Problem 1
The following quotes were observed for options on a given stock on November 1 of a given year:
|
Calls
|
Puts
|
Strike
|
Nov
|
Dec
|
Jan
|
Nov
|
Dec
|
Jan
|
105
|
8.40
|
10
|
11.50
|
5.30
|
1.30
|
2.00
|
110
|
4.40
|
7.10
|
8.30
|
0.90
|
2.50
|
3.80
|
115
|
1.50
|
3.90
|
5.30
|
2.80
|
4.80
|
4.80
|
a. Under what circumstances will the holder of the January 110 call make a gain?
b. Under what circumstances will the holder of the November 115 put make a gain?
c. Under what circumstances will the holder of the December 105 call make a gain of $200?
d. Under what circumstances will the December 105 call be exercised?
e. Under what circumstances will the holder of the November 110 put be obligated to exercise his option?
Problem 2
The following prices are available for call and put options on a stock priced at $50. The Black-Scholes model was used to obtain the prices.
|
Calls
|
Puts
|
Strike
|
March
|
June
|
March
|
June
|
45
|
6.84
|
8.41
|
1.18
|
2.09
|
50
|
3.82
|
5.58
|
3.08
|
4.13
|
55
|
1.89
|
3.54
|
6.08
|
6.93
|
Assume that each transaction consists of one contract (100 options) unless otherwise indicated.
1. What is the intrinsic value of the June 55 put?
2. What is the intrinsic value of the March 55 call?
3. What is the time value of the June 50 put?
4. What is the time value of the March 45 call?
5. Consider a bull money spread using the March 45/50 calls.
a. How much will the spread cost?
b. What is the maximum profit on the spread?
c. What is the maximum loss on the spread?
d. What is the profit if the stock price at expiration is $47?
6. Consider a long straddle constructed using the June 50 options.
a. What will the straddle cost?
b. What are the two breakeven stock prices at expiration?
c. What is the profit if the stock price at expiration is at $64.75?
d. Suppose a put is added to the straddle. This overall transaction is called a strip. Determine the profit at expiration on the strip if the stock price at expiration is $36.
Problem 3
Consider a stock priced at $30. There are put and call options available at exercise prices of 30 and a time to expiration of six months. The calls are priced at $2.89 and the puts cost $2.15. There are no dividends on the stock and the options are European. Assume that all transactions consist of 100 shares or one contract (100 options).
1. Suppose the investor bought a call, and hold it to expiration.
a. What is the investor's profit, if the stock price at expiration is $37?
b. What is the breakeven stock price at expiration?
c. What is the maximum profit on the transaction?
d. What is the maximum profit that the writer of a call can make?
2. Suppose the investor constructed a covered call.
a. At expiration the stock price is $27. What is the investor's profit?
b. At expiration the stock price is $41. What is the investor's profit?
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)