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1. Value-at-Risk (VaR)

1.1 Historical Method

It is easy to calculate as it does not require any sufficient statistical or programming knowledge.

• My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/historical%20value-at-risk%20calculation.R

1.2 Variance-Covariance Method

Requires knowledge of basic statistic and properties of mean, standard deviation and table of standard normal probabilities.

The drawback of the following method is the inconsistence with the distribution as financial instruments mostly follow fat tails distributions rather than Normal one.

• My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/VaR%20via%20Variance-Covariance%20Method.R

1.3 Monte-Carlo Method

The most advanced method

• My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/VaR%20via%20Monte%20Carlo.R

1.4 Other

• My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/VaR%20table.R

2. Expected Shortfall (Conditional VaR or CVaR or Average VaR)

Shows how bad returns can be when numbers exceed VaR numbers. Basically, it is a mean of the worst tail observations (e.g. 5% or 1%).

2.1 Historical Method

• My R script: to be written

2.2 Variance-Covariance Method

• My R script: to be written

2.3 Monte-Carlo Method

• My R script: to be written

3. Multi-Asset VaR (MVaR)

4. Monte-Carlo Simulation

• My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/Monte%20Carlo%20Method.R

References

Hull, J.C. (2012) Risk Management and Financial Institutions. 3rd edn. John Wiley &Sons.

Hull, J.C. (2015) Options, Futures, and other derivatives. 9th edn. Pearson Education.