Open AccessA new method for interpolating yield curve data, with applications to the South African market
Author(s) -
Eben Maré
Publication year - 2013
Publication title -
suid-afrikaanse tydskrif vir ekonomiese en bestuurswetenskappe/south african journal of economic and management sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.277
H-Index - 17
eISSN - 2222-3436
pISSN - 1015-8812
DOI - 10.4102/sajems.v16i4.388
Subject(s) - monotone cubic interpolation , monotone polygon , interpolation (computer graphics) , mathematics , swap (finance) , hermite interpolation , yield (engineering) , yield curve , function (biology) , hermite polynomials , mathematical optimization , pure mathematics , computer science , mathematical analysis , linear interpolation , polynomial interpolation , bond , geometry , economics , polynomial , artificial intelligence , materials science , finance , evolutionary biology , biology , metallurgy , motion (physics)
This paper presents a method for interpolating yield curve data in a manner that ensures positive and continuous forward curves. As shown by Hagan and West (2006), traditional interpolation methods suffer from problems: they posit unreasonable expectations, or are not necessarily arbitrage-free. The method presented in this paper, which we refer to as the “monotone preserving r(t)t method", stems from the work done in the field of shape preserving cubic Hermite interpolation, by authors such as Akima (1970), de Boor and Swartz (1977), and Fritsch and Carlson (1980). In particular, the monotone preserving r(t)t method applies shape preserving cubic Hermite interpolation to the log capitalisation function. We present some examples of South African swap and bond curves obtained under the monotone preserving r(t)t method