Masters Candidates

Testing Stochastic Dominance of Manufacturing Stocks at the NSE Market

Project Abstract

Stochastic dominance relationships between two or more variables is crucial in the field of actuarial science, econometrics and in studying reliability. This project applies Stochastic Dominance (SD) portfolio optimization methods to test the stocks that would do better during Kenyan electioneering periods. More and more scholars have shifted their attention to studying stochastic dominance relationships in decision theory. Some evidences presented by scholars in the area for many years have revealed that the methodology dominates many other solutions. Many methodologies assume contemporaneous as well as serial independence (assumption of no independence between samples and within a sample) which cannot be met by most observations in application since financial data features time series properties and positive correlation among observations from various samples. SD uses a distribution-free assumption framework which makes it suitable in checking dominance relationships between agricultural and manufacturing stocks. Besides, the SD relationships are based on empirical distribution differences. The methodology requires non-parametric statistical estimation as well as inference methods. SD is quite appealing to asset classes as well as investment strategies that exhibit asymmetric risk profiles. For example, small cap stocks and momentum strategies where variance would not adequately measure investment risk since it makes no distinction between bad risk and good risk. The assumptions of no arbitrage and tendency of investors to dislike risk are largely supported by capital market equilibrium models. The project focuses on first degree SD, second degree SD and third-degree SD tests to check for the stocks that would dominate the other in the two sectors of the economy during hard economic times brought about by electioneering periods.

Project Title: Modelling Determinants of Household Access to Credit in Rural Kenya

Project Abstract

The provision of credit has been considered as a stimulus to economic growth in the global economy. The improvement in access to credit services to households is seen as a method to alleviate poverty and better the well-being of rural households around the country. Financial services are mostly used by households to expand or start new businesses and cushion themselves from various income shocks. The investigator aimed to explore the various determinants of rural household access to credit through a multinomial probit, probit and tobit models, given the robustness of the data. The study also established how these determinants affect the access of credit by rural households. The study determined that those who have attained some level of education have a higher likelihood to access credit through a formal source as compared to individuals with no education in rural areas. It was also established that persons with low levels of education tend to access informal sources of credit more than the formal ones. The study additionally established that married couples borrowed more than un-married individuals.

Project Title: Modeling Household Electricity Consumption in Kenya using Top-down Approach Method

Project Abstract

Household electricity consumption has been a major contributor to the global energy demand and has increased quickly over the past decades. Therefore, this project attempts to examine the key factors influencing household electricity consumption in Kenya from a top-down perspective, by reviewing and evaluating previous research work. The study utilized both socio-economic indicators (e.g. gross domestic product, Number of households connected to the grid), demographic (population) and energy values (electricity tariff). Analysis results found that the gross domestic product and population provide significant impact on household electricity consumption. Nonetheless, the effect of the electricity tariff and the number of households connected to the grid failed to receive a significant support. This implies that future demand for household electricity demand in Kenya will significantly be determined by socioeconomic factors and demographic factors. Thus, these developments should be considered by policy makers in planning for energy in Kenya and developing economies.

Project Title: European Option Pricing Using Truncated Normal Distribution

Project Abstract

Option trading is one of the activities that take place in the financial market. Pricing these option is key for investor to ensure that the position they take offers good returns. The Black & Scholes model is widely used in pricing option although its underlying assumptions are inconsistent with the market dynamics. Some studies have been done aimed at improving the Black & Scholes model and in general the pricing of option. In this paper, we take the same motive but now use the truncated normal distribution instead of the normal distribution that has been used in previous studies. Under the truncated normal distribution, denoted by TND in this paper, the underlying asset’s log-return of is assumed to be bounded below and above. The boundary values are determined by the investor’s perceived realistic price ranges of the underlying asset. The basic statistics of the proposed model are derive. The martingale restriction and closed formulas for option pricing as well as the pricing error are presented. The put - call parity and duality and some of the Greeks are also formulated. From the numerical result of the study, the proposed model performs better than the classical Black & Scholes at different price ranges for European options.

