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Does Delivery Risk Exist in Cash-Settled Options?

No, delivery risk does not exist in cash-settled options because there is no physical transfer of the underlying asset. The settlement is purely a cash exchange based on the difference between the strike price and the final settlement price.

The only remaining risk is the counterparty risk of the clearing house or dealer.

What Is the Difference between Physical and Cash Settlement in Derivatives Contracts?
How Does a Clearing House Handle Settlement for Physically-Delivered Vs. Cash-Settled Futures?
How Does the Settlement Process Differ between Cash-Settled and Physically-Settled Futures?
What Is the Primary Difference between a Cash-Settled and a Physically-Settled Futures Contract?