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Answer:
The probability that after two period we will have the same value of $100 is:
Step-by-step explanation:
We can analyze this situation by cases.
Stock moves up two times
For this case the final value would be:
$100 *1.02*1.02= $104.04
And the probability associated to this event is 0.7*0.7=0.49
Stock moves down two times
For this case the final value would be:
$100 *(1/1.02)*(1/1.02)= $96.117
And the probability associated to this event is 0.3*0.3=0.09
Stock moves up and then down
For this case the final value would be:
$100 *(1.02)*(1/1.02)= $100
And the probability associated to this event is 0.7*0.3=0.21
Stock moves down and then up
For this case the final value would be:
$100 *(1/1.02)*(1.02)= $100
And the probability associated to this event is 0.3*0.7=0.21
So then the probability that after two period we will have the same value of $100 is :