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 $41. 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 $41 per share and the random numbers 0.5953, 0.8019, 0.0677 and 0.2427, simulate the price per share for the next four 3-month periods.

What is the ending simulated price per share?

$  

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

Explanation / Answer

The intervals are obtained by taking cumulative probaility.

Given current value of share is $41.

Random number : 0.5953 which lies in the interval 0.45 but less than 0.60.

Share price change is -1,so ending price per share is $(41-1)=$40

Random number: 0.8019 which lies in interval 0.80 but less than 1.00

Share price change is +2, so ending price per share is $(40+2)=$42( Take cumulative value)

Random number: 0.0677 which lies in interval 0.05 but less than 0.15

Share price change is -3, so ending price per share is $(42-3)=$39

Random number :0.2427 which lies in interval 0.15 but less than 0.45

Share price change is -2, so ending price per share is $(39-2)=$37

Ending price per share= $37

Stock Price Change Probability Interval -4 0.05 .00 but less than .05 -3 0.10 .05 but less than 0.15 -2 0.30 .15 but less than 0.45 -1 0.15 .45 but less than 0.60 0 0.15 .60 but less than 0.75 +1 0.05 .75 but less than 0.80 +2 0.20 0.80 but less than 1.00

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