A non-dividend paying stock currently trades at a price of $25. European and American call and put options on the stock with a time to expiration of 180 days have an exercise price of $26. You forecast that the stock price can go up 5% or down 4% in each period of length 90 days each. The annually compounded risk free rate is 3%. Use the two-period BOPM.

The risk-neutral probability that the stock price will go down in each period of length 90 days is closest to:

a.

0.4744

b.

0.2222

c.

0.5256

PLEASE SHOW ALL STEPS! BE CAREFUL FOR THE WORDING; they give an annual rate and the whole question is in days.