An option gives the right to buy ('call') or sell ('put') shares at a fixed 'strike' price, but only before an agreed date when the option expires. The person selling ('writing') the option needs to judge whether the price will rise or fall, and by how much. They hope the option will expire unused, meaning they keep the premium paid by the buyer for doing very little.
Insurers are like option writers homeowners pay premiums to receive a payout in case of disaster. Insurers calculate premiums using similar probability-based principles to option writers. If in doubt, they overcharge; few homeowners know how to price risk and would still insure even if they did. So optionality, exploited correctly, can be quite profitable.
Watch Tim Bennett's video tutorial: What are options and covered warrants?
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