1、A stock priced at $100 has a 70 percent probability of moving up and a 30 percent probability of moving down. If it moves up, it increases by a factor of 1.02. If it moves down, it decreases by a factor of 1/1.02. What is the probability that the stock will be $100 after two successive periods?

A)   9%.

B)   42%.

C)   21%.

D)   49%.

2、A stock priced at $20 has an 80 percent probability of moving up and a 20 percent probability of moving down. If it moves up, it increases by a factor of 1.05. If it moves down, it decreases by a factor of 1/1.05. What is the expected stock price after two successive periods?

A)   $20.05.

B)   $22.05.

C)   $21.24.

D)   $18.14.

3、A stock priced at $10 has a 60 percent probability of moving up and a 40 percent probability of moving down. If it moves up, it increases by a factor of 1.06. If it moves down, it decreases by a factor of 1/1.06. What is the expected stock price after two successive periods?

A)   $10.03.

B)   $11.24.

C)   $8.90.

D)   $10.27.

答案和详解如下：

1、A stock priced at $100 has a 70 percent probability of moving up and a 30 percent probability of moving down. If it moves up, it increases by a factor of 1.02. If it moves down, it decreases by a factor of 1/1.02. What is the probability that the stock will be $100 after two successive periods?

A)   9%.

B)   42%.

C)   21%.

D)   49%.

lick for Answer and Explanation B) 

For the stock to be $100 after two periods, it must move up once and move down once: $100 × 1.02 × (1/1.02) = $100. This can happen in one of two ways: 1) the stock moves up during period one and down during period two; or 2) the stock moves down during period one and up during period two. The probability of either event is 0.70 × 0.30 = 0.21. The combined probability of either event is 2(0.21) = 0.42 or 42%.

2、A stock priced at $20 has an 80 percent probability of moving up and a 20 percent probability of moving down. If it moves up, it increases by a factor of 1.05. If it moves down, it decreases by a factor of 1/1.05. What is the expected stock price after two successive periods?

A)   $20.05.

B)   $22.05.

C)   $21.24.

D)   $18.14.

The correct answer was C)

If the stock moves up twice, it will be worth $20 × 1.05 × 1.05 = $22.05. The probability of this occurring is 0.80 × 0.80 = 0.64. If the stock moves down twice, it will be worth $20 × (1/1.05) × (1/1.05) = $18.14. The probability of this occurring is 0.20 × 0.20 = 0.04. If the stock moves up once and down once, it will be worth $20 × 1.05 × (1/1.05) = $20.00. This can occur if either the stock goes up then down or down then up. The probability of this occurring is 0.80 × 0.20 + 0.20 × 0.80 = 0.32. Multiplying the potential stock prices by the probability of them occurring provides the expected stock price: ($22.05 × 0.64) + ($18.14 × 0.04) + ($20.00 × 0.32) = $21.24.

3、A stock priced at $10 has a 60 percent probability of moving up and a 40 percent probability of moving down. If it moves up, it increases by a factor of 1.06. If it moves down, it decreases by a factor of 1/1.06. What is the expected stock price after two successive periods?

A)   $10.03.

B)   $11.24.

C)   $8.90.

D)   $10.27.

The correct answer was D)

If the stock moves up twice, it will be worth $10 × 1.06 × 1.06 = $11.24. The probability of this occurring is 0.60 × 0.60 = 0.36. If the stock moves down twice, it will be worth $10 × (1/1.06) × (1/1.06) = $8.90. The probability of this occurring is 0.40 × 0.40 = 0.16. If the stock moves up once and down once, it will be worth $10 × 1.06 × (1/1.06) = $10.00. This can occur if either the stock goes up then down or down then up. The probability of this occurring is 0.60 × 0.40 + 0.40 × 0.60 = 0.48. Multiplying the potential stock prices by the probability of them occurring provides the expected stock price: ($11.24 × 0.36) + ($8.90 × 0.16) + ($10.00 × 0.48) = $10.27.