I am having difficulty solving some of the FRM exam questions. Like the one below. This question was asked in FRM in year 1999. Can someone help me in solving this?A two-month American put option on a market index has an exercise price of 480. The current value of the index is 484. The risk-free lending/borrowing rate is 5% per annum. The dividend yield on the index is 3% per annum and the volatility of the index is 25% per annum. All interest rates are expressed in continuously compounded terms. Using an equally spaced four-step Binomial Pricing model, with the Cox Ross Rubinstein choices for constructing the tree, the martingale probability that the index value will decline at each step is:Correct Answer: 50.80%

Manishs:My calculation did not give me 50.80%, but 50.46%. Details below:dt = 2/12/4 = 0.0417u=exp(sigma*sqrt(dt))=exp(0.25*sqrt(0.0417)=1.0524d = 1/1.0524P = (exp(r-div) - d)/(u-d) = (exp(0.05-0.03) -d/(u-d) = 0.4954=49.54%so down probability = 1- p = 50.46%Hope this helps.Paka