Processus de Lévy en Finance - Laboratoire de Probabilités et ...

3.2. CHOICE OF THE PRIOR 101
twice to the same set of option prices using prior models that were different but close to each
other (see Section 3.5.3 for the description of the calibration algorithm). Namely, in the test A
we used Merton model with diffusion volatility σ = 0.2, zero mean jump size, jump standard
deviation of 0.1 and intensity λ = 3, whereas in the test B all the parameters except intensity
had the same values and the intensity was equal to 2. The result of the test is shown in
Figure 3.1. The solid curves correspond to calibrated measures and the dotted ones depict
the prior measures. Notice that there is very little difference between the calibrated measures,
which means that, in harmony with Theorem 3.2, the result of calibration is robust to minor
variations of the parameters of prior measure, as long as its qualitative shape remains the same.
12
10
Test A
8
6
4
Test B
2
0
−1.2 −1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6
Figure 3.1: Lévy measures calibrated to the same data set using two prior measures similar to
each other. Solid curves correspond to calibrated measures and dotted ones depict the priors.
In the second series of tests we have again calibrated the Lévy measure twice to the same
set of option prices, this time taking two radically different priors. Namely, in test A we used
Merton model with diffusion volatility σ = 0.2, zero mean jump size, jump standard deviation
of 0.1 and intensity λ = 2, whereas in test B we took a uniform Lévy measure on the interval
[−1, 0.5] with intensity λ = 2. The calibrated measures (solid lines in Figure 3.2) are still similar
but exhibit much more differences than in the first series of tests. Not only they are different