A particular stock whose current price is 100 either increas

A particular stock, whose current price is $100 either increases 2% or decreases 1% in an given day. There is a 50% chance that the stock price will increase on any given day, independent of previous price movements. Determine the probability that the stock\'s price is more than double its current pricce 50 trading days from now.

Solution

Current price =100

Increses 2% or decreases1%

Let x be the current price

If increases by 2% after t days price =100 (1.02)t

If decreases by 1% then stock price after t1 days = 100(0.99)t1

t1+t2 =50

Increase chance =0.50

P(price after 50days)>200

=P[100(1.02)t(0.99)50-t] >200

This is a binomial distribution with out replacement with p = 0.5 and q =0.5

For increase p =0.5