Introduction to Levy Processes

In the book, an introduction to Levy processes we deliberate on the option price for two stochastic processes by making comparisons. The Black-Scholes, which was generally known as the Black-Scholes model, known to have obeyed the Geometric Brownian Motion in the financial market and the generalised hyperbolic model which was our focus by considering its structure. The book presents the concepts of Levy processes and their functions in mathematical finance including the logic of why the Levy processes are better to describe the statistical features of the financial markets. Also, deciding about the equivalent martingale measure, done by concentrating on Levy processes driven by the generalised hyperbolic distribution. It guides us through the derivation of the European option price formula for a call, for the Black-Scholes and generalised hyperbolic model under the martingale measure based on the Escher-transform. Ultimately, it presents the comparisons of both the derived option price for the generalised hyperbolic model with that of the standard Black-Scholes model.