School of Sciencehttp://hdl.handle.net/10500/27362014-04-19T05:30:14Z2014-04-19T05:30:14ZPricing European and American bond options under the Hull-White extended Vasicek ModelMpanda, Marc Mukendihttp://hdl.handle.net/10500/133462014-04-16T14:50:41Z2013-01-01T00:00:00ZPricing European and American bond options under the Hull-White extended Vasicek Model
Mpanda, Marc Mukendi
In this dissertation, we consider the Hull-White term structure problem with the boundary value condition given as the payoff of a European bond option. We restrict ourselves to the case where the parameters of the Hull-White model are strictly positive constants and from the risk neutral valuation formula, we first derive simple closed–form expression for pricing European bond option in the Hull-White extended Vasicek model framework. As the European option can be exercised only on the maturity date, we then examine the case of early exercise opportunity commonly called American option. With the analytic representation of American bond option being very hard to handle, we are forced to resort to numerical experiments. To do it excellently, we transform the Hull-White term structure equation into the diffusion equation and we first solve it through implicit, explicit and Crank-Nicolson (CN) difference methods. As these standard finite difference methods (FDMs) require truncation of the domain from infinite to finite one, which may deteriorate the computational efficiency for American bond option, we try to build a CN method over an unbounded domain. We introduce an exact artificial boundary condition in the pricing boundary value problem to reduce the original to an initial boundary problem. Then, the CN method is used to solve the reduced problem. We compare our performance with standard FDMs and the results through illustration show that our method is more efficient and accurate than standard FDMs when we price American bond option.
2013-01-01T00:00:00ZConcerning ideals of pointfree function ringsIghedo, Oghenetegahttp://hdl.handle.net/10500/133422014-04-11T06:15:39Z2013-11-01T00:00:00ZConcerning ideals of pointfree function rings
Ighedo, Oghenetega
We study ideals of pointfree function rings. In particular, we study the lattices of z-ideals
and d-ideals of the ring RL of continuous real-valued functions on a completely regular
frame L. We show that the lattice of z-ideals is a coherently normal Yosida frame; and
the lattice of d-ideals is a coherently normal frame. The lattice of z-ideals is demonstrated
to be
atly projectable if and only if the ring RL is feebly Baer. On the other hand, the
frame of d-ideals is projectable precisely when the frame is cozero-complemented.
These ideals give rise to two functors as follows: Sending a frame to the lattice of
these ideals is a functorial assignment. We construct a natural transformation between the
functors that arise from these assignments. We show that, for a certain collection of frame
maps, the functor associated with z-ideals preserves and re
ects the property of having a
left adjoint.
A ring is called a UMP-ring if every maximal ideal in it is the union of the minimal
prime ideals it contains. In the penultimate chapter we give several characterisations for
the ring RL to be a UMP-ring. We observe, in passing, that if a UMP ring is a Q-algebra,
then each of its ideals when viewed as a ring in its own right is a UMP-ring. An example
is provided to show that the converse fails.
Finally, piggybacking on results in classical rings of continuous functions, we show that,
exactly as in C(X), nth roots exist in RL. This is a consequence of an earlier proposition
that every reduced f-ring with bounded inversion is the ring of fractions of its bounded
part relative to those elements in the bounded part which are units in the bigger ring. We
close with a result showing that the frame of open sets of the structure space of RL is isomorphic to L.
2013-11-01T00:00:00ZLogistic regression to determine significant factors associated with share price changeMuchabaiwa, Honesthttp://hdl.handle.net/10500/132292014-03-29T22:01:33Z2013-02-01T00:00:00ZLogistic regression to determine significant factors associated with share price change
Muchabaiwa, Honest
This thesis investigates the factors that are associated with annual changes in the share price of Johannesburg Stock Exchange (JSE) listed companies. In this study, an increase in value of a share is when the share price of a company goes up by the end of the financial year as compared to the previous year. Secondary data that was sourced from McGregor BFA website was used. The data was from 2004 up to 2011.
Deciding which share to buy is the biggest challenge faced by both investment companies and individuals when investing on the stock exchange. This thesis uses binary logistic regression to identify the variables that are associated with share price increase.
The dependent variable was annual change in share price (ACSP) and the independent variables were assets per capital employed ratio, debt per assets ratio, debt per equity ratio, dividend yield, earnings per share, earnings yield, operating profit margin, price earnings ratio, return on assets, return on equity and return on capital employed.
