A put option gives the buyer the right (but not the obligation) to purchase the underlying stock at a specified price. The seller of the put option must sell the stock at that price if the buyer exercises the option. If the stock price drops, the buyer of the option will let the option expire without exercising it, because the buyer would be able to buy the stock for less on the open market. Selling a put option would earn the company a little revenue from the sale. But it would not provide a hedge against a possible decline in market value of the stock the company already holds, because as the seller of the option, the company would have no control over whether or not the option was exercised.
A put option is the right to sell stock at a given price within a certain period. If the market price falls, the put option may allow the sale of stock at a price above market, and the profit of the option holder will be the difference between the price stated in the put option and the market price, minus the cost of the option, commissions, and taxes. The company that issues the stock has nothing to do with put (and call) options.
A call option is the right to purchase shares at a given price within a specified period. That would not provide a hedge against a decline in market price of the shares the company already owns.
A warrant gives the holder a right to purchase stock from the issuer at a given price. A warrant is usually distributed by the issuing company along with debt. A warrant would not provide a hedge against a decline in market price of the shares the company already owns.
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