Modeling, Experimental Simulations And Probability Estimation Upon A Computationally-Efficient Discretization Algorithm For Jump-Type Lévy Processes

The present work aims at modeling, experimentally simulating and then implementing a computationally-efficient algorithm for jump-type Lévy processes. Within the paper, a pseudocode version for discretizing the continuous Brownian motion component of the Lévy processes is presented. The study also analyzes, through simulation experiments, the effect of each of the three process components upon the overall motion variance, slope and volatility of the result. Further model experiments are performed by tuning the jump size of the internal Poisson component, using four different types of distributions – namely: exponential, hyperexponential, normal and Pareto, in order to study the behavior of the Lévy processes. Finally, first-passage probabilities are estimated upon all these four distributions, which have many applications in financial and economics fields, as well as in the fields of mathematics, physics and engineering.