Project Title: Range-Based Approach to Modelling and Forecasting Value-at-Risk

Project Abstract

The purpose of this thesis is to model and forecast value-at-risk based on range-measuring rather than the commonly acknowledged volatility models that are based on closing prices. The use of close-to-close prices in modelling and forecasting value-at-risk might not capture important intra-day information about the price movement. As a result, crucial price movement information is lost and consequently the model becomes less efficient. This thesis recommends the inclusion or range-measuring, described as the difference between the highest and lowest prices of an underlying stock within a time interval, a day, to compute Value-at-Risk. The project uses data of an NSE-listed and trading company, SASN, between November 2009 and November 2019 on which the predictability of range-based and close-to-close estimates was established. It was observed that the values obtained by range-based models were more accurate than when only the daily closing prices are used. The range-based models successfully capture dynamics of the volatility and achieves improve performance relative to the GARCH-type models. These findings are fairly consistent and can be extended to applications like portfolio optimization.

Project Title:Eta- Ricci Soliton on W_3 and W_5-Semi Symmetric LP Sasakian Manifolfds

Abstract

The goal of this project is to study some properties of eta-Ricci soliton on LP-Sasakian manifolds. In this work, eta-Ricci solitons on LP-Sasakian manifolds which satisfy the semi-symmetric conditions R(X,Y).R(Z,U)=0 also given by U.C. De are considered. Particularly, we based our study on R(\xi,X).W_3(Y,Z)=0 and R(\xi,X).W_5(Y,Z)=0 The study is motivated by the results that are obtained in eta-Ricci solitons on Para-kenmotsu manifolds. This led us to study or simply to investigate the eta-Ricci solitons on W_3 and W_5 semi-symmetric LP-Sasakian manifolds satisfying the same conditions and see if a similar results are obtained. In addition, we prove that W_3 and W_5 semi-symmetric LP-Sasakian manifolds satisfying the semi-symmetric conditions R(\xi,X).W_3(Y,Z)=0 and R(\xi,X).W_5(Y,Z)=0, and having the eta-Ricci soliton structure are Einstein according to the value of lambda and a further conditions W_3(\xi,X).R(Y,Z)=0$ and $W_5(\xi,X). R(Y,Z)=0 where dot denote the derivative of algebra at every point of a tangent space, say $T_{p}(U)$.

Project Title :Hybrid GARCH(1,1) European Option Pricing Model with Ensemble Empirical Mode Decomposition

Abstract

Despite the option pricing importance in risk management and selection of portfolios, it is challenging to accurately price options due to unpredictable feature of asset prices. There are numerous risks in the nancial markets, mainly emanating from the inaccurate computation of option prices. The inaccuracy is mostly attributed to volatility. Using GARCH or other stochastic processes directly is unsuitable for option pricing. There is the need to decompose original series with some properties to attain more financial time series aspects. E-E-M-D generally performs well in capturing volatility and option pricing of financial data with non-linearity and non-stationarity properties. We construct a hybrid GARCH(1,1) model with the ensemble empirical mode decomposition in European option pricing. Using E-E-M-D, we decompose the original daily returns into low frequency, high frequency, and trend terms, and use these terms in the hybrid GARCH(1,1) European option pricing model in options pricing. We obtain option prices for different maturities by applying Monte Carlo simulation. Our empirical results clearly illustrates that the hybrid GARCH(1,1) European option pricing model eectively predicts volatility features and performs better than BSM73 and GARCH-M(1,1). The performance of the hybrid GARCH(1,1) European option pricing model incorporating just the low-frequency term further depicts the significance of decomposing the original returns using E-E-M-D by reducing option pricing errors significantly. Therefore, the hybrid GARCH(1,1) European option pricing model is a highly innovative and effective method of option pricing.

