In Stochastic Analysis and Applications, volume 27, number 6, pages 1191–1200, the figures were omitted from the article, “Approximation for the Normal Inverse Gaussian Process Using Random Sums,” by C. G. Pancheco-Gonzalez.
In the article, it is proposed a continuous time random walk for financial returns to model the tick-by-tick financial trading. For such a model, the limit behavior under an appropriate rescaling is studied, which turns out to be a normal inverse Gaussian (NIG) process. Here, we present some numerical simulations using SCILAB 4.1.2; Figure represents three simulated paths of the model treated in Section 4.1, and Figure represents a histogram of the process at time 1 using 100,000 simulations.
Figure 1 Three simulated paths.
Figure 2 Histogram with 3000 paths.
The purpose of the graphs is to show the behavior of the trajectories and the histogram. According to Theorem 4.1, the simulated paths approximate those ones of a NIG process, although visual inspection may suggest to use a Gaussian distribution for modeling.