013)
This study provides systematic analysis of points of structural change in probability distributions. In observed frequency data of earthquakes, such a threshold exists due to the non-detection of events below a certain magnitude. By examining the factors in uencing the operational risk exposure of institutions, a similar threshold is hypothesized to exist in operational loss data. In both elds of study, this threshold is termed the threshold of completeness, above which 100% of events are de- tected. External factors have caused this level of completeness to shift over time for earthquake data. The level of complete recording in uences the volume of data that can be consistently incorporated in a study of seismic activity. Such data can be used by re-insurers and direct writers of catastrophe agreements who deal in seismic hazard. Historically, a variety of methods have been proposed by authors in an attempt to gauge the location of the threshold of completeness in earthquake data. This study aims to evaluate the e cacy of some of the most prominent methods under di ering assumptions regarding the incomplete portion of the data. Furthermore, a new threshold estimation scheme (MITC) is developed and tested against the prevailing methods. Additionally, earthquake data and the wealth of literature will aid in introductory analysis and assessing applicability of esti- mation techniques in the context of operational losses.
Artificial neural networks and their application to modelling South African market returns
Smith, Matthew Lee (University of Pretoria, 2014)
The modelling technique known as Artificial Neural Networks (ANNs) is investigated. ANNs have the ability to detect and project non-linear relationships between variables. Further, they can adapt in dynamically changing environments while providing accurate results. A method of constructing ANNs in order to form a forecasting system is presented here. Further, in many of the applications studies, ANNs are fitted using crude guesses as to the efficient input parameters. In this study detailed investigations into parameter estimates are performed. In addition, ANNs and traditional models (ARIMA, seasonal smoothing, geometric Brownian motion, etc.) are constructed to forecast monthly inflation and the average monthly return on the money, bond and equity markets in South Africa from 1975 to 2010. The ANNs constructed are done through an integrated and isolated approach. The performance of the traditional and ANN models are compared. No general conclusion, as to which model is superior for all the applications considered, can be made. This suggests that ANNs perform as well as traditional models when forecasting financial markets. Further, it is found that the money market and inflation are forecast efficiently through all the models, over a single month. As the forecast period extends to three months the money market favours the traditional model. However, a forecast period of twelve months leads to the preference of ANNs in the case of the money market. Neither technique can forecast the equity or bond market accurately, as these require additional explanatory variables to those considered. As the forecast period increased, the forecast accuracy decreased for all the models. The integrated ANNs, which allow interaction between the markets, do not lead to improved forecasts which indicates that the relationships between the markets have a limited effect on the future values of the markets. Hybrid models are constructed, trained and tested for the money market and inflation. They are found to add value to traditional models when forecasting inflation but not the money market. The sensitivity of the performance of ANNs and the traditional model to different subsets of the inflation data is tested. No statistical difference between the models is found. The implementation advantages of ANNs are also described.
Top-down stress testing of the largest full service South African banks
Conradie, Dirk Cornelis Uys (University of Pretoria, 2020)
Banks are key to a well-functioning economy. Periods of economic stress could put banks and therefore the financial system at risk so regulators such as the Prudential Authority in South Africa need to know if banks are resilient to economic stress. A model that forecasts the impact of severe economic stress is developed using publicly available information. The model forecasts the credit losses, deposit volumes and other general equity movements of the biggest five full-service South African banks to assess capital and liquidity strain for any defined macroeconomic stress scenario over the next 3 years. The full-service banks being considered account for more than 90% of all bank lending in deposits in the market and therefore covers the vast majority of banking systemic risk in South Africa. It is shown that different macroeconomic factors affect these banks in different ways due to differences in the type of customers with deposits with each institution and differences in credit risk associated with various loan products. From an overall market perspective economic growth, lending levels, household debt levels and equity markets are the key drivers of deposit volumes. Credit risk in turn is primarily driven by interest rates, inflation and household debt to disposable income.
