Which Put is Worth more?

Consider two European put options on an underlying asset. The options are identical except that one has a longer time to expiration than the other. Which of the following statements best describes the value of the longer put versus the shorter put? a. The longer put is always worth more than the shorter put b. The longer put is never worth less than the shorter put. c. The longer put may be worth less than the shorter put. d. The shorter put is never worth less than the longer put. Enjoy.

b)

B as well

A… otherwise arbitrage will be made

Are you going to change your answer pepp?

C. It may be worth more, but it doesn’t have to be worth more. Nor can it be worth less.

I love it when the answers come like this…

this is not a simple problem, european options longer put will be valued more because of time value, and if the stock is below strike price. longer put will be valued more because of time value, if the stock is above strike price the longer put is ALWAYS WORTH MORE, and NEVER WORTH LESS. (they both have an equality in there) i’ll say that longer put will always be WORTH MORE because oof timing. so revised answer A

Hey let’s make this interesting - I’ll say D

mcf, clarify.

uh oh, i think remember reading now that time to expiration doesnt necessary affect a euro put, great questions Dreary!

Yes C is correct

this is an impossible question. unless you know how to answer this, you will definitely get this question wrong. I see why C is correct now too, but if I tried to explain it, i am afraid my answer will change.

at least you got the correct answer pepp…:slight_smile:

I know it for the call option (it also works for the put). Consider two call option, one with longer and one with shorter maturity. Assume that in one week a substantial dividend will be paid on the underlying asset. The dividend payment will lead to a decrease to the stock price. As a result, it is possible that the option with longer maturity is worth less that the option with shorter maturity.

With a european put option, it is possible for the shorter option to be worth more than a longer option. You have an opportunity cost of having to wait a longer period of time to sell an asset. If prevailing interest rates are extremely high, the lost interest income that could be earned from exercising the put option and reinvesting those funds makes the shorter option worth more than the longer option. This is better explained in the CFA texts, but the take away is that you definitely cannot say that a longer european option is worth more than a shorter option in all cases. For an American put option, this arguement does not hold.

mcf, almost right…the answer is simpler, if the price of the underlying asset goes to zero, then the shorter European put may be worth more than the longer European put because the put holder will receive the exercise price earlier and will be able to begin earning interest sooner. But here interest is on teh option proceeds, not the underlying as you stated.

mcf Wrote: ------------------------------------------------------- > With a european put option, it is possible for the > shorter option to be worth more than a longer > option. You have an opportunity cost of having to > wait a longer period of time to sell an asset. If > prevailing interest rates are extremely high, the > lost interest income that could be earned from > exercising the put option and reinvesting those > funds makes the shorter option worth more than the > longer option. > > This is better explained in the CFA texts, but the > take away is that you definitely cannot say that a > longer european option is worth more than a > shorter option in all cases. For an American put > option, this arguement does not hold. so lets be clear a longer maturity AMERICAN put is always worth more than a shorter term am put but this is NOT the case for european puts?

mcf Wrote: ------------------------------------------------------- > With a european put option, it is possible for the > shorter option to be worth more than a longer > option. You have an opportunity cost of having to > wait a longer period of time to sell an asset. If > prevailing interest rates are extremely high, the > lost interest income that could be earned from > exercising the put option and reinvesting those > funds makes the shorter option worth more than the > longer option. > AND WE AGREE THAT NO MATTER WHAT TYPE – AM OR EURO – HIGHER RATES HURT THE VALUE OF PUTS – ? PLEASE SAY YES

Yes. American, always. European, not always.