NULIR
The National University of Lesotho Institutional Repository (NULIR) is a digital archive that collects, preserves, and provides open access to the scholarly and intellectual output of the University.
Recent Submissions
Solving the barrier options model with linear time-dependent volatility numerically
(National University of Lesotho, 2025-07) Phate, Seeiso; Mr Nchejane, Ngaka
The main purp ose of this work is to approximate the solution of the barrier option pricing model whose evolution is described in terms of partial differential equation called Black-Scholes model. In this model, we consider volatility as a linear function of time. This is done primarily using a numerical approximation technique by the name of finite difference method. We consider Crank Nicolson scheme and forward difference scheme in time derivative to discretize the model and represent it as a tridiagonal matrix. Furthermore, we analyse the stability of the discretized model using Von Neumann stability analysis. We finally find the numerical solution to find key insights and the implications.
Solving the barrier options model with linear time-dependent volatility by symmetry analysis
(National University of Lesotho, 2025-07) Kometsi, Relebohile Veronecca; Mr Nchejane, Ngaka
This project aims to solve the barrier options model with linear time-dependent volatility, described as a Partial Differential Equation (PDE) using symmetry analysis. The only PDE to be considered will be the Black-Scholes model. Firstly, we use Lie symmetry to find symmetries of our model from our determining equations. Once the symmetries are found, they will b e picked at random to form characteristic equations needed to find invariant solutions. Lastly, the solutions will b e interpreted and graphed.
Integrating arts into curriculum to enhance entrepreneurship skills: A case of three Botha-Bothe Schools
(National University of Lesotho, 2025-10) Makhoabenyane, Palesa; Dr. B. M . Motebang
The introduction of the integrated curriculum in Lesotho led to a shift from individual subjects to a grouping of subjects under learning areas. Amongst the five learning areas in the new integrated curriculum is the Arts and Entrepreneurship learning area, which comprises content from subjects such as Business Education, ICT, Home Economics, Art, Crafts, Technical subjects, Music, Drama and Theatre. The Arts and Entrepreneurship learning area aims at developing creativity and entrepreneurial talents and abilities to curb societal problems such as unemployment. This research therefore studied the integration of arts into the curriculum and its significance in enhancing entrepreneurship skills. This investigation used a qualitative approach employing a case study research design which enabled an in-depth analysis of the phenomenon of arts in enhancing entrepreneurship skills. The participants in this research were Business Education teachers currently teaching Arts and Entrepreneurship in three Botha Bothe secondary schools. Two curriculum policy documents were analysed. Also, students’ artefacts were analysed as a form of triangulation. The findings in this study revealed that theintegration of arts into curriculum through its activities develops skills such as creativity, collaboration, problem-solving, and critical-thinking. Literature classifies the aforementioned skills as entrepreneurship skills, which implies that integrating arts into curriculum instills entrepreneurship skills. Therefore, it is crucial for arts to be integrated into curriculum as it enhances entrepreneurship skills.
Striking a balance between human rights protection and maintaining National Security
(National University of Lesotho, 2025-05-07) Ramakoala, Lebohang
This mini-dissertation explores the complex interplay between the protection of human rights
and the imperative of national security within the context of Lesotho’s constitutional
framework. In a democratic dispensation, it is essential for national security agencies to uphold
public safety while simultaneously, required to respect human rights and freedoms. The study
delves into the dilemmas faced by the security agencies as they navigate the often conflicting
demands of constitutional responsibilities and security imperatives. Through a case study
approach, the research examines the historical, legal, and social dimensions of national security
practices in Lesotho, highlighting instances where efforts to safeguard citizens have
encroached upon human rights.
The analysis draws on use of the qualitative research methodology and a review of legal
documents and case law. The findings reveal a persistent tension between the objectives of
national security and the commitment to uphold democratic values, with significant
consequences for human rights protection and public trust in security institutions. The mini-
dissertation concludes with recommendations for policy reforms aimed at fostering greater
accountability and transparency among national security agencies while enhancing their
capacity to protect human rights in the execution of their constitutional mandates. The research
contributes to the broader discourse on national security in a democratic setting, offering
insights that are particularly relevant for emerging democracies grappling with similar challenges.
The impact of the absence of electronic commerce legislation on data privacy and security in electronic transactions in Lesotho
(National University of Lesotho, 2025-05-10) Sephoso, Malefetsane Michael
Electronic commerce (e-commerce) refers broadly to all forms of commercial and/or
economic activity conducted through electronic means.1 It comprises of not only the
buying and selling of goods and services over the internet,2 but also activities such as
advertising, online banking, digital content delivery and many others.3 The growth of
e-commerce has, amongst others, reduced the need for buyers and sellers to meet
physically, as many transactional activities can now be carried out online. However,
with the increasing use of the internet and the expansion of e-commerce, concerns have
arisen regarding the adequate protection of consumer information.4 Thereby giving rise
to significant cybersecurity risks.5 Cybersecurity in this context is defined as the
practice of protecting the integrity and confidentiality of information in the digital
realm.6 It is for this reason that the problem that this study discusses is cybersecurity
in Lesotho. Particularly the right to privacy of information in e-commerce, data
protection and data security.