Modelling South African social unrest between 1997 and 2016
Smart, Sally-Anne (University of Pretoria, 2019)
Social unrest, terrorism and other forms of political violence events are highly unpredictable. These events are driven by human intent and intelligence, both of which are extremely difficult to model accurately. This has resulted in a scarcity of insurance products that cover these types of perils. Links have been found between the incidence of political violence and various economic and socioeconomic variables, but to date no relationships have been identified in South Africa. The aim of this study was to address this. Firstly, by identifying relationships between the incidence of social unrest events and economic and socio-economic variables in South Africa and secondly by using these interactions to model social unrest. Spearman’s rank correlation and trendline analysis were used to compare the direction and strength of the relationships that exist between protests and the economic and socio-economic variables. To gain additional insight with regards to South African protests, daily, monthly, quarterly and annual protest models were created. This was done using four different modelling techniques, namely univariate time series, linear regression, lagged regression and the VAR (1) model. The forecasting abilities of the models were analysed using both a one-step and n-step forecasting procedure. Variations in relationships for different types of protests were also considered for five different subcategories. Spearman’s rank correlation and trendline analysis showed that the relationships between protests and economic and socio-economic variables were sensitive to changes in data frequency and the use of either national or provincial data. The daily, monthly, quarterly and annual models all had power in explaining the variation that was observed in the protest data. The annual univariate model had the highest explanatory power (R2 = 0.8721) this was followed by the quarterly VAR (1) model (R2 = 0.8659), while the monthly lagged regression model had a R2 of 0.8138. The one-step forecasting procedure found that the monthly lagged regression model outperformed the monthly VAR (1) model in the short term. The converse was seen for the short-term performance of the quarterly models. In the long term, the VAR (1) model outperformed the other models. Limitations were identified within the lagged regression model’s forecasting abilities. As a model’s long-term forecasting ability is important in the insurance world, the VAR (1) model was deemed as the best modelling technique for South African social unrest. Further model limitations were identified when the subcategories of protests were considered. This study demonstrates that with the use of the applicable economic and socio-economic variables, social unrest events in South Africa can be modelled.
Quantitative topics in portfolio and risk management
Flint, Emlyn James (University of Pretoria, 2019)
English: The modern quantitative portfolio manager is the quintessential “jack of all trades”. Not only do they need to be an expert in the specific area of portfolio management, they also need to have a thorough understanding of the related areas of valuation, data processing, risk management and performance analysis. What this means practically is that quantitative portfolio managers are regularly faced with problems spanning the entire P − Q spectrum of quantitative finance. Spurred by this reality, the central research question motivating this thesis is exactly the core motivation behind every decision taken by a quantitative portfolio manager: What is the most efficient, practical method for constructing, managing and evaluating optimal multi-asset portfolios in dynamic, non-normal markets? In this thesis, we attempt to provide insight into this broad central research question by offering new perspectives and practical solutions to a selection of sub-problems that a quantitative portfolio manager would have to address in practice. In particular, this thesis is comprised of six essays that each tackle specific problems in the related areas of derivatives, return modelling, systematic trading strategies