Project Title: Claims Reserving for Non-life Insurers using a Bayesian Approach

Abstract

Claims reserving is a major role for actuaries in the general insurance industry. A deficiency in the level of the reserves could lead to a company failing to honour its obligations and even lead to insolvency. It is crucial that the methods used for calculating reserves be as accurate as possible in predicting the expected claims for an insurer. The estimation of claim reserves by actuaries revolves around incurred but not reported claims. There are different methods available for this estimation, broadly grouped into deterministic and stochastic methods. The Basic Chain Ladder method, a deterministic method, is compared to the Mack model, a stochastic model. The main advantage of the latter is that it has additional measures of precision of reserve estimates and can be used to determine the possible standard error associated with the model fit. Finally, a Bayesian approach to loss reserving is modelled by considering a growth curve for the claims development. This framework allows for additional information, not present in the data to be included in the model development. The model resulting from a Bayesian approach entails a predictive distribution of possible reserve estimates. The computational difficulties associated with using Bayesian methods are made easier to deal with using Markov Chain Monte Carlo techniques. The prediction power of all models are compared in order to determine whether the use of more complex models leads to improved reserve estimates.

Project Title: Modelling Efficacy of Demographic Changes on Capital Investment Returns: A Case of Kenya between 1965 and 2015

Abstract

Demographic changes have long been assumed to affect investment decisions. Little is known about the efficacy of demographic variables on capital investment despite the rising concerns in unemployment. Capital investment has been identified as important in solving the problems associated with demographic changes. There exists a huge gap in the literature between demographic changes and capital investment. Therefore, in this study, the focus is to establish the efficacy of demographics changes on capital investment returns using a case study of Kenya between for data collected between 1965 and 2015. The study specifically sorts to estimate mathematical model explaining the relationship between average age increase and capital investment, model population growth rate and capital investment returns, determine the relationship between life expectancy and capital investment returns and model dependency ratio, and capital investment returns. The study used secondary data sourced from the public website. Data analysis via SPSS, excel, and R establish that average age increase, population growth rate, life expectancy, and dependency ratio all have a positive correlation with capital investment returns since the Pearson’s correlation values obtained are 0:252; 0:492; 0:305 and 0:269 respectively. Regression analysis established that average age increase, dependency ratio, and life expectancy positively influence capital investment returns while population growth rate negatively impacts capital investment returns. Model analysis suggests that the average age increase positively impacts capital investment. The model equation for population growth rate and capital investment return have logarithmic relationships. The model analysis determines that life expectancy and capital investment return has direct proportionality. Dependency ratio and capital investment return have direct proportionality. The study concludes that demographic variables used are useful in predicting capital investment in Kenya. The study recommends an extension of the period under review and the addition of other demographic variables to add knowledge to the area.

Project Title: Monitoring Routine Health Indicators from District Health Information System (DHIS2): A Statistical Subsampling Approach

Abstract

Background: In Kenya, routine data is collected using the District Health Information System (DHIS2). This data is continuously collected and cheaper to obtain compared to surveys. Currently, there has been increased advocacy for using this data by governments and development organizations such as the World Health Organization (WHO) but it is unclear about how much DHIS2 data one needs to estimate indicators. All the studies that have used routine data use all the available reports to obtain estimates. This study proposes a novel sub-sampling approach to the estimation of indicators from routine data. This study hypothesized that subsamples of routine data can still provide credible estimates. Methods: We used data from 1,808 health facilities in Western Kenya from DHIS2. Information of 5 data elements, we computed three indicators, namely; the coverage of the third dose of pentavalent vaccine (DPT3), the proportion of pregnant women who receive LLINs, and the proportion of pregnant women who completed at least 4 ANC visits. The study then uses both spatial and non-spatial sampling to obtain proportions of data (90%, 80%, 70%, 60%, 50%, 40%, 30%, and 20%) from the entire dataset and compute estimates with corresponding confidence intervals (CIs). A z-test and power calculations were done to test for significant difference between the subsample estimates and the population estimates. Results: There was no significant difference between the population estimate and sub-sample estimates (all p-values > 0.05). However, smaller samples exhibited large CIs, mostly below 60% sample size. Conclusion: The results of this study imply that one doesn't need a universe of all health facilities to obtain estimates from DHIS2. The power calculation also supported this conclusion. However, based on the CIs of the estimates, we recommend sample sizes above 60%. Keywords: Routine data, Health facility data, Monitoring Indicators, Spatial sampling

