Why do they both have the different minimum values?
We all know that European puts cannot be exercised untill expiration, but American, can at any time.
Thanks!!
Because an American put option can be exercised immediately, if it is in the money its minimum value is the amount by which it is in the money (you could exercise it today and get that amount). Because a European put option cannot be exercised until its expiration date, if it is in the money the minimum value is the present value of the amount by which it is in the money, discounted at the risk-free rate.
As u said correctly that American options can be exercised anytime whereas Europeon options can only be exrecised at expiry .Therefore,value of american put option is Max (X-S,0) ,where X equals strike price and S equals to price of the underlying asset.Europeon put options value is max (X/(1+r)^t-S,0).in Europeon put option we calculate the present value of the exercise price since they can only be exercised at expiration .