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.

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.

About “t” vs “T” – My apologies about this. That’s a major typo. Thanks for correcting me.

Rather less time to expiry the more value because you discount the X for a shorter period of time.

American put will most probably be more valuable (all else equal) because you have the flexibility when to,exercise, so it cannot be less valuable than the European put.

in American put you don’t discount the X because you can exercise it when it’s in the money. Hence it can be more valuable. I don’t know where the curriculum says Eu put can be > or = than Am, I think it’s the other way around.