Project Title: Testing Weak Form of Market Efficiency of Exchange Traded Funds at NSE Market

Abstract

Market efficiency is defined as a case when the prices in a market reflects the information, which is currently available within the market, or otherwise, the market is said to be inefficient whenever the prices of a financial security in not reflected by the information available to all local and international investors who are trading in the securities market. Having a better understanding of the market efficiency when trading an Exchange Traded Fund of any given set of securities in an exchange market is extremely vital for any prospective investor who need to make sound investment decisions as well as market predictions. When trading in a market with few traders who likes dominating the market through insider trading, it is more likely to experience securities exchange market without confidence of investors thus depicting fragile shape of the systematical market efficiency. Nairobi Securities Exchange market is important in the economy especially for those companies that are looking forward to capital or startups in the Kenyan Market from a global perspective. While testing of the fragile shape of efficient market hypothesis or EMH of the Nairobi stock exchange (NSE) which is done on day to day or after a week basis securities guide data from NSE 20 share grade within the period, 2nd February 2002 to May 2nd 2019. The research study applies the use of secondary NSE data that was derived from Nairobi Stock Exchange market website. This research has deviated from the normal and conventional linear approach to test market efficiency and use of using unit roots to test serial correlation. The daily returns in aspect to skewness as well as kurtosis was found to be non-normal. Similar demonstrations resulted from the Kolmogorov Smirnov test. From the results, null hypothesis of the normality was not rejected. In this research, there is the use of fractional integration thus utilization of ARFIMA to test long term memory and even the traditional unit root test is incorporated to compare both results thus giving a perfect conclusion on whether NSE stock market is definitely weak form efficient. Moreover, NSE-20 share Index stocks are used to make an Exchange Traded Fund that is priced and forecasted that is important for investors looking forward to make investments at the NSE Market in Kenya due to its mimicking ability. Ultimately, the forecasted values of ETF is done on the trendlines similar to the NSE-20 share Index trends, which investors to make informed financial decisions when buying any securities traded in NSE market.

Project Title: A RE-EXAMINATION OF A GENERALIZED FIVE PARAMETER LINDLEY DISTRIBUTION (G5L).

Abstract

In this project ,Generalized Five Parameter Lindley distribution(G5L) has been proposed as a new generalization of Lindley capable of modeling different shapes with increasing, decreasing, constant and bathtub failure rates. It has been constructed using finite mixture as the tool and Gamma as the special function. Construction of G5L,has been expressed in terms of Probability density function, Cumulative distribution function, Survival function, Hazard function, Reverse hazard function, Residual lifetime function, Mean residual life function, Equilibrium distribution, Survival function of equilibrium distribution and Hazard function of equilibrium distribution.G5L was applied to real data from Nichols and Padgett on breaking stress of Carbon fibers(2006) to draw shapes and test goodness of fit. Parameters were then estimated using Moment matching method(Mom) and Maximum likelihood estimation(MLE).The results obtained proved that G5L provided better fit than other generalizations of Lindley hence more flexible. G5L is therefore, recommended for modeling lifetime data that fails to follow other generalizations of Lindley because of its extensiveness.

Project Title : Small area estimation with an application to bivariate spatial modelling of hypertension and diabetes prevalence in Kenya