and portfolio construction. Sepedi: Molaodi wa sebjalebjale wa photefolio ya bontši ke "motho wa mabokgoni ka moka” a bohlokwa. Ga se fela gore ba swanetše go ba setsebi ka lefapheng le le itšego la taolo ya potefolio, ba swanetše gape go ba le kwešišo ye e tseneletšego ya dikarolo tše amanago le yona tša tekolo ya boleng, tshepetšo ya datha, taolo ya kotsi le tshekatsheko ya go diragatša. Se gabotse se ra gore balaodi ba diphotefolio tša bontši ka mehla ba lebana le mathata ao a akaretšago sepektheramo ka moka sa P − Q sa boleng bja dipalo tša ditšhelete. Ka ge e hlohleletšwa ke seemo se, potšišo ya nyakišišo ye bohlokwa ye e hlohleletšago thesese ye ke yona gabotse tlhohleletšo ya motheo ka morago ga sephetho se sengwe le se sengwe seo se tšerwego ke molaodi wa photefolio ya bontši: Ke mokgwa ofe wo o šomago gabotse kudu, mokgwa wo o šomago wa go aga, go laola le go sekaseka diphotefolio tša matlotlo a mantši tše di loketšego mebaraka yeo e fetogago, yeo e sego ya tlwaelega? Ka thesese ye, re leka go fa temogo ka ga potšišo ye ya nyakišišo ya ye e nabilego ya bogareng ka go fa dipono tše mpsha le ditharollo tše di šomago kgethong ya mathata a mannyane ao molaodi wa photefolio ya dipalo a bego a tla swanelwa ke go a rarolla tirišong. Gabotsebotse, thesese ye e bopilwe ka ditaodišo tše tshela tšeo ye nngwe le ye nngwe e rarollago mathata a itšego ka dikarolong tše di amanago tša ditšweletšwa, mohlala wa poelo, thulaganyo ya maano a kgwebišano le kago ya diphotefolio. Afrikaans: Die moderne kwantitatiewe portefeuljebestuurder is die tipiese kenner op alle gebiede. Nie net moet hulle 'n kenner wees op die spesifieke gebied van portefeuljebestuur nie, maar hulle moet ook 'n deeglike begrip hê van die verwante areas van waardasie, dataverwerking, risikobestuur en prestasieontleding. Wat dit prakties beteken, is dat kwantitatiewe portefeuljebestuurders gereeld te kampe het met probleme wat die hele P – Q spektrum van kwantitatiewe finansies dek. Aangespoor deur hierdie werklikheid, is die sentrale navorsingsvraag wat hierdie proefskrif motiveer presies die kernmotivering agter elke besluit wat deur 'n kwantitatiewe portefeuljebestuurder geneem word: Wat is die mees doeltreffende, praktiese metode vir die konstruksie, bestuur en evaluering van optimale multibateportefeuljes in dinamiese, nienormale markte? In hierdie proefskrif poog ons om insig te bied in hierdie breë sentrale navorsingsvraag deur nuwe perspektiewe en praktiese oplossings te bied vir 'n seleksie van subprobleme wat 'n kwantitatiewe portefeuljebestuurder in die praktyk sal moet aanspreek. In die besonder bestaan hierdie proefskrif uit ses opstelle wat elk spesifieke probleme in die verwante gebiede van afgeleides, opbrengsmodellering, sistematiese handelstrategieë en portefeuljekonstruksie aanspreek. IsiZulu: Imenenja yephothifoliyo ephathelene nokubala yesimanje yiyona esezingeni eliphezulu “engusazikonke maqondana nohwebo”. Akudingeki nje ukuthi abe uchwepheshe emkhakheni othile wokuphatha iphothifoliyo, futhi badinga ukuqonda kahle imikhakha ehlobene yokulinganisa, ukucutshungulwa kwemininingwane, ukuphatha ubungozi kanye nokuhlaziywa kokusebenza kahle. Okushiwo yiloku ngokusebenzayo ukuthi amamenenja amaphothifoliyo avamise ukubhekana nezinkinga ezihlanganisa i-spectrum se--P - Q sonke ngokuphathelene nezokubalwa kwezezimali. Ngokugqugquzelwa yileli qiniso, umbuzo osemqoka wocwaningo ogqugquzela le thesisi uyisona sizathu esingumnyombo wokugqugquzela isinqumo esithathwe imenenja yephothifoliyo ephathelene nokubala: Yiyiphi indlela enempumelelo kakhulu kabi, esebenzayo yokwakha, ukuphatha kanye nokuhlola amaphothifoliyo ezimpahla eziningi ezimakethe eziguquguqukayo, ezingezona ezejwayelekile? Kulolu cwaningo, sizama ukunikeza ukuqonda kulo mbuzo obanzi ongumnyombo wocwaningo ngokunikeza imibono emisha nezisombululo ezisebenzayo ekukhethweni kwezinkinga ezincane imenenja yephothifoliyo yokuphathelene nokubala okufanele abhekane nako uma kusetshenzwa. Ikakhulukazi, lolu cwaningo luqukethe ama-eseyi ayisithupha okuthi i-eseyi ngayinye ibhekana nezinkinga ezithile emikhakheni ehlobene yokuphuma kokunye, ukubuyiswa kwemifanekiso, amasu okuhweba ahlelekile kanye nokwakhiwa kwephothifoliyo.
