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Does the Margin Requirement Change Based on the Volatility of the Underlying Asset?

Yes, margin requirements are dynamically adjusted based on the volatility of the underlying asset. When volatility increases, the potential for large, rapid price movements and thus larger losses increases.

The clearing house or exchange will raise both the initial and maintenance margin requirements to ensure that the collateral is sufficient to cover these greater potential losses, thereby protecting the integrity of the market.

How Do Capital Requirements for Prime Brokers Relate to the Risk of Exchange Default?
What Is the ‘Margin Requirement’ Set by a Clearing House?
Why Are Margin Requirements Higher for Volatile Assets?
How Does the “Greeks” Parameter Delta Affect the Price Movement and Potential Slippage of an Option?