Premium
PRICING CALLABLE BONDS BY MEANS OF GREEN'S FUNCTION 1
Author(s) -
Büttler HansJürg,
Waldvogel Jorg
Publication year - 1996
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1996.tb00112.x
Subject(s) - callable bond , bond valuation , vasicek model , bond , affine term structure model , short rate , function (biology) , mathematics , mathematical economics , economics , yield curve , finance , evolutionary biology , biology
This paper derives a closed‐form solutin for the price of the European and semi‐Amirican callable bond for two popular one‐factor models of the term structure of interest rates which have been proposed by Vasicek as well as Cox, Ingersoll, and Ross. the price is derived by means of repeated use of Green's function, which, in turn, is derived from a series solution of the partial differential equation to value a discount bond. the boundary conditions which lead to the well‐known formulae for the price of a discount bond are also identified. the algorithm to implement the explicit solution relies on numerical quadrature involving Green's function. It offers both higher accuracy and higher speed of computation than finite difference methods, which suffer from numerical instabilites due to discontinuous boundary values. For suitably small time steps, the proposed algorithm can also be applied to American callable bonds or to any American‐type option with Green's function being explicitly known.