Multidimensional Lévy Models - Computational Methods for Quantitative Finance - page 207

Fig. 14.3 Variance gamma
density in d = 2and
corresponding contour plot

Note that this is again an anisotropic α -stable process. We plot the density ( 14.14 )
for d = 2, ϑ = 0 . 5, η = 0 . 5 and α = ( 0 . 5 , 1 . 2 ) in Fig. 14.4 .

14.3.3 Admissible Models

We make the following assumptions on our models.

Assumption 14.3.4 Let X be a d -dimensional Lévy process with characteristic
triplet (

Q ,ν,γ) , Lévy density k and marginal Lévy densities k i , i = 1 ,...,d .

(i) There are constants β i > 0, β i

> 1, i = 1 ,...,d and C> 0 such that

C e − β i

| z | ,z<

− 1 ,

k i (z) ≤ (14.15)

e − β i z , z> 1 .