Abstract

Comorbidity of Hypertension and diabetes leads to significant risks of mortality and other non-communicable diseases (NCDs) such as heart attacks and strokes. Kenya, like many low and middle-income countries (LMICs), faces a rapid increase in non-communicable diseases (NCDs) burden. However, sub-national burden profiles to inform health policy at the county level; the current health planning units are implausible due to small sample sizes from the existing NCDs data sources in Kenya. The main objective of this study was to determine the distribution of hypertension and diabetes disease prevalence at county units in Kenya using small area estimation methods. Methods: Data from a nationally representative Kenya STEPwise survey for non-communicable diseases risk factors (STEPs-2015) was used. The survey collected health information (physical and biochemical measurements), risky behaviour and demographic indicators related to NCDs for 4,500 persons aged 18-69 years. Multivariate conditional autoregressive models that account for spatial autocorrelation and dependence between diseases (latent effects) were used to estimate the county-specific prevalence of hypertension and diabetes. Simple multivariate improper CAR, improper multivariate CAR, proper multivariate CAR and M-model latent effects were explored. A mixed-effects multinomial logistic regression model was t to identify the macro-risk factors of hypertension and diabetes in Kenya. Results: The M-model was selected as the best fit based on DIC. Substantial geographical variation in the prevalence of hypertension ranging from 9% in Wajir county and 54% in Nyeri county while diabetes ranged from 0.1% in Narok to 8.1% in Makueni were observed. Overall, 47% (22 counties) and 36% (17 counties) had hypertension and diabetes prevalence estimates above the national burden, 26.4% and 2.7% respectively. Notably, Mombasa, Kiambu, Embu and Nyeri had a substantial burden of both hypertension and diabetes. High cholesterol, central obesity, age, BMI, harmful alcohol intake and high sugar intake were significantly associated with hypertension and diabetes. Conclusion: The county-specific prevalence estimates provide the first evaluation of hypertension and diabetes burden that policymakers can use to inform interventions aimed at the prevention and treatment of NCDs in Kenya. Implementation of comprehensive screening programs and awareness building for NCDs control is crucial in reducing hypertension and diabetes burden in Kenya.

Project Title: Deformation and Resolution of Surface Singularities.

Abstract 

In this dissertation, we study ADE surface singularities in terms of Dynkin diagram obtained by deforming and resolving the singularity. Using classic invariant theory, we describe how these surface emerge as quotient of \mathbb{C}^2 /\Gamma, where $\Gamma \subseteq SL_2(\CC),$ is a finite subgroup of the group of $2×2$ matrix of determinant $1$ over C. We further describe how these hypersurface embed in \mathbb{C}^3 as an affine varieties. We deform $ A_n$ type singularity and show its relation to McKay-quivers. Finally, we investigate the the exceptional locus of the resolution of the those isolated singularities using sequence of blowup and from this we obtain the corresponding Dynkin diagram of ADE type.

Project Title: Modeling Interest Rate on Economic Growth of Kenya between 1970 and 2018

Abstract

The high-interest rate has been a problem in Sub-Saharan Africa, specifically Kenya, for a long time. The high-interest rates have prevented the growth of companies since they shun away from borrowing capital to grow their business. Most governments have used interest rate capping as a ceiling tool to regulate and control the excessive interest rate by financial institutions. During interest rate capping periods, the Kenyan government controls the official interest rate for banks operating within their borders, hence reducing banks’ appetite to deposit, which may reduce money in circulation, thus reducing demand and supply. Developing countries, like Kenya, tend to have a negative real interest rate resulting from administrative controls on nominal interest rates and burdensome regulations of their financial markets. Existing studies that have indirectly linked interest rates and economic growth are from Latin America and Asia. Furthermore, existing studies have adopted inappropriate mathematical tools to relate to interest rates and economic growth. The study sort to the model interest rate on the economic growth of Kenya between 1970 and 2018. The study specifically 1) Model interest rate capping and economic growth of Kenya. 2) Model mathematical relationship between the lending interest rate and economic growth of Kenya. 3) Estimate the mathematical relationship between the deposit interest rate and economic growth of Kenya and 4) Approximate mathematical relationship between the real interest rate and economic growth of Kenya. Data analysis based on SPSS, Matlab, Excel and R for secondary data central bank of Kenya website indicated that only the real interest rate has a positive correlation with economic growth. Regression analysis also suggests that only the real interest rate positively affects economic growth. Descriptive statistics indicated that the capping interest rate has the highest standard error mean (1.1536), and economic growth had the least standard error mean value (0.5936). The models formulated also show capping interest rates and lending interest rates have negative relationships with economic growth. The relationship between the deposit interest rate and economic growth is based on regression equation and deposit interest rate is estimated based on an optimization problem. The optimization problem solution indicates that the optimal deposit interest rate is 0.06039. The real interest rate model formulated also shows that a positive relationship with economic growth. The study concludes that the interest rate is significant in economic growth. The study suggests a future segmented short- and long-term effects of interest rate indicators on economic growth.

