Multiple choice on stocks. with calls, puts and premiums. Interest rates. Whick of the following statementsis?

Question

The stock of Greensleeves Clothing (GC) trades at a market price of $20. A call on the stock with an exercise price of $15 has a premium of $6. A put on the stock with an exercise price of $25 has a premium of $7. Interest rates are currently 10%. Which of the following statements is true?

1) If interest rates go up to 12%, the value of the call will go up.

2) If interest rates go up to 12%, the value of the put will go up.

3) If interest rates go up to 12%, the intrinsic value of the call will be $(5).

4) If interest rates go down to 8%, the intrinsic value of the call will be $(5).

Answer 1

If we are looking at American-style options, the options are mispriced unless either

(1) there are no shares available to be shorted or

(2) the stock will pay a dividend prior to expiration.

Since all exchange traded options on stocks in the United States are Amreican-style, one of those conditions would have to be true and would have an impact on the valuation model.

However, since you did not specify either of those conditions I will assume neither is true. That would mean:

1)"If interest rates go up to 12%, the value of the call will go up" is true.

2)"If interest rates go up to 12%, the value of the put will go up" is false.

3)"If interest rates go up to 12%, the intrinsic value of the call will be $(5)" is true.

4)"If interest rates go down to 8%, the intrinsic value of the call will be $(5)" is true.

Answer 2

there is not enough information to answer this question quantitatively, according to put-call parity.  at the new level of interest rates, we have two variables, call price and put price.  3 and 4 are true.  also on a general level, option prices decline with rising interest rates b/c you could sell the option and deposit the proceeds until expiration.  Arbitrage prevents this.  So 1 and 2 are false.