For the two-period (each period is 6 months) binomial option pricing model, So i

Question

For the two-period (each period is 6 months) binomial option pricing model, So is $50, Su is $52.5 and Sd is $48, and the annual interest rate with semiannual compounding is 6%. Calculate the probability (p) and the stock price moving up in one time step. This is on my sample test and our professor won't provide us with a solution. Every single one of us can't get his answer which is p =.7777. I understand how to make the chart and he "showed work" to get a final formula of P= ((1+r)- d)/(u-d) but I am lost.

Explanation / Answer

S0 = $ 50, Su = $ 52.5 and Sd= $ 48

% Up Movement = (52.5 - 50) / 50 = 0.05 or 5 % and $ Down Movement = (48-50) / 50 = - 0.04 or - 4 %

Interest Rate = 6 % per annum and Time Period = 1 year with two periods of 6 months each.

As the time period is divided into two parts of 6 months each the relevant interest rate (r value) to be used for probability calculation is half of the annual value of 6 %. Hence, r = 3 % per 6 months.

Therefore, p = [(1+0.03) - 0.96] / (1.05 - 0.96) = 0.777

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