Put option provides the holder or owner the right, but not the obligation, to sell a specified amount of an underlying security or asset at specified price within a specified time to the option's writer. Owners of this kind of option are banging on the price of the security or asset to decrease.
Call option is the exact opposite of Puts. Call option provides the holder the right to buy a specified amount of the underlying asset from the option's writer at a specifiied price within a specified period. Holder of this kind of options is hoping for the price of the asset to increase.
Basically, Call and Put options can be written by anyone, even between you and me as long as the owner of the options have the faith that the option's writer is credible enough to settle the contract when called upon.
Imagine if you and me want to do a bet on the future price of Toyota Corolla. You think that the price will increase. I, as the option's writer, is willing to sell you 10 tickets whereby you can chose to buy 10 Corollas at a specified fixed price. Here's how it works.
I sell you 10 tickets with an expiry date that allows you to buy a Toyota Corolla with each ticket. Each ticket will definitely cost a certain amount, say $1000 per ticket. But to exercise or use this ticket to claim your Corolla, the price of the Corolla must hit say $25000 on the open market. Assume the last done price while this deal is written, is $22000. For the owner of this Call option, i.e you are the holder, you are banging on the price to goes up between now to the expiry of the option. If in between, it trades at $28000 and you chose to claim 5 of your tickets, I must buy from the open market to deliver the 5 cars to you. Then if it goes up further to $35000, I must deliver the remaining to you if you chose to exercise. Then there is a trigger clause built in, which states that the writer must deliver all options if price hits $40000, this is to protect both you and me against you not able to claim any if i go illiquid, and me against bottomless loss.
Conversely, Put options work this way. Same case as the Corolla. 10 tickets which cost $1000 each. Total option cost is $10,000. The exercise price is $25000, but this time the last trading price of a Corolla is $28000. So you as the holder is banging for the price to fall as much as possible. If it falls to $20000, and you chose to exercise 5 tickets, you can buy 5 Corollas and deliver to me and I got to pay you $25 grand. Then the trigger clause is say $10,000. I as the option owner must settle this put obligation and you deliver the rest of the cars to me and I pay you $25 grand each.
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