R72 练习: 利率互换及其他互换的定价与估值
考纲范围
- describe how swap contracts are similar to but different from a series of forward contracts
- contrast the value and price of swaps
Q1.
The swap contract value:
A. is zero at initiation.
B. is fixed over the life of the contract.
C. is the same with the value of each component forward contract.
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答案：A
解析：互换合约在期初的价值为零（与远期一样是双务合同）。互换可视为一系列远期合约的组合，但各组成部分的远期合约价值可正可负，只是总和为零。
选项 判断 解析 A ✓ 正确。互换合约在期初价值为零 B ✗ 互换的价值在合约存续期间会随市场变化而变动 C ✗ 各组成远期合约的价值可能不同（有正有负），但总和为零 关联：R72: Pricing and Valuation of Interest Rates and Other Swaps
Q2.
Which of the following statements regarding interest rate swap is most likely correct?
A. A swap is equivalent to a series of forward contracts.
B. The value of the swap at initiation is always non-zero.
C. The price of a swap at initiation is always zero.
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答案：A
解析：互换可以视作一系列远期合约的组合。互换在期初的价值为零（不是B），互换的价格（固定利率）不为零（不是C说的价格为零）。
选项 判断 解析 A ✓ 正确。互换等价于一系列远期合约 B ✗ 互换在期初的价值为零，不是非零 C ✗ 互换的价格（swap rate/固定利率）不为零；为零的是价值 关联：R72: Pricing and Valuation of Interest Rates and Other Swaps
Q3.
GDN Asset Management Company currently has a \m fixed-rate bond position in its investment portfolio that is about to mature in six months. The proceeds of the bond will be reinvested to create another 3-year fixed income exposure. Which of the following instrument is suitable for GDN to hedge the reinvestment risk?
A. A series of pay-fixed FRAs, starts today with first settlement in 6 months.
B. A receive-fixed swap for 3 years, starts in 6 months.
C. A pay-fixed swap for 3 years, starts in 6 months.
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答案：B
解析：GDN面临再投资风险（担心利率下降导致再投资收益降低）。收取固定利率（receive-fixed）的互换可以锁定未来的固定收益，对冲再投资风险。
选项 判断 解析 A ✗ Pay-fixed FRA意味着支付固定利率，方向错误 B ✓ Receive-fixed swap锁定固定收益，对冲再投资风险 C ✗ Pay-fixed swap是支付固定利率，不能对冲再投资风险 关联：R72: Pricing and Valuation of Interest Rates and Other Swaps
Q4.
Which of the following interpretations of fixed swap rate is least correct?
A. A multiperiod breakeven rate making the expected future floating and fixed cash flows indifferent to the investors.
B. Arithmetic mean of the zero rates on each settlement date through the maturity of the swap.
C. The internal rate of return of cash flows based on the implied forward rates through the settlement periods.
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答案：B
解析：固定互换利率不是各结算日零利率的算术平均，而是使固定端和浮动端现金流现值相等的利率。它可以理解为多期盈亏平衡利率（A正确）或基于隐含远期利率的IRR（C正确）。
选项 判断 解析 A ✓ 正确。固定利率是使投资者对固定和浮动现金流无差异的盈亏平衡利率 B ✗ 错误。固定利率不是零利率的算术平均 C ✓ 正确。固定利率可解释为基于隐含远期利率的内部收益率 关联：R72: Pricing and Valuation of Interest Rates and Other Swaps
Q5.
The swap value is calculated by
A. adding up the present value of the fixed payments in the future.
B. adding up the present value of the floating payments in the future.
C. adding up the present value of the net cash payments in the future.
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答案：C
解析：互换的价值等于未来净现金支付（浮动端减固定端或固定端减浮动端）的现值之和。
选项 判断 解析 A ✗ 仅计算固定端不够，需要看净现金流 B ✗ 仅计算浮动端不够，需要看净现金流 C ✓ 正确。互换价值 = 未来净现金支付的现值之和 关联：R72: Pricing and Valuation of Interest Rates and Other Swaps
Q6.
Flexi entered a 5-year receive-fixed US 1 million interest rate swap on three-month MRR. The swap was priced at 2.05% and the initial three-month MRR was quoted at 2%. What is the settlement value for Flexi in three months?
A. US 125
B. US -2375
C. US 500
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答案：A
计算过程：
- Flexi是receive-fixed方，收取固定利率2.05%，支付浮动利率MRR
- 第一期结算使用初始MRR = 2%
- 净结算 = (固定利率 - 浮动利率) 名义本金 期限
- 净结算 = (2.05\% - 2\%) \times \1{,}000{,}000 \times (3/12)$
- = 0.05\% \times \1{,}000{,}000 \times 0.25 = $125$
选项 判断 解析 A ✓ (2.05\% - 2\%) \times 1,000,000 \times 0.25 = \125$ B ✗ 计算有误 C ✗ 未按季度计算 关联：R72: Pricing and Valuation of Interest Rates and Other Swaps
Q7.
When the floating-rate receiver of a swap contract has a positive MTM value on a settlement date, it may indicate:
A. the last period MRR is higher than the swap rate.
B. the current settlement value plus the present value of all the future net settlements is higher for the floating receiver.
C. the present value of the future floating interest is higher than the fixed interest.
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答案：C
解析：互换的盯市价值（MTM value）包含结算价值和未来预期净结算的现值。对于浮动利率接收方，正的MTM价值意味着未来浮动利息的现值大于固定利息的现值。注意区分结算价值（仅看当期）和MTM价值（看全局）。
选项 判断 解析 A ✗ 上一期MRR高于swap rate只说明当期结算有利，不能说明整体MTM为正 B ✗ 说法不够准确，MTM是从一方角度看的整体价值 C ✓ 正确。浮动端收款方MTM为正意味着未来浮动利息现值 > 固定利息现值 关联：R72: Pricing and Valuation of Interest Rates and Other Swaps