Section "Continuous tenor extension of affine LIBOR models" focuses on the continuous tenor extension of affine LIBOR models and studies the properties of interpolating functions.
Let Open image in new window be an interpolating function and consider the continuous tenor extension of the affine LIBOR model ({ X,mathcal {X},T_{N},u,v)}).
Let Open image in new window be a continuously differentiable interpolating function, i.e., Open image in new window, and consider the continuous tenor extension of the affine LIBOR model ({ X,mathcal {X},T_{N},u,v)}).
The definition of the interpolating function yields immediately that bond prices in the continuous tenor extension coincide with those of the discrete tenor affine LIBOR model for all maturities.
Then, Open image in new window is a continuous tenor extension of the affine LIBOR model, i.e., an arbitrage-free model for all maturities Open image in new window, such that for all maturities (Tin mathcal {T}) the bond prices coincide with those of the (discrete tenor) affine LIBOR model.
We would like in the sequel to provide conditions such that the short rate resulting from a continuous tenor extension of an affine LIBOR model exhibits "reasonable" behavior, in the sense that it neither jumps at fixed times, nor drops to zero at each maturity date.
Vocabulary: Enveloped, juncture, divisive, gauge, spectacle, constituency, traction, derisive, contradicts, grapples, downcast, subdued, denounce, amid, superdelegate, tenor, incendiary Extension Activities: 1.
His Chisciotte, certainly, was a famed virtuoso, and Steven Tharp, the one nonyoung artist on the roster, acquitted himself well (particularly in his showpiece aria at the end of Act I), with a clear tenor and a good lower extension.
He identifies Presley as a high baritone, calculating his range as two octaves and a third, "from the baritone low G to the tenor high B, with an upward extension in falsetto to at least a D-flat.
A more important auxiliary instrument than, say, the tenor oboe was the basset horn, which provided an extension of the bore to take the chalumeau range down to c.
His father, an agricultural extension agent, bought Mr. Person his first tenor at 16; his mother, an English teacher, required him to listen to the Metropolitan Opera's Saturday-afternoon radio broadcasts.
