# How do you handle implied volatility performing a VaR Monte-Carlo simulation using a stochastic volatility process calibrated on the underlying

Say you have a portfolio consisting of options each having a market implied volatility. If you now use some stochastic volatility model like GARCH to calibrate the real world volatility of the underlying, and then perform simulations of the correlated stock processes using the GARCH stochastic volatility. What volatility would you use when revaluing the options at the end of the simulation? Some possibilities I imagine are:

1.The same IV used at the start to get the market prices of the options.

2.The stochastic GARCH volatility at the end of the period.

3.The Implied volatility multiplied by $$\frac{\sigma_{2}^{GARCH}}{\sigma_{1}^{GARCH}}$$, where $$\sigma_{1}^{GARCH}$$ and $$\sigma_{2}^{GARCH}$$ is the volatility at the start and end period respectively.

Does any of these options make sense? Is there a "right" answer?

As a bonus question, what correlation would you use for the simulation? Can you use simply the standard EWM correlation as you would with constant volatility, or is there an equivalent to GARCH volatility for correlation?