1. The Derivative of a Solution to a Second Order Parameter Dependent Boundary Value Problem with a Nonlocal Integral Boundary Condition

    Jeffrey W. Lyons and Joseph K. Miller

    Abstract: We discuss derivatives of the solution of the second order parameter dependent boundary value problem with an integral boundary condition \[y” = f(x,y,y’,\lambda ), y(x_{1})=y_{1}, y(x_2 ) + \int_c^d  \,ry(x)dx = y_2 \] and its relationship to a second order nonhomogeneous differential equation which corresponds to the traditional variational equation. Specifically, we show that given a solution y(x) of the boundary value problem, the derivative of the solution with respect to the parameter λ is itself a solution to the aforementioned nonhomogeneous equation with interesting boundary conditions.

    Pages: 43 – 50 | Full PDF Paper
  2. Extraction of Zero Coupon Yield Curve for Nairobi Securities Exchange: Finding the Best Parametric Model for East African Securities Markets

    Lucy Muthoni, Silas Onyango, Omolo Ongati


    We seek to construct a zero coupon yield curve (ZCYC) for Nairobi Securities Exchange (NSE). The objective of this paper is to construct a ZCYC that is differentiable at all points and at the same time, produces continuous and positive forward curve. We will use the classical Nelson-Siegel model, Svensson Model, Rezende-Ferreira model and Svensson extended model.

    These models have linear and nonlinear guidelines making them have multiple local minima. This condition causes model estimation more difficult to estimate. We therefore use L-BFGS-B method as the optimization approach for estimating the models.

    We compare the models’ performance in terms of continuity and differentiability of the ZCYC, and positivity of the forward curve. We use bond data from Central Bank of Kenya (CBK). The best parametric model to be used for the Kenyan securities market and, consequently, the East African Securities markets is chosen if and only if it depicts the aforementioned qualities.

    Keywords: BFGS, zero coupon yield curves, parametric models, Nairobi Securities Exchange.

    Pages: 51 – 74 | Full PDF Paper