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Chapter Fifteen
Markets for Options and Contingent Claims
This chapter contains 50 multiple choice questions, 15 short problems, and 9 longer problems.
Multiple Choice
1. An option to buy a specified item at a fixed price is a(n) ________; an option to sell is a ________.
(a) put; call
(b) spot option, call
(c) call; put
(d) put; spot option
Answer: (c)
2. A(n) ________ option can be exercised up to and on the expiration date, whereas a(n) ________ option can only be exercised on the expiration date.
(a) American-type; Bermudan-type
(b) American-type; European-type
(c) European-type; American-type
(d) Bermudan-type; European-type
Answer: (b)
3. The difference between exercise price and current stock price is the tangible value of an ________, and the difference between the current stock price and exercise price is the tangible value of an ________.
(a) out of the money put option; in the money call option
(b) in the money put option; out of the money call option
(c) in the put money option; at the money call option
(d) at the money put option; in the money put option
Answer: (b)
4. A call option is said to be out of the money if its ________.
(a) exercise price is equal to the price of the underlying stock
(b) current stock price is greater than its strike price
(c) strike price is greater than the current stock price
(d) strike price is less than its current stock price
Answer: (c)
5. The time value of an option is ________.
(a) the difference between an options stock price and its tangible value
(b) the difference between the current stock price and exercise price
(c) the difference between the exercise price and the stock price
(d) the difference between an options market price and its tangible value
Answer: (d)
6. The prices of puts are ________ the higher the exercise price, and the prices of calls are ________ the higher is the exercise price.
(a) lower; higher
(b) higher; lower
(c) lower; lower
(d) higher; higher
Answer: (b)
Questions 7 through 10 refer to the following hypothetical information:
Listing of LePlastrier Options (symbol: LLB)
(Prices listed are closing prices.)
February 27, 2009
CALLS
Stock Price on NYSE
Exercise Price
January
February
April
109.75
109.75
109.75
107
110
113
3.375
0.625
0.125
5.625
2.1875
0.875
7.125
4.875
2.375
PUTS
Stock Price on NYSE
Exercise Price
January
February
April
109.75
109.75
109.75
107
110
113
1.75
3.625
9
3.375
5.875
10
5.875
7.375
11.75
7. What is the tangible value of the April LLB 110 put?
(a) 0
(b) 0.25
(c) 3.25
(d) 7.375
Answer: (b)
8. What is the tangible value of the February LLB 107 call?
(a) 0
(b) 5.625
(c) 0.75
(d) 2.75
Answer: (d)
9. In what state is the January LLB 107 call?
(a) in-the-money
(b) out-of-the-money
(c) at-the-money
(d) zero state
Answer: (a)
10. In what state is the February LLB 113 put?
(a) in-the-money
(b) out-of-the-money
(c) at-the-money
(d) zero state
Answer: (a)
11. Which is the correct formula describing the put-call parity relation?
(a) S + C =
(b) S + P =
(c) S + P =
(d) S + C =
Answer: (c)
12. A protective-put strategy is where one ________.
(a) buys a share of stock and a call option
(b) buys a put option and a call option
(c) buys a put option and a share of stock
(d) sells a put option and buys a call option
Answer: (c)
13. SPX options are effectively calls or puts on a hypothetical index fund that invests in a portfolio composed of the stocks that make up the S&P 500 index, each of the 500 companies ________.
(a) equally represented with respect to the others
(b) in proportion to the total value of its shares outstanding
(c) in proportion to the trading volume of its shares
(d) rotating on a proportional basis dependent on earnings
Answer: (b)
14. The SPX contract specifies that if the call option is exercised, the owner of the options __________.
(a) pays a cash settlement of $100 times the difference between the index value and the strike price
(b) receives a cash payment of $100 times the difference between the index and tangible values
(c) receives a cash payment of $100 times the difference between the index value and the strike price
(d) receives a payment of index shares $100 times the difference between the index value and strike price
Answer: (c)
15. The stock of Deneuvre Ltd, currently lists for $370 a share, while one-year European call options on this stock with an exercise price of $150 sell for $290 and European put options with the same expiration date and exercise price sell for $58.89. Infer the yield on a one-year zero-coupon U.S. government bond sold today.
(a) 2.49%
(b) 8.00%
(c) 11.11%
(d) 24.90%
Answer: (b)
16. The stock of Fellini Ltd, currently lists for $550 a share, while one-year European call options on this stock with an exercise price of $250 sell for $380 and European put options with the same expiration date and exercise price sell for $56.24. Infer the yield on a one-year zero-coupon U.S. government bond sold today.
