Economics at your fingertips  


Florian Gach ()
Additional contact information
Florian Gach: Austrian Financial Market Authority, Otto-Wagner-Platz 5, Vienna 1090, Austria

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 07, 1-16

Abstract: Since the entry into force of Solvency II as of 1 January 2016, all European insurance companies concerned have to use the Smith–Wilson interest rate curve to determine the value of their insurance obligations and thus of a substantial part of their balance sheet. Although Smith & Wilson introduce the underlying discount curve P̲(t) as the sum of a ‘long-term’ discount curve e−f∞t and a linear combination of the so-called Wilson function W(t,u) evaluated at different payment dates uj, that is, P̲(t) = e−f∞t +∑ jβjW(t,uj), a mathematically sound derivation of its shape is missing in the literature. The aim of this paper is to close this gap. To this end, we reformulate the infinite-dimensional optimization problem stated in Smith & Wilson (2000) within an analytically rigorous framework. We prove that it has a unique minimizer and explicitly derive the formula displayed above. In doing so, we show that W(t,u) is in fact the kernel function of a particular reproducing kernel Hilbert space, which is the key result to fully understanding the shape of P̲(t).

Keywords: Smith–Wilson; interest rate term structure; ultimate forward rate; EIOPA curve (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (1) Track citations by RSS feed

Downloads: (external link)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link:

Ordering information: This journal article can be ordered from

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().

Page updated 2019-01-19
Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:07:n:s0219024916500394