R70 练习: Pricing and Valuation of Forward Contracts

R70 练习: 远期合约的定价与估值

考纲范围

• explain how the value and price of a forward contract are determined at initiation, during the life of the contract, and at expiration
• explain how forward rates are determined for interest rate forward contracts and describe the uses of these forward rates

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Q1.

Which of the following statements about pricing and valuation of derivatives is most accurate?

A. The pricing of forward is the same concept as valuation, which is to find the intrinsic value of the asset.

B. The value of a forward is the difference between “with the position” from “without the position”.

C. The forward price equals its value at initiation.

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答案：B

解析：对于双务合同，价格（price）和价值（value）是不同的概念。价格是期初确定的，一旦确定不再改变。价值是”有合约”与”无合约”之间的差异。

选项	判断	解析
A	✗	定价（pricing）和估值（valuation）是不同概念
B	✓	正确。远期合约的价值是签约与不签约之间的差异
C	✗	远期合约在期初的价值为零（不是等于价格）

关联：R70: Pricing and Valuation of Forward Contracts

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Q2.

A food processing enterprise, facing rising storage cost for corn, agrees to enter a forward contract with contract size of 10 tons corn and maturity of 6 months. At initiation of the contract, the spot price of corn was $380 per ton, assume the present value of the increased storage cost is $50 per ton, and risk-free rate is 3%. Calculate the no-arbitrage forward price of this contract.

A. $436.41 B. $436.40 C. $430.00

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答案：B

计算过程：

• 远期价格公式：$F_0=(S_0+\text{Costs})\times (1+r{)}^T$
• $S_0=380$，存储成本现值 $=50$，$r=3\%$，$T=0.5$
• $F_0=(380+50)\times (1+0.03{)}^{0.5}=430\times 1.01489=436.40$

选项	判断	解析
A	✗	未正确计入存储成本
B	✓	$(380+50)\times (1.03{)}^{0.5}=436.40$
C	✗	计算有误

关联：R70: Pricing and Valuation of Forward Contracts

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Q3.

Robert, a portfolio manager, has entered a long six-month USD/EUR FX forward position. The USD/EUR spot exchange rate at inception is 1.3100, the six-month USD risk-free rate is 1.25%, and the six-month EUR risk-free rate is 2%. The no-arbitrage forward price is closest to:

A. 1.3149

B. 1.3051

C. 1.3002

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答案：B

计算过程：

• 外汇远期价格公式：$F_0=S_0\times \frac{(1+r_{price}{)}^T}{(1+r_{base}{)}^T}$
• USD/EUR 报价中，USD是price currency，EUR是base currency
• $F_0=1.3100\times \frac{(1+0.0125{)}^{0.5}}{(1+0.02{)}^{0.5}}=1.3100\times \frac{1.00623}{1.00995}=1.3100\times 0.99631=1.3051$

选项	判断	解析
A	✗	利率分子分母放反了
B	✓	\times \frac{(1.0125)^{0.5}}{(1.02)^{0.5}} \approx 1.3051$
C	✗	计算有误

关联：R70: Pricing and Valuation of Forward Contracts

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Q4.

Among derivative instruments, the contract value is zero at initiation except for:

A. commodity forwards.

B. fixed income futures.

C. interest rate options.

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答案：C

解析：双务合同（远期、期货、互换）在期初的价值为零。期权（单务合同）在期初的价值不为零，买方需支付期权费（premium）。

选项	判断	解析
A	✗	商品远期是双务合同，期初价值为零
B	✗	固定收益期货是双务合同，期初价值为零
C	✓	利率期权是单务合同，期初价值不为零（需支付premium）

关联：R70: Pricing and Valuation of Forward Contracts

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Q5.

Suppose that Feng, power plant owner, contracts to buy 100 tons of thermal coal from Luck, coal boss, on 15th Oct. at ¥620 per ton. Which of the following statements about the payoff from the forward is most accurate?

A. Feng makes a profit when the price of the underlying asset at maturity is greater than the forward price.

B. Luck makes a profit when the price of the underlying asset at maturity is greater than the forward price.

C. Feng makes a profit when the price of the underlying asset at maturity is less than the forward price.

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答案：A

解析：Feng是远期合约的买方（long），当到期时标的资产价格高于远期价格时，买方获利（以较低的远期价格买入高价资产）。Luck是卖方（short），在价格下跌时获利。

选项	判断	解析
A	✓	Feng是long方，标的价格 > 远期价格时获利
B	✗	Luck是short方，标的价格 > 远期价格时亏损
C	✗	标的价格 < 远期价格时，Feng（long方）亏损

关联：R70: Pricing and Valuation of Forward Contracts

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Q6.

The one-year spot rate is 3.8%, the two-year spot rate is 4.3%, and the three-year spot rate is 5.2%. The implied one-year forward rate two years from now is closest to:

A. 7.02%.

B. 6.38%.

C. 4.32%.

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答案：A

计算过程：

• 利用即期利率求远期利率：$(1+S_3{)}^3=(1+S_2{)}^2\times (1+f_{2,1})$
• $(1.052{)}^3=(1.043{)}^2\times (1+f_{2,1})$
• = 1.08785 \times (1 + f_{2,1})$
• $f_{2,1}=\frac{1.16370}{1.08785}-1=0.06974\approx 7.02\%$

选项	判断	解析
A	✓	$(1.052{)}^3/(1.043{)}^2-1\approx 7.02\%$
B	✗	计算有误
C	✗	计算有误

关联：R70: Pricing and Valuation of Forward Contracts

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Q7.

Forward rate agreement (FRA) is a forward contract where the underlying is an interest rate. More specifically,

A. the long can hedge against an increase in interest rate by buying an FRA.

B. the short can hedge against an increase in interest rate by selling an FRA.

C. the short can hedge against an decrease in interest rate by buying an FRA.

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答案：A

解析：FRA的long方（借款方）在利率上升时获利，因此可以通过买入FRA来对冲利率上升的风险。Short方（贷款方）在利率下降时获利。

选项	判断	解析
A	✓	Long FRA在利率上升时获利，可用于对冲利率上升风险
B	✗	Short方在利率下降时获利，不是对冲利率上升
C	✗	对冲利率下降应该sell FRA（short FRA），不是buy

关联：R70: Pricing and Valuation of Forward Contracts

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Q8.

A corporation will take a loan on a 90-day MRR in one month. It worries that the interest rate will increase at that time, so the best strategy that it can take is:

A. short a 30-day interest rate forward contract.

B. long a 30-day FRA on 90-day MRR.

C. long a 3 months plain vanilla swap.

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答案：B

解析：公司将在1个月后以90天MRR利率贷款，担心利率上升。买入（long）一个30天后到期的、基于90天MRR的FRA，可以锁定借款利率，对冲利率上升风险。

选项	判断	解析
A	✗	Short利率远期在利率下降时获利，无法对冲利率上升风险
B	✓	Long FRA在利率上升时获利，可以对冲借款人面临的利率上升风险
C	✗	3个月的plain vanilla swap的期限和结构不匹配该需求

关联：R70: Pricing and Valuation of Forward Contracts