**5. Conclusion**

This article models the inflation dynamics of the Eurozone with a novel approach. We utilize a stochastic differential equation driven by fractional Brownian motions and a Lévy process. Empirical inflation data show that the distribution is right-skewed. Thus, any standard approach using the normality assumption in econometrics fails. Therefore, we propose the use of fractional Brownian motions and Lévy processes in order to model time-dependence and jumps. Those processes cover short- and long-term phenomena, which is a prerequisite for empirical distributions.

We find that our modeling and numerical simulation provide good results to the calibrated inflation data. Inflation dynamics of the Eurozone is according to 1000

*Modeling Inflation Dynamics with Fractional Brownian Motions and Lévy Processes DOI: http://dx.doi.org/10.5772/intechopen.92292*

runs of our simulation stable and strongly anchored at the 2.0% inflation target. Even in the worst negative or positive shock, inflation numbers do not reach levels persistently below 0 or above 4%.

That said, the stable and low inflation rates of the Eurozone are highly contingent of the inflation target defined by the European Central Bank. Currently, inflation expectations are well anchored below the 2% level. Yet, our model simulation demonstrates that proposals to increase the inflation target, such as by Blanchard et al. [9], are highly risky because it leads to a de-anchoring of inflation. In the end, you might have higher volatility and the risk of de-anchored inflation expectations. The latter can create a strong upward bias in inflation rates out of the control of a central bank.
