R73 练习: Pricing and Valuation of Options

R73 练习: 期权的定价与估值

考纲范围

• explain the exercise value, moneyness, and time value of an option
• contrast the use of arbitrage and replication concepts in pricing forward commitments and contingent claims
• identify the factors that determine the value of an option and describe how each factor affects the value of an option

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Q1.

The time value of an option reflects the combined effect of time and volatility. Time value of an option:

A. represents the sum of the market price of the option and its exercise value.

B. refers to the portion of an option’s premium that is attributable to the amount of time remaining until the expiration of the option contract.

C. decrease gradually to zero at expiration and the process is called time value of money.

查看答案与解析

答案：B

解析：期权的时间价值是期权费中超出内在价值的部分，反映了到期前标的价格波动可能带来的额外价值。时间价值随到期临近而衰减（time decay），不是”time value of money”。

选项	判断	解析
A	✗	时间价值 = 期权费 - 内在价值，不是两者之和
B	✓	正确。时间价值是期权费中归因于剩余时间的部分
C	✗	时间价值衰减的过程叫time decay，不是time value of money

关联：R73: Pricing and Valuation of Options

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Q2.

Jan, CFA, a fixed income fund manager for Southern Shores Investments. He wants to add options to his portfolio to decrease market risk and enters into a six-month call option of stock ABC with strike price of $55 and premium of $3. What is the moneyness of the option when the price of ABC stock at expiration is $50?

A. In-the-money

B. At-the-money

C. Out-of-the-money

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答案：C

解析：对于看涨期权（call），当标的价格($50) < 行权价($55)时，期权处于虚值状态（out-of-the-money）。价值状态只与S和X有关，与期权费premium无关。

选项	判断	解析
A	✗	Call in-the-money需要 $S>X$，但此处 $50 < 55$
B	✗	At-the-money需要 $S=X$，但此处 $50 \neq 55$
C	✓	S(\50) < X($55)$，call option处于虚值状态（OTM）

关联：R73: Pricing and Valuation of Options

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Q3.

The exercise value of an option is considered as the value of an option if it were exercised today. Which of the following is correct regarding exercise value?

A. For call options, exercise value can be calculated as the present value of exercise price minus underlying price if the result is positive.

B. For put options, exercise value can be calculated by subtracting the present value of exercise price from the market price of the underlying asset if the result is positive.

C. An option’s total value equals exercise value plus time value.

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答案：C

解析：期权的总价值 = 内在价值（exercise value）+ 时间价值（time value）。这是期权定价的基本分解。

选项	判断	解析
A	✗	Call的内在价值 = $\max (0,S-PV(X))$，是标的价格减行权价现值（方向反了）
B	✗	Put的内在价值 = $\max (0,PV(X)-S)$，是行权价现值减标的价格（方向反了）
C	✓	正确。期权总价值 = 内在价值 + 时间价值

关联：R73: Pricing and Valuation of Options

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Q4.

Consider a European call option in which the exercise price is $X$ and the underlying price is $S_0$. Which of the following is the lower limit of the European call price?

A. $Max\left[0,S_0-\frac{X}{(1+r{)}^T}\right]$

B. $Max\left[0,\frac{X}{(1+r{)}^T}-S_0\right]$

C. $Max[0,S_0-X]$

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答案：A

解析：欧式看涨期权的价格下限为 $\max (0,S_0-X(1+r{)}^{-T})$，即标的价格减去行权价的现值，取较大值与零比较。

选项	判断	解析
A	✓	欧式call的下限：$\max (0,S_0-X/(1+r{)}^T)$
B	✗	这是欧式put的下限公式
C	✗	这是到期时call的payoff公式，不是存续期间的价格下限

关联：R73: Pricing and Valuation of Options

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Q5.

Consider a European put option in which the exercise price is $X$ and the underlying price is $S_0$. Which of the following is the lower limit of the European put price?

A. $Max\left[0,S_0-\frac{X}{(1+r{)}^T}\right]$

B. $Max\left[0,\frac{X}{(1+r{)}^T}-S_0\right]$

C. $Max[0,X-S_0]$

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答案：B

解析：欧式看跌期权的价格下限为 $\max (0,X(1+r{)}^{-T}-S_0)$，即行权价的现值减去标的价格，取较大值与零比较。

选项	判断	解析
A	✗	这是欧式call的下限公式
B	✓	欧式put的下限：$\max (0,X/(1+r{)}^T-S_0)$
C	✗	这是到期时put的payoff公式，不是存续期间的价格下限

关联：R73: Pricing and Valuation of Options

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Q6.

Which of the following factors is positively correlated with the value of a call option?

A. The exercise price.

B. The risk-free rate.

C. Benefits of holding the asset.

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答案：B

解析：无风险利率与看涨期权价值正相关。利率上升 → 行权价现值下降 → call价值上升。行权价与call负相关，持有收益与call负相关。

选项	判断	解析
A	✗	行权价与call价值负相关（X越高，call价值越低）
B	✓	无风险利率与call价值正相关（r上升，PV(X)下降，call价值上升）
C	✗	持有收益（如股息）与call价值负相关（收益高则S会下降）

关联：R73: Pricing and Valuation of Options

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Q7.

John, CFA, manages assets for high-net-worth individuals and family. He hopes to provide protection for equity funds through European put options. He realizes that the volatility of the underlying price will strongly affect the value of European put options. When the volatility of the underlying price increase, the value of European put options will likely to:

A. increase.

B. decrease.

C. remain the same.

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答案：A

解析：波动率（volatility）与所有期权（无论call还是put）的价值正相关。波动率增加意味着标的价格大幅变动的可能性增加，期权持有者可以从有利方向获益，同时不利方向的损失有限（最多损失premium）。

选项	判断	解析
A	✓	波动率上升 → put option价值上升
B	✗	波动率与期权价值正相关，不会导致价值下降
C	✗	波动率变化会影响期权价值

关联：R73: Pricing and Valuation of Options

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Q8.

Which of the following statements about factors affecting put option value is most accurate?

A. The higher the benefit on underlying asset, the higher a put option value.

B. The higher the cost on underlying asset, the higher a put option value.

C. The longer time to expiration, the higher a put option value.

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答案：A

解析：持有收益（benefit/income）越高，标的资产价格会因分红等而下降，有利于put option持有者。持有成本与put负相关，到期时间对欧式put的影响不确定（有例外）。

选项	判断	解析
A	✓	持有收益高 → 标的价格倾向下降 → put价值上升
B	✗	持有成本高 → 远期价格上升 → 不利于put → put价值下降
C	✗	到期时间对欧式put的影响不确定（有例外情况可能导致put价值下降）

关联：R73: Pricing and Valuation of Options

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Q9.

Which of the following factors is positively correlated with the value of a put option?

A. Time to expiration.

B. Exercise price.

C. Cost of holding the asset.

查看答案与解析

答案：B

解析：行权价与put价值正相关（行权价越高，put持有者的卖出价越有利）。到期时间对欧式put影响不确定，持有成本与put负相关。

选项	判断	解析
A	✗	到期时间对欧式put的影响不确定（有例外可能导致下降）
B	✓	行权价越高，put价值越高（卖出价更有利）
C	✗	持有成本(C)与put价值负相关

关联：R73: Pricing and Valuation of Options