Estimating Value at Risk using Python
Measures of exposure to financial risk
Overview
Value at risk (VaR) is a measure of market risk used in the finance, banking and insurance industries. It involves the use of statistical analysis of historical market trends and volatilities to estimate the likelihood that a given portfolio’s losses will exceed a certain amount. It is widely used for risk management and risk limit setting.
We will examine how to estimate VaR using Monte Carlo simulation techniques, analyze the effect of portfolio diversification and correlation between stocks on financial risk, and use copula methods to sample from correlated random variables and estimate portfolio VaR.
This submodule is a part of the risk analysis module.
Learning objectives
Upon completion of this module, you should be able to:

Understand how financial risk is modeled, characterized and quantified

Understand the impact of correlated risks on risk metrics

Implement a Monte Carlo simulation procedure for stochastic estimation of some poorly known quantity
Course material
Estimating Value at Risk 

Notebook on analyzing risk of a stock market portfolio 
Applications are run using Python and the NumPy and SciPy libraries (these are all free software that you can install on your own computer).
After reading this material, you may be interested in the submodule on copula methods for representing multivariate dependencies.
Other resources
We recommend the following sources of further information on this topic:

The Coursera course Financial Engineering and Risk Management (Columbia University)

Iversity course Monte Carlo Methods in Finance by Prof. Alberto Suárez, Universidad Autónoma de Madrid (including copulas)

Video lecture Value at Risk models from MIT’s Topics in Mathematics with Applications in Finance undergrad course

An Introduction to Computational Finance Without Agonizing Pain, by Peter Forsyth (UWaterloo), gives much more detail on Monte Carlo methods than the brief overview provided here

Material for the Introduction to Computational Finance and Financial Econometrics course at University of Washington (Prof. E. Zivot), covering time series concepts, maximum likelihood estimation, portfolio theory and the capital asset pricing model