# P1.19 American Options, Effects of Dividends, Early Exercise [products]

Discussion in 'P1.T3. Financial Markets & Products (30%)' started by ert, Apr 26, 2012.

1. ### ertNew Member

Question: Sam Seel has a small portfolio of options. Since the options are currently in-the-money, he is considering the possibility of early exercise. Which of the following statements is correct?

a. It is never optimal to exercise European call options early.
b. It is best to exercise a put option when it is just in-the-money.
c. Early exercise of put options becomes more attractive when interest rates rise.
d. Early exercise of put options becomes more attractive when interest rates decline.

Explanation:When interest rates rise, stock prices have a tendency to fall. This increases the value of a put option on a stock. All options benefit from high volatility.

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Could someone please help to advise on this? I thought an increase in interest rates would cause the put option value to decrease and not increase?

Thanks!

2. ### Aleksander HansenWell-Known Member

a) looks tempting but is incorrect since one cannot exercise early. Would perhaps argue this is misleading since it is never optimal to exercise early because it is not possible. Answer option should be rephrased or changed.

C) While true, the reason given violates the ceteris paribus assumption and is thus a poor explanation (although it can be true it doesn't have to be if you let all variables float around). Again, it should be qualified by American put option.

You would usually be correct in that it reduces the value of the put. However, you have to read between the lines here: it's talking about potential early exercise when rates are increasing....is that ever optimal?
As r increases sufficiently it can be shown that the interest you expect to earn on your strike is weakly stochastically dominating the value of the optionality and insurance a put option offers.

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3. ### Cipher2014New Member

Hi ert,

I was confused for the same reasons at first.

The catch here is that we are going to Exercising the option. It no longer matters how the price of the option changes if we decide to exercise. Hence the 6 factors that changes option prices should be out of the picture.

We should now only consider factors that impact the value of the proceeds from the exercise.

Makes sense?

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4. ### ertNew Member

Alek & Ying2,

I got it now. Thanks!

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