A naked option is an option that is not covered with an offsetting position in the underlying. In other words, it is an option for which the buyer or seller has no underlying asset position. A writer of a naked call option, therefore, does not have a long position in the underlying on which the call has been written. Likewise, the writer of a naked put doesn’t own a short position in the underlying on which the put has been written.

Exchanges usually apply initial margins to written naked options. For example, the CBOE defines the initial margin required for a written naked call and a written naked put in the greater of two values.

For a written naked call, it is the greater of:

• A total of 100% of the option’s premium plus 20% of the underlying price less the amount by which the option is out of the money, if any.
• A total of 100% of the option’s premium plus 10% of the underlying price irrespective of its moneyness.

For a written naked put, it is the greater of:

• A total of 100% of the option’s premium plus 20% of the underlying price less the amount by which the option is out of the money, if any.
• A total of 100% of the option’s premium plus 10% of the exercise price.

For more, see: writing naked options: an example.