R71 练习: 期货合约的定价与估值
考纲范围
- compare the value and price of forward and futures contracts
- explain why forward and futures prices differ
Q1.
Which of the following statements regarding mark-to-market is least accurate?
A. Mark-to-market allows futures contracts to be settled daily.
B. Mark-to-market can eliminate the default risk.
C. Mark-to-market causes the value of futures contracts to return to zero at the end of every trading day.
查看答案与解析
答案：B
解析：逐日盯市（mark-to-market）使期货合约每日结算，合约价值每日归零。但逐日盯市不能”消除”违约风险，只能大幅降低违约风险。
选项 判断 解析 A ✓ 正确。逐日盯市使期货每日结算 B ✗ 逐日盯市降低但不能消除（eliminate）违约风险 C ✓ 正确。每日结算后，期货合约价值归零
Q2.
Robert, a derivatives trader at Meihao investment, is required to price a six-month futures contract. The corresponding underlying is ABC stock, which is trading for $120 and pays a $2 dividend in six months. Assuming the annual interest rate is 2%, the futures price is closest to:
A. $119.19 B. $121.19 C. $118.00
查看答案与解析
答案：A
计算过程：
- 期货定价公式与远期相同：
- PV(\text{Div}) = \frac{2}{(1.02)^{0.5}} = \frac{2}{1.00995} = \1.98$
- F_0 = (120 - 1.98) \times (1.02)^{0.5} = 118.02 \times 1.00995 = \119.19$
或者更直接地：F_0 = S_0 \times (1+r)^T - \text{Div} = 120 \times (1.02)^{0.5} - 2 = 121.19 - 2 = \119.19$
选项 判断 解析 A ✓ $120 \times (1.02)^{0.5} - 2 \approx $119.19$ B ✗ 计算有误 C ✗ 计算有误
Q3.
If the futures price is higher than an identical forward price, the reason might be that:
A. futures prices and interest rates are positively correlated.
B. futures prices and interest rates are negatively correlated.
C. futures prices and interest rates are uncorrelated.
查看答案与解析
答案：A
解析：当期货价格与利率正相关时，利率上升 → 期货价格上升 → 多头盈利可以以更高利率再投资；利率下降 → 期货价格下降 → 多头亏损但以更低利率融资。这种优势使期货价格高于远期价格。
选项 判断 解析 A ✓ 正相关时，期货多头有再投资优势，期货价格 > 远期价格 B ✗ 负相关时，期货价格 < 远期价格 C ✗ 不相关时，期货价格 = 远期价格
Q4.
According to FRA and interest rate futures, which of the following statements is most accurate?
A. Interest rate futures is more liquid and standardized compared to FRAs.
B. A borrower can long FRA or interest rate futures to hedge a liability.
C. The long side of the interest rate futures will profit when future MRR rises.
查看答案与解析
答案：A
解析：利率期货是场内交易，比FRA（场外交易）更具流动性和标准化。对于利率期货，价格 = 100 - 利率，利率上升时价格下降，long方亏损。借款人想对冲利率上升应long FRA或short利率期货。
选项 判断 解析 A ✓ 正确。利率期货是场内标准化合约，流动性更强 B ✗ 借款人应long FRA但应short（而非long）利率期货来对冲 C ✗ 利率上升时利率期货价格下降，long方亏损而非获利
Q5.
Flexi bought an interest rate futures contract on three-month MRR with a price of 97.25, and now the futures price has increased to 98. Calculate the cumulative gain of Flexi if the contract notional principle is $2,000,000. A. -3,750
B. 1,250
C. 3,750
查看答案与解析
答案：C
计算过程：
- 利率期货价格从97.25上升到98，变动 = 98 - 97.25 = 0.75
- 隐含利率变动 = 0.75%（价格上升意味着利率下降）
- BPV（基点价值）= 名义本金 0.01% 时间
- BPV = \2{,}000{,}000 \times 0.0001 \times 0.25 = $50$ /bp
- 变动 = 75 bps
- 累计收益 = 75 \times \50 = $3{,}750$
或直接：$2,000,000 \times 0.75% \times (3/12) = 3,750$
选项 判断 解析 A ✗ 符号错误，long方在价格上升时获利 B ✗ 计算有误 C ✓ \2{,}000{,}000 \times 0.75% \times 0.25 = $3{,}750$