Different variable selection methods were used and it was established that the backward elimination method produced the best model. It was established that the probability of success of a share is higher if the shareholders are anticipating a higher return on capital employed, and high earnings/ share. It was however, noted that the share price is negatively impacted by dividend yield and earnings yield. Since the odds of an increase in share price is higher if there is a higher return on capital employed and high earning per share, investors and investment companies are encouraged to choose companies with high earnings per share and the best returns on capital employed.
The final model had a classification rate of 68.3% and the validation sample produced a classification rate of 65.2%
2013-02-01T00:00:00ZAssessment of polycyclic aromatic hydrocarbon (PAHs) and heavy metals in the vicinity of coal power plants in South AfricaOkedeyi, Olumuyiwa Olakunlehttp://hdl.handle.net/10500/120012013-11-16T22:00:41Z2013-11-12T00:00:00ZAssessment of polycyclic aromatic hydrocarbon (PAHs) and heavy metals in the vicinity of coal power plants in South Africa
Okedeyi, Olumuyiwa Olakunle
The distribution and potential sources of 15 polycyclic aromatic hydrocarbons (PAHs) in soils and Digitaria eriantha in the vicinity of three South African coal-fired power plants, Matla, Lethabo and Rooiwal were determined by gas chromatography–mass spectrometry. An ultrasonic assisted dispersive liquid-liquid microextraction (UA-DLLME) method was developed for the extraction of polycyclic aromatic hydrocarbon in soil, followed by determination using gas chromatography mass spectrometry. The study showed that an extraction protocol based on acetonitrile as dispersive solvent and C2H2Cl2 as extracting solvent, gave extraction efficiencies comparable to conventional soxhlet extraction for soil samples. The extraction time using ultrasonication and the volume of the extraction solvent was also investigated. Using a certified reference material soil (CRM), the extraction efficiency of UA-DLLME ranged from 64 to 86% in comparison with the Soxhlet result of 73 to 95%. In comparison with the real sample, the CRM result did not show a significant difference at 95% C.I. The UA-DLLME proved to be a convenient, rapid, cost-effective and greener sample preparation approach for the determination of PAHs in soil samples. PAH compound ratios such as phenanthrene/phenanthrene + anthracene (Phen/ Phen + Anth) were used to provide a reliable estimation of emission sources. The total PAH concentration in the soils around three power plants ranged from 9.73 to 61.24 μg g−1, a range above the Agency for Toxic Substances and Disease Registry levels of 1.0 μg g−1 for a significantly contaminated site. Calculated values of the Phen/Phen + Anth ratio were 0.48±0.08, 0.44±0.05, and 0.38+0.04 for Matla, Lethabo and Rooiwal, respectively. The flouranthene/fluoranthene + pyrene (Flan/ Flan + Pyr) levels were found to be 0.49±0.03 for Matla, 0.44±0.05 for Lethabo, and 0.53±0.08 for Rooiwal. Such values indicate a
xx
pyrolytic source of PAHs. Higher molecular weight PAHs (five to six rings) were predominant, suggesting coal combustion sources. The carcinogenic potency B[a]P equivalent concentration (B[a] Peq) at the three power plants ranged from 3.61 to 25.25, indicating a high carcinogenic burden. The highest (B[a] Peq) was found in samples collected around Matla power station. It can, therefore, be concluded that the soils were contaminated with PAHs originating from coal-fired power stations.
Nine metals (Fe, Cu, Mn, Ni, Cd, Pb, Hg, Cr and Zn) were analysed in soil and the Digitaria eriantha plant around three coal power plants (Matla, Lethabo and Rooiwal), using ICP-OES and GFAAS. The total metal concentration in soil ranged from 0.05 ± 0.02 to 1835.70 ± 70 μg g-1, 0.08 ± 0.05 to 1743.90 ± 29 μg g-1 and 0.07 ± 0.04 to 1735.20 ± 91 μg g-1 at Matla, Lethabo and Rooiwal respectively. The total metal concentration in the plant (Digitaria eriantha) ranged from 0.005 ± 0.003 to 534.87 ± 43 μg g-1 at Matla, 0.002 ± 0.001 to 400.49 ± 269 μg g-1 at Lethabo and 0.002 ± 0.001 to 426.91 ± 201 μg g-1 at Rooiwal. The accumulation factor (A) of less than 1 (i.e. 0.003 to 0.37) at power plants indicates a low transfer of metal from soil to plant (excluder). The enrichment factor values obtained (2.4 – 5) indicate that the soils are moderately enriched, with the exception of Pb that had significant enrichment of 20. The Geo-accumulation Index values of metals indicate that the soils are moderately polluted (0.005 – 0.65), except for Pb that showed moderate to strong pollution (1.74 – 2.53).
2013-11-12T00:00:00Z