Value at Risk (VaR): A new technique using Multilevel Monte Carlo Simulation for a derivative portfolio

This paper will try to look into the two important methods for the calculation of Value at Risk (VaR) for non linear portfolio using Monte Carlo Simulation method. The two techniques Closed form VaR and Multilevel Monte Carlo VaR for valuing the derivative portfolio are explained in details. In case of multilevel Monte Carlo simulation, it has been found that with decrease in the number of inner Monte Carlo simulation, VaR values changes only little. The two methods viz. closed form method and the Multilevel Monte Carlo method is compared with the result of the closed form VaR (taken as reference VaR). It has been concluded that when closed form formula is not available for the valuation of a derivative, then multilevel method VaR can be preferred over the closed form method VaR, the former being more efficient in terms of accuracy and computational time.