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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 e-0.04x1[p x 0 + (1 - p)89 - 78. 69]= e-0.04x1(0.59910 x 0 + 0.4009 x 10. 31)= 3. 9712
How do you get risk neutral probability = 0.59910?
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