(a) 6.67%
(b) 10.5%
(c) 19.76%
(d) 23.76%
Answer: (b)
17. Consider a stock that can take only one of two values a year from now, either $250 or $90. Also consider a call option on the stock with an exercise price of $160 expiring in one year. At expiration, the call will pay either $90 if the stock price is $250 or it will pay nothing if the stock price is $90. Calculate the call options hedge ratio.
(a) 0.3600
(b) 0.4444
(c) 0.5625
(d) 0.6400
Answer: (c)
18. Consider a stock that can take only one of two values a year from now, either $320 or $130. Also, consider a call option on the stock with an exercise price of $200 expiring in one year. At expiration, the call will pay either $120 if the stock price is $320 or it will pay nothing if the stock price if $130. The risk-free rate is 5% per year. Calculate the hedge ratio.
(a) hedge ratio = 0.3750
(b) hedge ratio = 0.4063
(c) hedge ratio = 0.6000
(d) hedge ratio = 0.6316
Answer: (d)
19. As one attempts to improve the two state model, we can further subdivide time intervals into shorter increments and build the ________.
(a) Binomial option pricing model
(b) Black-Scholes model
(c) Discrete model
(d) a and b
Answer: (d)
20. When the ________ price of the underlying stock equals the ________, this reasoning leads to the simplified Black-Scholes formula.
(a) future; price of the call
(b) current; future value of the strike price
(c) current; present value of the strike price
(d) future; price of the put
Answer: (c)
21. Which is the correct formula using Black-Scholes method for a European call option on a non-dividend paying stock?
(a) C = N(d1)S + N(d2)Ee-rT
(b) C = N(d2)S + N(d1)Ee-rT
(c) C = N(d1)S N(d2)Ee-rT
(d) C = N(d1)E N(d2)Se-rT
Answer: (c)
22. Use the Black-Scholes formula to find the value of a European call option on the following stock:
Time to maturity 6 months
Standard deviation 50 percent per year
Exercise price 60
Stock price 60
Interest rate 10 percent per year
Assume it is a non-dividend paying stock. The value of a call is ________.
(a) $6.83
(b) $9.76
(c) $9.96
(d) $14.36
Answer: (b)
23. Use the Black-Scholes formula to find the value of a European call option on the following non-dividend paying stock:
Time to maturity 4 months
Standard deviation 45 percent per year
Exercise price 65
Stock price 60
Interest rate 11 percent per year
(a) $5.09
(b) $7.75
(c) $9.66
(d) $11.43
Answer: (a)
24. The Black-Scholes formula has four parameters that are directly observable and one that is not. Which of the following parameter is not directly observable?
(a) exercise price
(b) stock price
(c) volatility of the stock return
(d) risk-free interest rate
Answer: (c)
25. As a financial analyst at Dodgie Brothers investment house, you are asked by a client if she should purchase European call options on Angel Heart Ltd shares that are currently selling in U.S. dollars for $45.00. The options on Angel Heart Ltd have an exercise price of $65.00. The current stock price for Angel Heart is $70 and the estimated rate of return variance of the stock is 0.09. If these options expire in 35 days and the riskless interest rate over the period is 6%, what should your client do?
(a) The call is valued at $19.63; this is less than $70 and not worth buying.
(b) The call is valued at $5.37; this is less than $45 and not worth buying.
(c) The call is valued at $70; this is greater than $45 and worth buying.
(d) The call is valued at $15; this is greater than $6 and worth buying.
Answer: (b)
26. Use the linear approximation of the Black-Scholes model to find the value of a European call option on the following stock:
Time to maturity 6 months
Standard deviation 0.3
Exercise price 50
Stock price 50
Interest rate 10 percent per year
What is the discrepancy between the value obtained from the linear approximation and traditional Black-Scholes formula?
