Browsing by Author "Phate, Seeiso"

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    Solving the barrier options model with linear time-dependent volatility numerically
    (National University of Lesotho, 2025-07) Phate, Seeiso; Nchejane, Ngaka John
    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.