An analysis of the determinants of sovereign credit ratings
Yang, Jack Chao (University of Pretoria, 2018)
The study aims to quantitatively assess the extent to which sovereign ratings could be explained by a set of economic variables. A wide variety of factors could potentially bias a credit rating agency’s decision. The analysis begins with replicating the results found in a seminal analysis by Cantor and Packer (1996). This analysis expanded by including more countries, dynamic over time and time lags. Multiple complementary statistical models and a Random Forest model are explored in this study. To ensure robustness of the model, out-sample-testing is applied. The results show that GNI per capita, GDP growth, total debt to GDP, inflation rate, default amount, default indicator, HDI, change in HDI and IMF indicator are statistically significant. It is observed that current account to GDP, GDP growth and inflation rate have a time-lagged effect on sovereign ratings. A further analysis by separating between developing and developed countries using the IMF indicator suggests that there is a discrepancy between developing countries ratings and developed country ratings. The model results also support the existence of subjective decisions or adjustments in sovereign risk assessment.
Network structure indirect losses and financial contagion in inhomogeneous stochastic interbank networks
Walters, Nadine Mari (University of Pretoria, 2019)
We introduce new tiered bank network structures, allowing for many di erent bank sizes, and compare risk propagation in these structures with the well-known Erd˝os-R´enyi, assortative and disassortative structures. The simulations indicate that in the presence of market sentiment and liquidity e ects, the details of the structures in combination with the distribution of assets, the system’s interconnectedness and its size are crucially important in determining the risk of major capital loss in the network. In fact, even networks with similar levels of tiering can behave markedly di erent depending on these factors. In the absence of market sentiment and liquidity e ects, the di erences between the network structures is smaller. This highlights the importance of considering the network structure in conjunction with network characteristics, market sentiment and liquidity e ects. This implies that policy actions aimed at influencing a network’s characteristics must consider all aspects unique to that particular system and cannot follow a ‘one-size-fits-all’ approach. The framework is illustrated with an application using South African bank balance sheet data. Spikes in simulated assessments of systemic risk agree closely with spikes in documented subjective assessments of this risk. This indicates that network models can be useful for monitoring systemic risk levels. In a large network setting, the study then considers the fraction of nodes that default in stochastic, inhomogeneous financial networks following an initial shock to the system. Results for deterministic sequences of networks are generalized to stochastic networks to account for interbank lending relationships that change frequently. A general class of inhomogeneous stochastic networks is proposed for use in systemic risk research, and we illustrate how results that hold for Erd˝os-R´enyi networks can be generalized to the proposed network class. The network structure of a system is determined by interbank lending behaviour which may vary according to the relative sizes of the banks. We then use the results to illustrate how network structure influences the systemic risk inherent in large banking systems.
Hattendorff’s theorem and Thiele’s differential equation generalized
Messerschmidt, Reinhardt (University of Pretoria, 2007-02-20)
Hattendorff's theorem on the zero means and uncorrelatedness of losses in disjoint time periods on a life insurance policy is derived for payment streams, discount functions and time periods that are all stochastic. Thiele's differential equation, describing the development of life insurance policy reserves over the contract period, is derived for stochastic payment streams generated by point processes with intensities. The development follows that by Norberg. In pursuit of these aims, the basic properties of Lebesgue-Stieltjes integration are spelled out in detail. An axiomatic approach to the discounting of payment streams is presented, and a characterization in terms of the integral of a discount function is derived, again following the development by Norberg. The required concepts and tools from the theory of continuous time stochastic processes, in particular point processes, are surveyed.
