**Author details**

Last but not least, by running several simulations we find that inflation dynamics is with high likelihood in a range of [2, 5] in the Eurozone. Hence, even with severe positive or negative shocks the inflationary process is stable and anchored around the target level of 2%. Finally, in a scenario analysis, we set the mean-reverting level to the target rate of 4% as proposed by Blanchard et al. [9]. We find inflation dynamics is more volatile and still face deflationary levels during severe negative shocks. In that regard, a higher inflation target does not eliminate deflation events as with the target level of 2% today. Of course, the buffer towards deflation is greater if the inflation target is 4%. But economically, we proclaim that a higher inflation target creates a higher volatility and de-anchor inflation expectations subsequently. Consequently, increasing the inflation target is not free of any risk due to growing

*Simulation of equation (7) with calibrated parameters. Top panel denotes all inflation processes and bottom*

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

uncertainty about inflation expectations and price-stability in general.

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 prereq-

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

**5. Conclusion**

**10**

**Figure 6.**

*panel the histogram. Source: B Herzog (2020).*

uisite for empirical distributions.

Bodo Herzog1,2,3

1 ESB Business School, Reutlingen University, Reutlingen, Germany


\*Address all correspondence to: bodo.herzog@reutlingen-university.de

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Chapter 2**

Assessments

*and Mentje Gericke*

**Abstract**

method.

**13**

**1. Introduction**

Construction of Forward-Looking

Financial institutions are concerned about various forms of risk that might impact them. The management of these institutions has to demonstrate to shareholders and regulators that they manage these risks in a pro-active way. Often the main risks are caused by excessive claims on insurance policies or losses that occur due to defaults on loan payments or by operations failing. In an attempt to quantify these risks, the estimation of extreme quantiles of loss distributions is of interest. Since financial companies have limited historical data available in order to estimate these extreme quantiles, they often use scenario assessments by experts to augment the historical data by providing a forward-looking view. In this chapter, we will provide an exposition of statistical methods that may be used to combine historical data and scenario assessments in order to estimate extreme quantiles. In particular, we will illustrate their use by means of practical examples. This method has been implemented by major international banks and based on what we have learnt in the process, we include some practical suggestions for implementing the recommended

**Keywords:** operational risk, loss distribution approach, aggregate loss distribution,

Financial institutions need to carefully manage financial losses. For example, the claims made against short-term insurance policies need to be analysed in order to enable an insurance company to determine the reserves needed to meet their obligations and to determine the adequacy of their pricing strategies. Similarly, banks are required in terms of regulation to set aside risk capital to absorb unexpected losses that may occur. Of course, financial institutions are more interested in the total amount of claims or the aggregate loss occurring over one year in the future, than the individual claims or losses. For this reason, their focus will be on what may happen in the year ahead rather than what has happened in the past. Popular modelling methods involve the construction of annual aggregate claim or loss distributions using the so-called loss distribution approach (LDA) or random sums

historical data, measures of agreement, scenario assessments

Distributions Using Limited

Historical Data and Scenario

*Riaan de Jongh, Helgard Raubenheimer*
