Geodesic
Estimating the short rate from term structures in the Chan-Karolyi-Longstaff-Sanders model
Vladimír Mosný1 ; Beáta Stehlíková2 ; Vladimír Mosný ; Beáta Stehlíková
1FINAMIS, Na križovatkách 29, 821 04 Bratislava, Slovakia
2Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia
Acta mathematica Universitatis Comenianae, Tome 89 (2020) no. 2, pp. 361-375 
Vladimír Mosný; Beáta Stehlíková; Vladimír Mosný; Beáta Stehlíková. Estimating the short rate from term structures in the Chan-Karolyi-Longstaff-Sanders model. Acta mathematica Universitatis Comenianae, Tome 89 (2020) no. 2, pp. 361-375. http://geodesic.mathdoc.fr/item/AMUC_2020_89_2_a14/
@article{AMUC_2020_89_2_a14,
     author = {Vladim{\'\i}r Mosn\'y and Be\'ata Stehl{\'\i}kov\'a and Vladim{\'\i}r Mosn\'y and Be\'ata Stehl{\'\i}kov\'a},
     title = { Estimating the short rate from term structures in the {Chan-Karolyi-Longstaff-Sanders} model},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {361--375},
     year = {2020},
     volume = {89},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2020_89_2_a14/}
}
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Voir la notice de l'article provenant de la source Comenius University

Short rate models are formulated in terms of a stochastic differential equation for the instantaneous interest rate, so called short rate. The interest rates with other maturities, forming the term structure of interest rates, are then determined by bond prices which are solutions to the partial differential equation. We study the Chan-Karolyi-Longstaff-Sanders model and estimate the dependence of volatility on the short rate using the observed term structures together with estimating the unobservable short rate process. Starting with minimizing the sum of squares of erros, we make two approximatinos of this original optimization problem: Firstly, we relax the constraints regarding zero short rates and allow only positive vales. Secondly , the partial differential equation for the bond prices has a closed form solution only in special cases and we use an analytical approximation formula in a convenient form. Finally, we apply the proposed algorithm to real data.