Interest Rate Models - Computational Methods for Quantitative Finance - page 90

Fig. 7.2 Swaption price in the CIR model

Example 7.2.3 Consider the CIR model with parameters α = 0 . 05, β = 0 . 2,

σ = 0 . 3, K = 0 . 05 and tenor structure T 1 = 0 . 25, T 2 = 0 . 5, T 3 = 0 . 75, T 4 = 1,

T 5 = 1 . 5, ... , T 10 = 4.TheswaptionpriceisshowninFig. 7.2 .

Remark 7.2.4 A widely used extension of the models described above is the con-
sideration of a deterministic shift function, i.e. instead of considering the solution
r t of ( 7.1 ), the short rate model r t +

ϕ t is considered. This extension can be fitted
to any observed term structure. The pricing of derivatives in the extended model is
analogous to the described method applying a change of variable.

7.3 Further Reading

For an introduction to interest rate models, we refer to Brigo and Mercurio [29]. Li-
bor market models in the Lévy setting were considered by Eberlein and Özkan [60].
For theoretical results, we refer to Keller-Ressel et al. [101]. The equations arising
in this context can be solved as described in Chap. 10. Recently, forward rate mod-
els have received significant attention, we refer to Carmona and Tehranchi [31] and
Hepperger [78] for details. Keller-Ressel and Steiner [102] consider attainable yield
curve shapes in an affine setting.