The price of a share of a particular stock listed on the New York Stock Exchange

Question

The price of a share of a particular stock listed on the New York Stock Exchange is currently $45. The following probability distribution shows how the price per share is expected to change over a three-month period:

Set up intervals of random numbers that can be used to generate the change in stock price over a three-month period. If required, round your answers to two decimal places.

With the current price of $45 per share and the random numbers 0.6769, 0.4927, 0.2555 and 0.7773, simulate the price per share for the next four 3-month periods.

What is the ending simulated price per share? $_____

Stock Price Change ($) Probability -2 0.10 -1 0.30 0 0.20 1 0.10 2 0.15 3 0.05 4 0.10

Explanation / Answer

Stock Price Change($)

Probability

Cumulative probability

-2

0.10

0.10

-1

.30

0.40

0

.20

0.60

1

.10

0.70

2

.15

0.85

3

.05

0.90

4

.10

1

Is the given values and probabilities.

So we can see the probabilities associated with each expected change.

So if we define,

Stock Price Change ($) = -2        if 0 x 0.10

                                                = -1        if 0.10 < x 0.40

                                                = 0          if 0.40< x 0.60

                                                = 1          if 0.60 < x 0.70

                                                = 2          if 0.70 < x 0.85

                                                = 3          if 0.85 < x 0.90

                                                = 4          if 0.90 < x 1

;(Since X is a continuous random variable so putting and < both are same cause P(X= a particular constant in between (0,1)) =0

Note that by defining this, all the conditions are satisfying.

B. With the current price of $45 per share and the random numbers 0.6769, 0.4927, 0.2555, and 0.7773, simulate price per share for the next four 3month periods. What is the ending simulated price per share.

Here we can see the obtained values for the random variable X are 0.2555 associated with stock change -1, 0.7773 associated with stock change 2 and so on.

So consider the following table.

No

Current months Stock price

Obtained r.v

Associated stock change

Next three months forecast

1

45

0.6769

1

45+1=46

2

46

0.4927

0

46+0=46

3

46

0.2555

-1

46-1=45

4

45

0.7773

2

45+2=47

So the simulated prices are $46, $46, $45 and $47.The ending simulated price per share is $47

Stock Price Change($)

Probability

Cumulative probability

-2

0.10

0.10

-1

.30

0.40

0

.20

0.60

1

.10

0.70

2

.15

0.85

3

.05

0.90

4

.10

1

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