IBM stock currently sells for 86 dollars per share. Over 12 months the price will either go

by 12. 5 percent or down by 8. 5 percent. The risk-free rate of interest is 4.0 percent

continuously compounded. What is the value of a put option with strike price 89 and

maturity 12 months?

Solution:

The risk neutral probability is = 0.59910

The payoff on the stock is either Su = 96. 75 or Sd = 78. 69

The payoff on the put is either 0 or 89 78. 69 = 10. 31

Under RNVR the option value equals the expected payoff discount back to present at the risk-free rate.

Put price equals e0.04x1[p x 0 + (1 - p)89 78. 69]= e0.04x1(0.59910 x 0 + 0.4009 x 10. 31)= 3. 9712

How do you get risk neutral probability = 0.59910?