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A covered call option is one whereby the writer owns the underlying asset on which the option is written. Generally, a covered call would only be written if the writer believed volatility to be overpriced in the market – the lower the volatility, the less premium the writer gains in return for giving up their upside in the underlying.
A covered put option is one whereby the writer sells the option while holding cash. This technique is used to increase income by receiving option premium. If the market goes down and the option is exercised, the cash can be used to buy the underlying to cover.
Covered put writing is often used as a way of target buying. If an investor has a target price at which he wants to buy, he can set the strike price of the option at that level and receive option premium to increase the yield of the asset. Investors also sell covered puts if markets have fallen quickly but seem to have bottomed, because of the high volatility typically received in the option.
* see also naked option