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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.

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

• R script for histogram: https://github.com/vladislavpyatnitskiy/Data-Visualisation-for-finance-in-R/blob/main/Histogram/Histogram%20for%20VaR.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 of three. Here is used Monte Carlo method where the worst value of modelled returns for selected quantile.

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

1.4 Table with all 3 types of VaR

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

1.5 VaR via Duration

My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/Value-at-Risk/VaR%20via%20Duration.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%). The script for VaR calculation may be used with a few additional code.

2.1 Historical Method

The mean of the 5% worst returns for the period.

• My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/Expected%20Shortfall%20(CVaR)/Historical%20CVaR.R

2.2 Variance-Covariance Method

• My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/Expected%20Shortfall%20(CVaR)/CVaR%20via%20Variance-Covariance.R

2.3 Monte-Carlo Method

• My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/Expected%20Shortfall%20(CVaR)/CVaR%20via%20Monte.R

2.4 Rachev Ratio

My R script: https://github.com/vladislavpyatnitskiy/Risk-Management-Analytics/blob/main/Rachev%20Ratio.R

3. Multi-Asset VaR (MVaR)

VaR version is for portfolios which assumed to have several securities. It takes into account portfolio returns and weights

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

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.