What are the strengths and weaknesses of historical simulation, Monte-Carlo simulation, and Variance-Covariance method in VaR calculation?

Answer 1

If We look at past crises we can see how a particular portfolio would have fared in these crises. Major drawback. History seldom repeats itself (but it does rhyme)

With Monte Carlo we do a large number of simulated tress tests but you have to have a decent knolwledge of the distributions of the stressors and their linkages.

VCOV allows for inter-relationships in the returns however these covariances are usually not stable and Long term covariarances are typically smaller than short term covariances

hope this helps