The term used to describe the strategy in which an investor owns the underlying security and also writes a straddle on that security. This is not really a covered position.
Cover: To close out an open position - to buy back as a closing transaction an option that was initially written. This term is used to describe the purchase of an option or stock to close out an existing short position for either a profit or loss.
Covered: A written option is considered to be covered if the writer also has an opposing market position on a share-for-share basis in the underlying security. That is, a short call is covered if the underlying stock is owned, and a short put is covered (for margin purposes) if the underlying stock is also short in the account. In addition, a short call is covered if the account is also long another call on the same security, with a striking price equal to or less than the striking price of the short call. A short put is covered if there is also a long put in the account with a striking price equal to or greater than the striking price of the short put.
Covered Straddle: An option strategy in which one call and one put with the same strike price and expiration are written against 100 shares of the underlying stock. In actuality, this is not a "covered" strategy because assignment on the short put would require purchase of stock on margin. This method is also known as a covered combination.
Straddle: The purchase or sale of an equivalent number of puts and calls on the underlying stock with the same exercise price and expiration date.