VAR Monte Carlo Simulation

We say that if we increase the sample size, the Monte Carlo Simulation and VAR will be the same. What about the historical VAR? What happens if we increase the sample size of the returns, will that make the historical the same as the parametric var?

Likely case NO.

Historical VAR assumes a discrete distribution of return set, whereas Parametric assumes a continuous distribution. HS VAR follows a single path innovation and often it is Non-Normal