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      Welcome to 'Elementary Quantitative Risk Assessment'

      This course was created in cooperation with the Universities Würzburg and Nürnberg-Erlangen, the Universities of applied sciences Amberg-Weiden and Coburg, as well as the Bavarian virtual university.

      The course Elementary Quantitative Risk Assessment offers a step-by-step introduction from the methods of risk classification through risk identification to the mathematical-statistical procedures of risk analysis. The individual steps are made tangible by giving practical examples that illustrate the procedures. Calculations are demonstrated by giving examples which can be further explored using interactive software.

      This course consists of 3 modules. Module 1, “Concepts and Terminology in Quantitative Risk Modelling” explains the systematic survey of the respective case of risk exposure and introduces the concepts of risk phenomenon, risk variable and loss and profit types, among others, for a precise description of the risk exposure.

      Module 2 “Mathematical and statistical principles of risk modelling” focusses on the concept of statistical distributions. These provide an integral part of the adequate modelling of risk variables in Module 3. These statistical distributions are discussed and fitted onto data examples. Further, the distributions are classified by their tail behaviour, as this proves important for their usage in risk analysis.

      Module 3 then concludes the course and combines the previous concepts into the estimation of Value at Risk and Conditional Value at risk. These two key figures are well suited for describing risks and are also already requested by the Basel III banking regulation guideline for risk management.

      We wish you a good start into the course.

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      Timeframe Learning Modules Learning Goals
      DEMO
      		 1) Concepts and Terminology in quantitative Risk Modelling
      		The objective is to master the following material content:
      - Central terms and schemes of risk modelling
      - Basics of systematic risk identification
      - Description of cases of risk exposure
      - Dealing with terminology such as risk phenomenon, risk object, direct danger, indirect danger, risk indicator and risk measure
      - Loss and profit type as well as upside and downside risks
      DEMO
      		 0) Introduction to the R Programming Language
      		This module is optional, it is not relevant for the examination, nor do the following modules build on it. This course module gives an introduction to the programming language R, which is very popular for data analysis and risk calculations.
      DEMO
      		 2) Mathematical and statistical Principles of Risk Modelling
      		The aim is to master the following material content:
      - Formal and quantitative basics for the description of risk phenomena and corresponding data.
      - Fundamentals of the probability calculus
      - Stochastic inequalities
      - Specific probability distributions and their parameters
      - Parameter estimation (point estimation and interval estimation)
      - Tail behaviour of theoretical and empirical frequency distributions (light- and heavy-tailed)
      DEMO Holidays

      DEMO
      3A) Stochastical risk measures: The purpose of stochastic risk measures

      3B) Stochastical risk measures: Value at Risk
      		The aim is to master the following material content:
      - Empirical (based on order statistics) quantiles of a data set.
      - Theoretical quantiles of a distribution
      - Fitting a distribution and its parameters to data
      - Four common methods for estimating VaR, and their strengths and weaknesses: Distribution-free, Distribution-based, using Peaks over Threshold (POT) method, and using Hill-Weissman method.
      - Interval estimation of VaR

      DEMO
      3C) Stochastical risk measures: Conditional Value at Risk
      		The aim is to master the following material content:
      - Fitting a distribution and its parameters to data
      - Three common methods for estimating CVaR, and their strengths and weaknesses: Distribution-free, Distribution-based and using Peaks over Threshold (POT) method.
      - Interval estimation of CVaR

      DEMO
      		Repeat the material and do the concluding example

      DEMO
      		 Exam


  • Concepts and terminology in quantitative risk modelling

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      Welcome to the module Concepts and terminology in quantitative risk assessment.

      This module introduces and explains the central concepts in the context of risk modelling. In particular, it offers a fundamental building block to support systematic risk identification. Likewise, the approach for the precise description of a case of risk exposure is presented, thereby explaining terms such as risk phenomenon, risk object, direct hazard, indirect hazard, risk indicator and risk measure.

      Particular attention is paid to understanding the concept of loss and profit types, as this is an elementary feature of the further assessment of risk variables. Thus, in the case of a loss variable, a high value is critical and therefore to be assessed as a risk, whereas in the case of a profit, a high value is quite desirable. Conversely, a small loss is not risk-relevant, whereas a small profit certainly is.

      We hope you enjoy working through this module.

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      Learning goals for module 1 | Concepts and terminology in quantitative risk modelling

      The objective is to master the following material content:
      - Central terms and schemes of risk modelling
      - Basics of systematic risk identification
      - Description of cases of risk exposure
      - Dealing with terminology such as risk phenomenon, risk object, direct danger, indirect danger, risk indicator and risk measure
      - Loss and profit type as well as upside and downside risks

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      Learning module 1 | Concepts and terminology of quantitative risk modelling

      - Central terms of risk modelling
      - Variables of loss and profit type
      - Upside and downside risks
      - Risks in learning of risks

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