Course Template

Monte-Carlo Simulation: From Sensor Noise to Portfolio Risk

Simulates noise measurements, Monte Carlo methods, and risk analysis with Python.

Category: Statistics Language: Python 3 Modules: 5

Includes teaching materials: PowerPoint slides and instructor handouts

Educational Goals

This course template teaches basic stochastic simulation procedures and systematically introduces the application of Monte Carlo methods. The focus is on building competencies in statistical modeling, simulating random processes, and interpreting numerical results. The modules connect mathematical models with their concrete implementation in Python, promoting a deeper understanding of the connection between theory and code. The template is located in the field of Statistics, Numerical Methods, and Data-Based Analysis.

Key Competencies

• Simulation of noise measurements using random numbers and normal distributions
• Use of reproducible random processes through controlled seeds
• Statistical evaluation of samples (mean, standard deviation, distributions)
• Application of Monte Carlo methods for estimating quantities like π and integrals
• Analysis of convergence behavior and error development in dependence on sample size
• Visualization and interpretation of data through histograms and scatter plots
• Conducting risk analyses with stochastic models (GBM) and key figures such as Value-at-Risk

Structure of the modules

Simulating measurement noise: Seed, Histogram, Statistics

Introduction to simulating random measurement values with normal distribution and their statistical evaluation and visualization.

45 min 🧩 4 Aufgaben

Monte Carlo estimation of Pi with random points

Application of the Monte Carlo principle for approximating π by random points and analysis of the uncertainty of the estimate.

45 min 🧩 4 Aufgaben

Monte Carlo integration: Integral as mean value

Implementation of Monte Carlo integration by sample mean values and comparison with analytical solutions.

45 min 🧩 3 Aufgaben

Monte Carlo convergence in log-log plot

Investigation of the convergence behavior of Monte Carlo methods through error analysis and log-log visualization.

45 min 🧩 3 Aufgaben

Monte-Carlo Risk Analysis with GBM and VaR

Application of stochastic models for simulating portfolio risks and calculating central risk indicators.

45 min 🧩 3 Aufgaben

The clearly structured modules enable transparent competence development and can be flexibly integrated into existing lesson series.

Test the template in your own teaching and adapt the individual modules specifically to your learning group.