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Consider two European put options, written on the same asset, with the same maturity, but different strike prices: K1< K2

Which option is more expensive?

Then Answer the same question, but using call options instead.

It made sense to me that a put option - a sell option, with a higher strike price, would be worth more, hence is more expensive. And a call option - a buy option, with a higher strike price would be bought for more, so again is worth more and is more expensive? Or is that completely wrong?

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    Think about extreme cases. For the call option, would you rather have the option to buy a share of Apple stock for $1, or $1000000? Which option would be more valuable to you? – Nate Eldredge May 8 '16 at 17:50
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In the scenario you describe, and really, in any scenario, by the nature of how option contracts work:

  • a higher strike put will necessarily be more expensive than the lower strike put (everything else being equal).

  • the lower strike call will necessarily be more expensive than the higher strike call (everything else being equal).

In put options, the buyer has the right to sell stock for the strike price. So the higher the strike price, the more money the buyer of the put option can make by selling the shares of stock at a higher price.

In call options, it's the exact opposite: buyers of the call option have the right to buy stock at the strike price. The lower the strike price, the better for the buyer: they have the right to buy stock for a lower amount of money. So it must be worth more.

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