Risk evaluation techniques in a general insurance environment
Van den Heever, Rudolf Johannes (University of Pretoria, 2005-11-01)
Please read the abstract in the section 00front of this document
Die wanbetaling van lewensversekering : ‘n analise van die redes, die gevolge vir die versekeraar, kliënt, bemarker en remediërende optrede (Afrikaans)
Van der Walt, Phillipus Jacobus (University of Pretoria, 2011-04-07)
AFRIKAANS: Die lewensversekeringsbedryf in Suid-Arrika is ‘n groot mobi1iseerder van langtermyn diskresionêre kapitaal en verleen beskerming teen finansiële ver1iese wat weens die intrede van persoonlike risiko’s voorkom. Die mate waarin fondse na die bedryf vloei toon dat die publiek lewensversekering wel belangrik ag en dat dit reeds ‘n algemene begrip en ‘n belangrike komponent van die uitgawes of kontantvloei van baie huishoudings vorm. Soos in die res van die wêreld. gaan die plaaslike bedryf ook gebuk onder die probleem dat k1iënte hulle versekering tot nadeel van al die belanghebbers ontydig beëindig. Daar bestaan nie ‘n bepaalde of dominante rede vir die wanbetaling van versekering nie, maar dit kan aan die sameloop van verskillende faktore toegeskryf word. Groot bedrae geld word op hierdie wyse oneffektief aangewend en nie benut waarvoor dit bedoel was nie. Uit die studie het dit duidclik geword dat die kliënte baie onkundig met betrekking tot persoonlike finansiële beplanning is waar ’n versekering ‘n besondere belangrike rol speel. Tydens die bemarkingsproses maak kliënte hoofsaaklik op die tussengangers se ervaring. kennis, betroubaarheid, integriteit ens., staat om van die “beste of toepas1ike advies" voorsien te word. Dit plaas lewensversekering in die kader van finansiële dienste en moet die kenmerke, te wete. nie-tasbaarheid. bederfbaarheid ens., deeglik in ag geneem word. K1iënte se reaktiewe optrede veroorsaak dat die meeste versekering aan hulle verkoop en nie gekoop word nie. Voorspruitend hieruit rus ‘n verpligting op versekeraars om toe te sien dat hulle tussengangers toegerus is om aan die kliënte se verwagtinge te voldoen. Indien nie, is die beskerming wat tans aan die kliënte via selfregulering, die Suid-Afrikaanse reg, ens., verleen word, so gebrekkig dat dit van nul en gener waarde is. Die belanghebbers se interafhanklikheid vereis dat elkeen ‘n verpligting het om toe te sien dat die diskresionêre kapitaal optimaal benut word. Die versekeraars se onherroeplike enIof onbeperkte afhanklikheid van kliënte en tussengangers noodsaak daadwerklike optrede deur hulle om die posisie te verbeter. Daar is egter geen beperking op versekeraars om aksie te neem nie, behalwe dit wat hulle self opgelê het. Die persepsie is dat die versekeraars poog om hulle verpligtinge teenoor die kliënte te systap. Die versekeraars kan die probleem op ‘n gefragmenteerde basis hanteer. Die gevaar is egter dat die simptome, in plaas van die probleem aangespreek word. Die ideaal is om die probleem holisties aan te spreek waarby die totale bemarkingsproses in heroorweging geneem behoort te word. Dit is egter twyfelagtig of statutêre intervensie enige oplossing gaan bied.
A framework for modelling losses arising from natural catastrophes in South Africa
Grobler, Roger R. (University of Pretoria, 2003-05-15)
Property insurance covers policyholders against losses arising out of a wide range of occurrences. Premiums are calculated by taking into account estimates of the frequency and the severity of the losses. Estimating the frequency and severity arising from claims caused by natural catastrophes is difficult, due to the relatively low frequency of natural catastrophes, and the unavailability of historical catastrophe claims data. The accumulation of a large number of claims in the geographical area affected by the catastrophe is of particular interest to insurers and reinsurers alike. This dissertation discusses the fundamental issues underlying the modelling insurance losses from natural catastrophes in South Africa. A suggestion is given of the key parameters that need to be taken into account, and a framework is given for models describing losses arising from floods, hail and tornadoes. Copyright

Browse

Recent Submissions