R69 练习: 套利、复制与衍生品定价中的持有成本
考纲范围
- explain how the concepts of arbitrage and replication are used in pricing derivatives
- explain the difference between the spot and expected future price of an underlying and the cost of carry associated with holding the underlying asset
Q1.
Which of the following is least likely a characteristic of an arbitrage opportunity?
A. No initial capital required.
B. If holding a risk-free portfolio generates a return higher than risk-free rate, then an arbitrage opportunity exists.
C. A riskless profit can be sustained.
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答案：C
解析：套利（arbitrage）具有两个核心特征：1）无风险，2）无初始投入。套利利润不会持续存在，套利活动会迅速消除套利机会。
选项 判断 解析 A ✓ 正确。套利不需要初始资本投入 B ✓ 正确。无风险组合的收益超过无风险利率意味着存在套利机会 C ✗ 错误。套利利润不可持续，市场套利活动会迅速消除套利机会 关联：R69: Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
Q2.
The Law of one price is a result of arbitrage. More specifically,
A. the law of one price exists because differences between asset prices in different locations would eventually be eliminated due to the arbitrage activities.
B. the law of one price exists because differences between asset prices in different locations would not be eliminated as arbitrage is very difficult.
C. the law of one price exists because differences between asset returns in different locations would eventually be eliminated due to arbitrage activities.
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答案：A
解析：一价定律（Law of One Price）是套利活动的结果。不同地点的相同资产的价格差异会因套利活动而最终消除，使相同资产在各处价格趋同。
选项 判断 解析 A ✓ 正确。套利活动会消除不同地点间的资产价格差异 B ✗ 错误。套利并非困难，价格差异会被消除 C ✗ 一价定律是关于价格（price）而非收益（returns）的趋同 关联：R69: Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
Q3.
Replication is widely used in derivatives pricing and valuation. Which of the following replication is correct?
A. A long risk-free asset can be replicated by a long asset and a short derivative.
B. A long derivative can be replicated by a long asset and a long risk-free asset.
C. A short asset can be replicated by a long derivative and a short risk-free asset.
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答案：A
解析：复制的基本公式：Asset + Derivative = Risk-free asset，即 Long asset + Short derivative = Long risk-free asset。变形可得各种复制关系。
选项 判断 解析 A ✓ Long risk-free = Long asset + Short derivative，正确 B ✗ Long derivative = Long risk-free + Short asset（不是Long asset + Long risk-free） C ✗ Short asset = Short derivative + Short risk-free（不是Long derivative + Short risk-free） 关联：R69: Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
Q4.
Which of the following factors is least likely to influence the price of a forward contract?
A. The dividends on a stock.
B. The convenience yield on holding the underlying.
C. The default risk premium.
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答案：C
解析：远期价格的影响因素包括：即期价格、持有成本（包括无风险利率/机会成本、存储成本）和持有收益（包括股息、便利收益）。违约风险溢价不影响远期价格。
选项 判断 解析 A ✓ 股息作为持有收益（benefit of carry）会影响远期价格 B ✓ 便利收益（convenience yield）会影响远期价格 C ✗ 违约风险溢价不在远期定价公式中，最不可能影响远期价格 关联：R69: Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
Q5.
Which of the following is (are) true regarding benefits and costs of holding an asset?
I. Convenience yield are usually associated with commodities which maintain tight supplies.
II. Dividends are benefits that boost the forward price.
III. Opportunity cost is the risk-free rate.
A. I only
B. I and III only
C. I, II, and III
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答案：B
解析：便利收益通常与供应紧张的商品相关（I正确）；机会成本是无风险利率（III正确）；但股息是持有收益，会降低远期价格而非提高（II错误）。
选项 判断 解析 A ✗ 不完整，III也正确 B ✓ I和III正确。便利收益与紧缺商品相关，机会成本是无风险利率 C ✗ II错误。股息是持有收益（benefit），会降低远期价格，不是提高 关联：R69: Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
Q6.
Which of the following statements about pricing and valuation of forward contracts is most accurate?
A. Benefits of holding an asset will increase forward price at initiation.
B. Costs of holding an asset will decrease forward price at initiation.
C. Benefits of holding an asset will decrease forward price at initiation.
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答案：C
解析：远期价格公式：。持有收益（benefits）会降低远期价格，持有成本（costs）会提高远期价格。牢记”加成本减收益”。
选项 判断 解析 A ✗ 持有收益降低远期价格，不是提高 B ✗ 持有成本提高远期价格，不是降低 C ✓ 正确。持有收益（如股息、便利收益）会降低远期价格 关联：R69: Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives