Which VAR type ranks outputs based on random scenarios?

Monte Carlo Value at Risk (VAR) is a method that utilizes random sampling and statistical modeling to assess the potential loss in value of an asset or portfolio under various scenarios. This technique involves generating a large number of random price paths for the underlying assets, based on their statistical properties, such as mean return and volatility.

Once the random scenarios are created, the potential future values of the portfolio are calculated, allowing for the determination of the worst losses over a specified holding period. The results are then ranked to determine the level of risk that corresponds to a given confidence interval, thereby offering insights into extreme loss possibilities.

This method is particularly powerful because it can accommodate a wide range of inputs and assumptions, making it very flexible when assessing risk across different market conditions and asset classes. Also, Monte Carlo simulations can capture non-linearities and fat tails in the return distribution, which may not be as effectively modeled through other approaches.

On the other hand, Analytical VAR relies on normal distribution assumptions, Historical VAR uses past data and assumes that future returns will follow the same pattern, and Static VAR does not make use of scenario generation. Thus, they do not employ the same level of randomness and scenario analysis that Monte Carlo VAR does.