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I have over 1000 simulated stock prices for an option that is expiring in 3 months. I have calculated the EU call option payoff of 1000 simulated prices and now I have 1000 simulated payoffs of call. I am looking to calculated the VaR of Long and short call but without the delta approach. I know how to estimate VAR of stocks (Standard devaition * Z-score). How do I estimate 95% VAR for call options?

Thank you!

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You have 1000 simulated payoffs, now find 1000 simulated P&L's:

For Long Call, P&L = simulated payoff - Black Scholes value at time 0

For Short Call, P&L = Black Scholes value at time 0 - simulated payoff

Now find the 5% quantile in both cases, i.e. P&L for the 50th worst outcome out of 1000

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