El Qalli Yassine Term Structure Equations Under Benchmark Framework EERI

EERIEconomics and Econometrics Research Institute Term Structure Equations Under Benchmark Framework El Qalli Yassine EERI Research Paper Series No 13/2009 ISSN: 2031-4892 EERIEconomics and Econometrics Research Institute Avenue de Beaulieu 1160 Brussels BelgiumTel: +322 299 3523 Fax: +322 299 3523 www.eeri.euCopyright © 2009 by El Qalli Yassine Term Structure Equations Under BenchmarkFramework∗Yassine EL QALLIDepartment of Mathematics, Faculty of Sciences SemlaliaCadi Ayyad University, BP 2390, Marrakesh, Moroccoy.elqalli@ucam.ac.maAbstractThis paper makes use of an integrated benchmark modeling framework that allows us toderive term structure equations for bond and forward prices. The benchmark or numeraire ischosen to be the growth optimal portfolio (GOP). For deterministic short rate the solution ofthe bond term structure equation coincides with the explicit formula obtained in Platen(2005).The resulting term structure equations are used to explain moves in bond and forward prices byintroducing GOP as a factor and therefore constructing a hedge portfolio for bond consistingof units of the GOP and the saving account. The paper also derives an affine term structureequation for forward price in term of the GOP factor. In the case of stochastic short rate werestrict our selves to give only a term structure equation for the bond price.JEL Classification. E43, G13.Key words and phrases. Term structure, Benchmark approach, GOP, Forward price, ...