Estimating Call Option VaR from Simulated Payoffs

Summary

The document explains how to estimate 95% value at risk for long and short European calls when simulated terminal stock prices and their option payoffs are already available. Rather than applying a stock-return standard deviation and z-score through a delta approximation, it converts each simulated payoff into a profit and loss relative to the option’s initial Black–Scholes value.

For a long call, each simulated P&L is payoff minus the initial option value; for a short call, it is the initial value minus payoff. The lower five-percent tail of each resulting P&L distribution identifies the loss threshold, with the example describing the fiftieth-worst outcome among one thousand simulations. This is a historical or Monte Carlo quantile method based on the supplied scenarios. The answer does not discuss confidence intervals, market value changes before expiry, or whether the simulated price distribution adequately captures risk.

Key ideas

• Convert each simulated option payoff into P&L relative to the option’s initial value.
• Long-call P&L is simulated payoff minus the initial option value.
• Short-call P&L reverses that subtraction.
• Use the lower five-percent P&L quantile to obtain the stated 95% VaR threshold.
• The estimate depends on the simulated scenarios and does not itself validate their risk assumptions.

Tags

# VAR of Long & Short European Call Options


# VAR of Long & Short European Call Options












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!

## Answer by nbbo2 (score 1)

https://quant.stackexchange.com/a/64036

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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