Strathmore Institute of Mathematical Sciences (SIMs)http://hdl.handle.net/11071/39332022-11-30T14:41:40Z2022-11-30T14:41:40ZUsing semi-Markov process to model incremental change in HIV staging with cost effectAndrew, Joram Maluluihttp://hdl.handle.net/11071/129122022-08-02T06:23:01Z2021-01-01T00:00:00ZUsing semi-Markov process to model incremental change in HIV staging with cost effect
Andrew, Joram Malului
Over the past years, parametric and non-parametric methods have been used in modelling cost and effectiveness according to one studied event or one health state. In this study we used semi-Markov model in which the distributions of sojourn times are explicitly defined. Weibull distribution was chosen and used in modelling the hazard function for each transition. Using a regression model for cost, a cumulative cost function of cost was developed enabling us to determine the estimated mean cost per patient in each state defined in the semi-Markov model. ICER was used for cost effectiveness analysis in comparing two strategies (Patients in DCM and patients not in DCM) of follow up. Using viral load, three states were defined; V L < 200ml, 200ml < V L < 1000ml, V L > 10000ml and an absorbing state death. The mean cost of the patients for each state 1, 2 and 3 was $765, $829 and $1395 respectively. The calculated ICER ratio was $483.8268/life-year-saved. The cost of keeping patients in state 1 (on DCM) was relatively cheaper and efficient compared to the other states.
A Research Thesis Submitted to the Graduate School in partial fulfillment of the requirements for the Award of Master of Science Degree in Statistical Sciences at Strathmore University
2021-01-01T00:00:00ZModelling and forecasting of crude oil price volatility: comparative analysis of volatility modelsNg’ang’a, Faith Wacukahttp://hdl.handle.net/11071/129072022-07-25T08:52:40Z2021-01-01T00:00:00ZModelling and forecasting of crude oil price volatility: comparative analysis of volatility models
Ng’ang’a, Faith Wacuka
This study aims at providing an in-depth analysis of forecasting ability of different GARCH
models and to find the best GARCH model for VaR estimation for crude oil. The VaR forecasting performance of GARCH-type models are analyzed and compared in a long horizon; based on the Kupiecs POF-test and Christoffersens interval forecast test as well as a Backtesting VaR Loss Function. Crude oil is one of the most important fuel sources and has contributed to over a third of the world’s energy consumption. Oil shocks have influence on macroeconomic activities through various ways. Sharp oil price changes delay business investment because they raise uncertainty thus reducing aggregate output for some time. Modelling and forecasting of crude oil prices plays a significant role in supporting policy and decision making in the economy. Successive developments of models used provide opportunities to analyse crude oil market in depth and improve the accuracy of oil price forecasting. The study uses Brent Crude Oil prices data over a period of ten years from the year 2011 to 2020. The study finds that the IGARCHT distribution model is the best model out of the five models for VaR estimation based on LR.uc Statistic (0.235) and LR.cc Statistic (0.317) which are the least among the values realized. ME and RMSE for the five models used for forecasting have negligible difference. However, the IGARCH model stands out with IGARCH- T-distribution being the best out of the five models in this study with ME of 0.0000963591 and RMSE of 0.05304335. We therefore conclude that the IGARCH- T distribution model is the best model out of the five models used in this study for forecasting Brent crude oil price volatility as well as for VaR estimations.
Research thesis submitted to Strathmore University in fulfillment of the requirements for the Master of Science in Mathematical Finance
2021-01-01T00:00:00ZModelling the relationship between spot and futures prices: an empirical analysis of the South African Power PoolMutembei, Kellyjoy Makenahttp://hdl.handle.net/11071/129062022-07-25T08:39:25Z2021-01-01T00:00:00ZModelling the relationship between spot and futures prices: an empirical analysis of the South African Power Pool
Mutembei, Kellyjoy Makena
This study investigates the relationship between electricity spot and future prices in the South African Power Pool (SAPP). The objectives of the study included investigating whether forward prices in the SAPP are a true and unbiased estimate of the observable spot prices by determining whether or not a forward premium exists in the market. Investigating whether the forward premium (if it exists) can be explained by the behaviour of spot prices in the market in the period preceding delivery and lastly whether current future prices in the SAPP can be used to predict future spot prices in the market. The study used daily electricity spot prices in the SAPP for the period between April 1, 2017 and January 31, 2021 and electricity futures price data for weekly and monthly contracts during the same period. Relying on methodologies highlighted in the expectation hypothesis to describe the relationship between spot and futures prices, results indicate the existence of positive significant premiums in the market for the sample period. The premiums decrease with increasing maturity with the value of relative forward premiums ranging between 1.23 USD/MWh for peak weekly contracts to 0.46 USD/MWh for peak monthly contracts. Power purchasers in the SAAP are on average incurring a cost that inflates their cost of power by 0.24% to 1.23% depending on the hedging strategy they adopt and type of contracts they select. To explain the risk premia, the study followed methodologies highlighted in the General Equilibrium Model. Ordinary Least Square (OLS) regression results for forward premia modelling suggests that for some of the contracts in the SAPP, forward premiums can be at least partially explained by the mean, variance, standard deviation and skewness of the spot prices in the period preceding delivery. Particularly, the premiums have a negative relationship with average spot prices and a positive relationship with skewness. This implies that the higher the average spot price level, the lower the likelihood of overestimating future prices thus the lower the premium. Additionally, the higher the probability of upward price spikes, the higher the futures price thus the higher the premium. Lastly, to investigate forecasting ability of electricity futures in the SAPP, the study relied on the fundamentals of futures pricing suggested in the expectation hypothesis. Results reveal that future’s prices at the SAPP do not contain significant forecasting power over future spot prices in the SAPP. They reveal that variations in the forward premiums in the market are attributable to time varying risk premiums. The SAPP to a large extent relies on coal and nuclear power for electricity generation thus this could explain the reason why results led to the conclusion of the existence of time varying risk premiums.
Research thesis submitted to Strathmore University in fulfillment of the requirements for the Master of Science in Mathematical Finance
2021-01-01T00:00:00ZEmpirical performance of alternative risk measures in portfolio selection - the case of South African stock marketMacharia, Richardhttp://hdl.handle.net/11071/129052022-07-25T07:27:05Z2021-01-01T00:00:00ZEmpirical performance of alternative risk measures in portfolio selection - the case of South African stock market
Macharia, Richard
Portfolio selection is the process of apportioning capital to a finite number of assets given the wider set of all investment options. The decision of best combination of assets to invest in is the subject of debate among practitioners and researchers alike. Individuals face a multitude of constraints when making allocation decisions thus their patterns of investing are wildly different. However, economists have studied asset price patterns for long enough to be able to pick out aggregate patterns and develop a theory of decision making: Utility Theory.
Research thesis submitted to Strathmore University in fulfillment of the requirements for the Master of Science in Mathematical Finance
2021-01-01T00:00:00Z