(a) Linear approx = $3.01; Discrepancy = $1.0154
(b) Linear approx = $4.24; Discrepancy = $1.2016
(c) Linear approx = $3.01; Discrepancy = $1.2016
(d) Linear approx = $4.76; Discrepancy = $1.2153
Answer: (b)
27. Use the Black-Scholes formula to find the value of a European call option and a European put option on the following stock:
Time to maturity 0.5
Standard deviation 30% per year
Exercise price 100
Stock price 100
Risk-free interest rate 10 percent per year
The values are closest to:
(a) Value of call = $16.73; Value of put = $7.22
(b) Value of call = $12.27; Value of put = $9.32
(c) Value of call = $10.90; Value of put = $6.02
(d) Value of call = $8.28; Value of put = $3.40
Answer: (c)
28. Use the Black-Scholes formula to find the value of a European call option and a European put option on the following stock:
Time to maturity 0.5
Standard deviation 42% per year
Exercise price 100
Stock price 110
Risk-free interest rate 12 percent per year
The values are closest to:
(a) Value of call = $29.26; Value of put = $7.95
(b) Value of call = $21.53; Value of put = $5.73
(c) Value of call = $10.30; Value of put = $13.90
(d) Value of call = $8.28; Value of put = $3.40
Answer: (b)
29. Call options become more valuable as the exercise price ________, as the stock price ________, as the interest rate ________, and as the stocks volatility ________.
(a) increases; increases; increases; increases
(b) increases; decreases; decreases; increases
(c) decreases; increases; decreases; increases
(d) decreases; increases; increases; increases
Answer: (d)
30. Implied volatility is the value of s that makes ________ of the option equal to the value computed using the option-pricing formula.
(a) the exercise price
(b) the observed market price
(c) the historical market price
(d) the call value
Answer: (b)
31. Calculate the implied volatility of a stock which has a time to maturity of 3 months, a risk-free rate of 8%, exercise price of $70, current stock price of $65, and does not pay dividends. Use the linear function of the option price. The value of the call is $6.50
(a) » 15%
(b) » 35%
(c) » 46%
(d) » 50%
Answer: (d)
32. Calculate the implied volatility of a stock using the linear function of the option price for the following data: time to maturity = 4 months, call value = $5.80, stock price = $50 and risk-free rate = 10%. The value is closest to:
(a) » 14.54%
(b) » 36.78
(c) » 45%
(d) » 50.50%
Answer: (d)
33. The same methodology used to price options can be used to value many other contingent claims, including:
(a) corporate stocks and bonds
(b) loan guarantees
(c) real options embedded in research and development
(d) all of the above
Answer: (d)
34. The replication strategy used in contingent claims analysis is known as:
(a) claims financing
(b) self-financing
(c) replicating financing
(d) risk adjusted financing
Answer: (b)
Questions 35-37 refer to the following information:
Crabby Tabby Corporation is in the cat food business and has a total market value of $140 million. The corporation issues two types of securities: common stock (850,000 shares) and zero-coupon bonds (95,000 bonds each with a face value of $1,000). The bonds are considered to be default-free and mature in one year. The risk-free interest rate is 4.5% per year.
35. What is the market value of Crabby Tabbys bonds?
(a) $99,275,000
(b) $95,000,000
(c) $92,476,091
(d) $90,909,091
Answer: (d)
36. What is the market value of Crabby Tabbys stocks?
(a) $45,000,000
(b) $43,062,201
(c) $46,976,946
(d) $49,090,909
Answer: (d)
37. What is Crabby Tabbys share price?
(a) $52.94
(b) $55.26
(c) $57.75
(d) $58.26
Answer: (b)
Questions 38-40 refer to the following information:
The Callas Corporation is in the music publishing business, and has a total market value of $115 million. The corporation issues two types of securities: common stock (800,000 shares) and zero-coupon bonds (90,000 bonds each with a face value of $1,000). The bonds are considered to be default-free and mature in one year. The risk-free interest rate is 6% per year.
38. What is the market value of Callas bonds?
(a) $95,400,000
(b) $90,000,000
(c) $84,905,650
(d) $83,333,333
Answer: (c)
39. What is the market value of Callas stock?
(a) $30,094,340
(b) $27,042,314
(c) $25,000,000
(d) $19,600,000
Answer: (a)
40. What is Callas share price?
(a) $24.50
(b) $31.25
(c) $37.62
(d) $41.66
Answer: (c)
41. The Gobbi Corporation has a total market value of $120 million. The corporation issues two types of securities: common stock (950,000 shares) and zero-coupon bonds (95,000 bonds, each with a face value of $1,000). There is risk associated with the bonds, however, because the bonds mature in one year. What do the stockholders receive a year from now, if the value (denoted V1) of the firms assets falls short of $95 million?
(a) The company will default on the debt and the stockholders will get nothing.
(b) The company will default on the debt and the stockholders will receive all of the firms assets.
(c) The stockholders receive V1 $95 million.
(d) None of the above.
Answer: (a)
42. Lenski Corporation has issued two types of securities: common stock (2 million shares) and zero-coupon bonds with an aggregate face value of $95 million (95,000 bonds each with a face value of $1,000). Lenskis bonds mature one year from now. If we know that the
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