Chapter 15
Stock Options
Concept Questions
1. Assuming American-style exercise rights, a call option confers the right, without the obligation, to
buy an asset at a given price on or before a given date. An American-style put option confers the
right, without the obligation, to sell an asset at a given price on or before a given date. European-
2. a. The buyer of a call option pays money for the right to buy….
3. In general, the breakeven stock price for a call purchase is the exercise price plus the premium paid.
4. If you buy a put option on a stock that you already own, you guarantee that you can sell the stock for
6. The intrinsic value of a put option at expiration is max{0, K – S}. By definition, the intrinsic value
7. The call is selling for less than its intrinsic value; an arbitrage opportunity exists. Buy the call for
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Education.
11. The March call and the October put are mispriced. The call is mispriced because it is selling for less
than its intrinsic value. The arbitrage is to buy the call for $3.50, exercise it and pay $55 for a share
of stock, and sell the stock for $59 for a riskless profit of $0.50. The October put is mispriced
12. The covered put would represent writing put options on the stock. This strategy is analogous to a
The protective call would represent the purchase of call options as a form of insurance for the short
13. The call is worth more. To see this, we can rearrange the put-call parity condition as follows:
C – P = S – K/(1+r)T
If the options are at the money, S = K, then the right-hand side of this expression is equal to the stock
14. Looking at the previous answer, if the call and put have the same price (i.e., C – P = 0), it must be
Solutions to Questions and Problems
NOTE: All end of chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this
solutions manual, rounding may appear to have occurred. However, the final answer for each problem is
found without rounding during any step in the problem.
Core Questions
1. Your options are worth $64 – 60 = $4 each, or $400 per contract. With eight contracts, the total value
2. Your options are worth $45 – 39 = $6 each, or $600 per contract. With five contracts, the total value
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Education.
3. The stock costs $50 per share, so if you invest $97,500, you’ll get 1,950 shares. The option premium
is $1.95, so an option contract costs $195. If you invest $97,500, you’ll get $97,500 / $195 = 500
If the stock is selling for $50, your profit is $0 on the stock, so your percentage return is 0%. Your
7. Stock price = $90:
Initial revenue = 30(100)($10.10) = $30,300
8. P = C – S + K / (1 + r)T
9. S = C – P + K / (1 + r)T
10. C = S + P – K / (1 + r)T
Intermediate Questions
11. Div = $1.45 / (1 + .04)2/12 = $1.44
12. Div = $2.10 / (1 + .06)3/12 = $2.07
S = C – P + Div + K / (1 + r)T
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Education.
13. Div = $1.40 / (1 + .05)2/12 = $1.39
14. You get to keep the premium in all cases. For 10 contracts and a $2.75 premium, that’s $2,750. If the
15. You get to keep the premium in all cases. For 15 contracts and a $2.40 premium, that’s $3,600. If the
16. The contract costs $1,400. At maturity, an in-the-money SPX option is worth 100 times the
17.
Stock price Short profit
Short put
payoff
Short
put profit Net profit
$50.00 $10.00 –$10.00 –$8.20 $1.80
18.
Stock price Short profit Call payoff Call profit Net profit
$60 $10 $0 –$3.40 $6.60
$65 $5 $0 –$3.40 $1.60
19.
Stock price Short profit
Short
Put payoff
Protective
Call payoff Total payoff
$70 $10 –$10 $0 $0
20. Stock price Put payoff Call payoff Total payoff
$70 –$10 $0 –$10
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Education.
21. Cost of strategy = $4.20 + 2.80 = $7.00
Stock price Call payoff Put payoff Total payoff Total profit
$65 $0 $10 $10 $3.00
22.
Index level
Long call
payoff
Short call
payoff Total payoff
2050 0 0 0
23.
Index level
Long put
payoff
Short put
payoff Total payoff
2000 100 –125 –25
24.
Index level
Long call
payoff
Short put
payoff Total payoff
2000 0 –100 –100
25.
Index level
Long call
payoff (1300)
Long call
payoff (1500)
Short call (2)
payoff (1400) Total payoff
1900 0 0 0 0
1950 0 0 0 0
2050 50 0 0 50
2100 100 0 0 100
2150 150 0 –100 50
$80.00
$85.00
$90.00
$95.00
$100.00
$105.00
$110.00
$115.00
$120.00
$125.00
$130.00
$(20.00)
$(15.00)
$(10.00)
$(5.00)
$–
$5.00
$10.00
$15.00
$20.00
$25.00
Total payof
Total profit
27. Total cost = $4.55 – 1.24 = $3.31
Stock price Long call payoff Short call payoff Total payoff Total profit
$15.00 $0 $0 $0 –$3.31
$17.00 $0 $0 $0 –$3.31
$20.00 $0 $0 $0 –$3.31
$21.00 $1.00 $0 $1.00 –$2.31
$22.00 $2.00 $0 $2.00 –$1.31
$23.00 $3.00 $0 $3.00 –$0.31
$24.00 $4.00 $0 $4.00 $0.69
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Education.
$15.00
$17.00
$20.00
$21.00
$22.00
$23.00
$24.00
$25.00
$28.00
$30.00
$(4.00)
$(3.00)
$(2.00)
$(1.00)
$–
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
Total payof
Total profit
28. Total cost = $0.45 – 1.64 = -$1.19
Stock price Long put payoff Short put payoff Total payoff Total profit
$15.00 $5.00 –$10.00 –$5.00 –$3.81
$17.00 $3.00 –$8.00 –$5.00 –$3.81
$20.00 $0 –$5.00 –$5.00 –$3.81
$15.00
$17.00
$20.00
$21.00
$22.00
$23.00
$24.00
$25.00
$28.00
$30.00
$(6.00)
$(5.00)
$(4.00)
$(3.00)
$(2.00)
$(1.00)
$–
$1.00
$2.00
Total payof
Total profit
$25.00
$30.00
$35.00
$38.00
$40.00
$42.00
$45.00
$50.00
$55.00
$(2.00)
$(1.00)
$–
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
Total payof
Total profit
30. Total cost = –$0.90 + 2($2.35) – $5.10 = –$1.30
Stock price Long put payoff
Short put payoff
(2x) Long put payoff Total payoff Total profit
$25.00 $10.00 –$30.00 $20.00 $0 –$1.30
$30.00 $5.00 –$20.00 $15.00 $0 –$1.30
$35.00 $0 –$10.00 $10.00 $0 –$1.30
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Education.
$25.00
$30.00
$35.00
$38.00
$40.00
$42.00
$45.00
$50.00
$55.00
$(2.00)
$(1.00)
$–
$1.00
$2.00
$3.00
$4.00
$5.00
$6.00
Total payof
Total profit
CFA Exam Review by Kaplan Schweser
1. b
Put-call parity states: S + Vp = Vc + Xe-rt
2. a
3. b
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Education.