Question

1. The following quotes were observed for options on a given stock on November 1 of a given year. These are American calls except where indicated.

	Calls			Puts
Strike	Nov	Dec	Jan	Nov	Dec	Jan
105	8.38	10	11.5	0.31	1.25	2
110	4.38	7.13	8.25	0.94	3	3.75
115	1.50	3.88	5.25	2.81	4.75	4.75

The stock price was 113.25. The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January). The times to expiration were .0384 (November), .1342 (December), and .211 (January). Assume no dividends unless indicated.

What is the intrinsic value of the January 110 call?

1. $2.25  B. $2.75  C. $3.00  D. $3.25  E. $3.50

2. The stock price was 113.25. The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January). The times to expiration were .0384 (November), .1342 (December), and .211 (January). Assume no dividends unless indicated.

What is the time value of the January  110 call?

1. $2.38  B. $3.88  C. $4.00  D. $4.13  E. $5.00

3. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January). The times to expiration were .0384 (November), .1342 (December), and .211 (January).  Assume no dividends unless indicated.

What is the intrinsic value of the December 115 put?

3. 1. $1.25  b. $1.75  c. $2.20  d. $2.50  e. $2.75
4. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January).  The times to expiration were .0384 (November), .1342 (December), and .211 (January).  Assume no dividends unless indicated.

What is the time value of the December 115 put?

1. $2.50  B. $2.88  C. $3.00  D. $3.38  E. $3.88

5. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January).  The times to expiration were .0384 (November), .1342 (December), and .211 (January).  Assume no dividends unless indicated.

What is the lower bound of the November 110 call?

1. $3.55  B. $4.31  C. $4.56  D. $5.35  E. $5.23

6. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January).  The times to expiration were .0384 (November), .1342 (December), and .211 (January).  Assume no dividends unless indicated.

What is the lower bound of the December 115 put?

1. $1.25  B. $1.52  C. $1.65  D. $1.75  E. $1.94

7. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January).  The times to expiration were .0384 (November), .1342 (December), and .211 (January).  Assume no dividends unless indicated.

What is the lower bound of the December 115 put if the option were European options?

1. $0.64  B. $0.87  C. $1.33  D. $1.44  E. $1.67

8. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January).  The times to expiration were .0384 (November), .1342 (December), and .211 (January).  Assume no dividends unless indicated.

From American put-call parity, what is the minimum value that the sum of the stock price and November 110 put price can be?

1. $111.56  B. $114.08  C. $117.67  D. $118.25  E. $119.67

9. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January).  The times to expiration were .0384 (November), .1342 (December), and .211 (January).  Assume no dividends unless indicated.

From American put-call parity, what is the maximum value that the sum of the stock price and November 110 put price can be?

1. $111.33  B.  $114.38  C. $117.33  D. $118.25  E. $119.67

10. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January).  The times to expiration were .0384 (November), .1342 (December), and .211 (January).  Assume no dividends unless indicated.

How much is the maximum difference between the December 105 and 115 calls?

A. $5 B. $7.50 C. $10 D. $12.50 E. $15

11. In the above question, if these options were European options, how much is the maximum difference between the December 105 and 115 calls?

A. $5.53 B. $7.86 C. $9.90 D. $12.14 E. $14.57

12. The stock price was 113.25.  The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January).  The times to expiration were .0384 (November), .1342 (December), and .211 (January).  Assume no dividends unless indicated.

Suppose you knew that the December 115 options were correctly priced but suspected that the stock was mispriced. Using put-call parity, what would you expect the stock price to be? For this problem, treat the options as if they were European.

A. $112.33 B. $112.71 C. 112.89 D. $113.02 E. $113.45

Answer 1

1]

When stock price > strike price of call option, intrinsic value of call option = stock price - strike price of call option

intrinsic value of call option = $113.25 - $110 = $3.25

2]

time value = option price - intrinsic value

time value = $8.25 - $3.25 = $5.00

3]

When stock price < strike price of put option, intrinsic value of put option = strike price of put option - stock price

intrinsic value of putl option = $115 - $113.25 = $1.75

4]

time value = option price - intrinsic value

time value = $4.75 - $1.75 = $3.00