# European Puts

Hello All,

I read that with the value of Eur Puts increases as the time period increases. However, the lower bound for Eu Put at time t = Max ( {X/((1+r)^T-t)}, 0).

Given this, if T increases (for the same t), the denominator increases and the overall value of X/… decreases, reducing the value of Put. Any thoughts how we can prove this without using Black scholes merton (which is very complex and I don’t understand) ?

You cannot exercise a european put until the expiration date, so the maximum value is the present value of the intrinsic value of the put when the price of the underlying is zero. The more time until expiration, the lower the value of the put option.

T does not increase. Only the t increases. If I understand the notation well.

Correct: T is the original amount ot time to expiration of the option, t is the time that has elapsed since inception.

Hello Moosey and S2000magician,

As you have said, the less time to expiration, the less value Eu Put has, as compared with Am Put. However, under what circumstances will Eu Put be more valuable than Am Put? The curriculum says that Eu Put can be > = or < Am Put. I am not sure about the “>” part especially when we are solely comparing the time to expiration, ceteris paribus.