Monte Carlo Simulation

A Python practice project exploring Monte Carlo simulation techniques and their applications.

Overview

This repository contains implementations of various Monte Carlo simulations—a statistical method for modeling and analyzing systems with random variables. The project demonstrates the power of using statistical sampling to solve complex problems and estimate quantities that are difficult to calculate analytically.

Project Structure

Monte-Carlo-Simulation/
│
├── main.py
│
├── export_json.py                     # exports results of each simulation as json 
├── export_csv.py                      # exports results of each simulation as csv
│
├── calculate_european_options.py      # calculates results of each simulation
├── calculate_int.py
├── calculate_mcmc_bayes.py
├── calculate_pde_sde.py
├── calculate_pi.py
├── calculate_rare_event.py
├── calculate_confidence.py
├── calculate_sequential.py
│
├── visualizationInt.py                # visualizes results of each simulation using matplotlib
├── visualizationMCMC.py
├── visualizationPDE_SDE.py
├── visualizationPi.py
├── visualizationRareEvent.py
├── visualizationSequential.py
│
├── README.md
├── LICENSE.md

Video Resources

Monte Carlo Pi Estimation

• "DataMListic": https://youtu.be/lY4rSeX8IL4?si=5dUTObqbJ73dSNQc4

Monte Carlo Integration

• "lj37": https://youtu.be/0zbLv2k17vU?si=bVJ2NB_j9vA4dzgR

Markov Chains

• "Veritasium": https://youtu.be/KZeIEiBrT_w?si=WUUBXs1a3AdS_zEl
• "SISL": https://youtu.be/3qodjHRUxAo?si=AwqZTTr_warI1HFc
• "DataMListic": https://youtu.be/nndtTssgtZE?si=BSZdz250n0NFnsnx
• "ritvikMath": https://youtu.be/yApmR-c_hKU?si=AhyUATM4EMC-zjJ8

PDE & SDE

• "Jafar Ghazanfarian": https://youtu.be/8w7v_pM6GWM?si=lYTgmc0Xu5afSyeg

European Options

• "QuantPy": https://youtu.be/fk38oX9GsxE?si=6T5Jlrj-Xe1kpNF5

Miscellaneous

• "The Synthetic Mind": https://youtu.be/WjmNedsX1T0?si=uSVoNJQRyHhcCifr
• "Decision Lab": https://youtu.be/psOYFdx838E?si=dRDkmuvgSk-EPnJg
• "MIT OpenCourseWare": https://youtu.be/OgO1gpXSUzU?si=iEBuJNuf8liokxNn