[2008]Topic 13: Determination of Forward and Futures Prices相关习题 index, 1015, contract, expected, current

Baran

AIM 4: Compute the forward price, given the underlying asset’s price, with or without considering the income or yield the underlying  asset generates.

 

1、The S& 500 index is trading at 1015. The S& 500 pays an expected dividend yield of 2 percent and the current risk-free rate is  4.1 percent. The value of a 3-month futures contract on the S& 500 is closest to:

A) 979.86.
 
B) 1,350.59.
 
C) 1,020.34.
 
D) 997.68.

[此贴子已经被作者于2009-6-24 16:05:18编辑过]

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Baran

The  correct answer is D
The formula is: 1650e(0.024)(270/360) = 1,679.97, or $1,680.

Baran

2、Using the continuous time forward pricing model, what is the no-arbitrage price of a 3-month forward contract if the interest rate is 3.2 percent and the spot price of the asset is $750?

A) $780.
 
B) $756.
 
C) $744.
 
D) $729.

Baran

The  correct answer is B
The formula is: F0 = S0erT. Using this formula we calculate the forward price as 750e(0.032)(0.25) = $756.

Baran

AIM 7: Define and provide an example of the cost-of-carry model for forward prices where the assets have no interim cash flows.

 

1、Using the continuous time forward pricing model, what is the no-arbitrage price of a 9-month forward contract if the interest rate is 2.4 percent and the spot price of the asset is $1,650?

A) $1,664.
 
B) $1,689.
 
C) $1,621.
 
D) $1,680.

Baran

5、At the inception of a six-month forward contract on a stock index, the value of the index was $1,150, the interest rate was 4.4 percent, and the continuous dividend was 1.8 percent. Three months later, the value of the index is $1,075. Which of the following statements is TRUE? The value of the:

A) long position is -$82.41.
 
B) long position is $82.41.
 
C) long position is $47.56.
 
D) short position is $47.56.

Baran

The  correct answer is A
At the inception of the forward contract, the delivery price would have been:
1,150e(0.044-0.018)(0.5) = $1,165.05.

The value to the long position after three months is: 1,075e(-0.018)(0.25) - 1,165.05e(-.044)(.25) = 1,070.17 - 1,152.31 = -$82.41. 

Therefore, the value of the short position is $82.41.

Baran

4、At the inception of a one-year forward contract on a stock index, the value of the index was $1,100, the interest rate was 2.6 percent, and the continuous dividend was 1.2 percent. Six months later, the value of the index is $1,125. Which of the following statements is TRUE? The value of the:

A) long position is -$17.17.
 
B) short position is -$17.17.
 
C) long position is $25.00.
 
D) short position is -$22.19.

Baran

The  correct answer is B
At the inception of the forward contract, the delivery price would have been:
1,100e(0.026 - 0.012) = $1,115.51.

The value to the long position after six months is: [1,125e(-0.012)(0.5)] - [1,115.51e(-0.026)(0.5)] = 1,118.27 – 1,101.10 = $17.17.

Therefore, the value of the short position is -$17.17.