Project Title: Modelling Effects of Crude Oil Prices on GDP Growth and Inflation in Kenya using ARDL Model

Abstract

The project seeks to investigate the change in inflation and GDP growth brought by changes in crude oil prices in Kenya. Two Auto Regressive Distributed Lag Models (ARDL) have been applied on a yearly data from 1980 to 2018. The first ARDL model establishes a relationship between crude oil prices and the GDP growth, while the second gives a relationship between crude oil prices and the inflation in Kenya. Control variables relevant to the two models were identified after a thorough literature review. ARDL bound test cointegration framework has been utilized in establishing the existence of a long-term relationship. According to study findings, there exists a long-term relationship between oil prices and GDP growth, and oil prices and inflation. Moreover, a highly significant short-term outcome in a one-year period for the two macroeconomic variables has been identified.

Project Title: A spatial survival model for risk factors of under-five child mortality in Kenya

Abstract

Child mortality is high in Sub-Saharan Africa compared to other regions in the world. In Kenya, the risk of mortality is assumed to vary from region to region due to diversity in socio-economic and even climatic factors. Recently, the country was split into 47 different counties and health care devolved to those county governments further aggravating the spatial differences in health care from county to county. This study examines the spatial variation in the risk factors of Under 5 Child Mortality (U5CM) in Kenya. Data from the Kenya Demographic Health Survey (KDHS-2014) with newly introduced counties was used to analyze this risk. Using a spatial cox proportional hazard model, an intrinsic conditional Autoregressive Model was fitted to account for the spatial variation among the counties in the country while the Cox model was used to model the risk factors associated with time to death of a child. Inference on the risk factors and the spatial variation was made in a Bayesian setup based on the MCMC technique to provide posterior estimates. Our findings showed that there exists a significant spatial variation on the risk of mortality in the country. Different rates and determinants for under-five mortality were observed from county to county. Counties in central Kenya have the highest hazard of death, while western counties have the lowest hazard of death. Demographic factors such as sex of the child and the household head, and social economic factors such as level of education account for most variation when the spatial differences are accounted for. The findings can help the country to plan on health care intervention at a subnational level, by ensuring that counties with higher risk of under five mortality are considered differently from counties experiencing much less risk of death.

Project Title: ON ALUTHGE TRANSFORMS AND SPECTRAL PROPERTIES OF DIFFERENT CLASSES OF OPERATORS IN HILBERT SPACES.

Abstract

For any linear operator T acting on a Hilbert space H, its Aluthge transform is another linear operator on H. It is known that Aluthge transform of an operator preserves the spectral properties of that operator and more importantly that an operator T has a non trivial closed invariant subspace if and only if its Aluthge transform has.

Project Title: INCIDENCE AND DERTERMINANTS OF LOST TO FOLLOW UP AMONG PATIENTS ON ANTIRETROVIRAL THERAPY

ABSTRACT

Death is ofttimes ignored in lost to follow up studies yet it is a competing event in such cases as it is informative of its probability. A couple of studies have been done on incidence and determinants of lost to follow up however solid estimates may be found if death as a competing event is taken into account rather than censoring. The goal of the study seeks to find out the incidence and determinants of lost to follow up with and without death as a competing event. Cox proportional hazards model and Fine-Gray's subdistribution hazards model were employed to model the outcome of the determinants on lost to follow up. Kaplan-Meier graph was done to describe the probability of lost to follow up in the cox proportional hazards model while cumulative incidence function was done to describe the incidence of lost to follow up while taking death as competing event into account. Each variable was tested for the assumption of proportional hazards before inclusion in the final model using Schoenfeld residuals. 1047 patients were included in the study. The overall lost to follow up rate was 14% with 2.4 per 100-person years incidence rate. Being male, having CD4 count of < 200 mm^3 and a younger age (15-30 years) were significant determinants of lost to follow up, hence there is need to give extra attention to these groups of people in order to improve HIV care service delivery.