#### meanreversion

##### Senior member

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Hi Martinghoul, how have you been? Long time no see~~

I posted a thread about protective put strategy. There is something I really don't understand:

strike is K, and current stock price is S. Amercian put option is always worth more than the corresponding European put option (under same strike and maturity), since American put option is sometimes worth its intrinsic value K-S, it must hold true that the corresponding European put is sometimes worth less than its intrinsic value K-S, so does it mean that when the European put is worth less than the intrinsic K-S, I implement the protective put by buying the European put with premium p (less than its intrinsic K-S), then the worst case would be I only make profit of (K-S)-p?

just take a simple example: current stock price $3, strike price for a European put is $5, it seems possible for the European put to have premium less than ($5-$3)=$2, say $1.8 premium (because an American put can be worth its intrinsic $2 and american put is worth more than the european put). so it is possible for the protective put strategy to always have positive profit, right? Minimum profit is $5-$3-$1.8=$0.2. I know this should be a mistake but I don't know where I am wrong??

many thanks, mate

It's not possible for an option to be worth less than its intrinsic value, whether American or European. In your example, the very minimum the (future value) of a $5 put can be is $2, if the market is trading at $3 (i.e. your suggested price of $1.80 cannot happen).