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I fit the parameters of Heston model, using option data for SPX. Now I have the process S and P 500 is expected to follow. I make 100,000 simulations of this process and then calculate the expected return. The average of lowest 1% return is 99%-CVAR.
Why does the method not work. I get that I can not calibrate r the drift of S&P 500 because of risk neutral measure thing. But say I somehow use MLE or MM to get estimates for the drift. Will this method work.
Given the main uses of the VaR relate to risk management such as limit management, and measurement of P&L volatility, it is usually calculated under the physical/real world measure. Reason being that the risk measure are normally used to predict or explain the P&L movements from one day to another, which one can relate to their historical movements. Risk neutral dynamics are usually very different than the historical measure. So that’s the reason physical measure is more widely used in risk management. For Heston, you can use use maximum likelihood approach to estimate the parameters from historical data. Here is a good reference:
