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Computing VaR with Monte Carlo Simulations very similar to Historical Simulations. The main difference lies in the first step of the algorithm – instead of using the historical data for the price (or returns) of the asset and assuming that this return (or price) can re-occur in the next time interval, we generate a random number that will be used to estimate the return (or price) of the asset at the end of the analysis horizon.
In the previous post, we learned the algorithm to compute VaR using Monte Carlo Simulation. Let us compute VaR for one share to illustrate the algorithm. We apply the algorithm to compute the monthly VaR for one stock. We will only consider the share price and thus work with the assumption we have only one share in our portfolio. Therefore the value of the portfolio corresponds to the value of one share.
The fundamental assumption of the Historical Simulations methodology is that you base your results on the past performance of your portfolio and make the assumption that the past is a good indicator of the near-future. The below algorithm illustrates the straightforwardness of this methodology. It is called Full Valuation because we will re-price the asset or the portfolio after every run. This differs from a Local Valuation method in which we only use the information about the initial price and the exposure at the origin to deduce VaR.
