Cannot figure out the last question, part c. The answer for part c is NOT 19.44

Question

Cannot figure out the last question, part c. The answer for part c is NOT 19.44 or 17.18. please advise

Data: So-102:X= 116, 1 + r= 1.08. The two possibilities for ST are 150 and 82. The range of S is 68 while that of P is 34 across the two states. What is the hedge ratio of the put? Round your answer to 2 decimal places. Negative amount should be indicated by a minus a. sign.) Hedge ratio (Omit the "S" sign in your response.) Nonrandom payoff S 47 b-1. Form a portfolio of one shares of stock and two puts. What is the (nonrandom) payoff to this portfolio? 150 b-2. What is the present value of the portfolio? (Round your answer to 2 decimal places. Omit the "$" sign in your response.) Present value Given that the stock currently is selling at $102, calculate the put value. (Round your answer to 2 138.89 c. decimal places. Omit the "S" sign in your response.) Put value

Explanation / Answer

using binomial model we can answer

formula value of P = Pup+Pd(1-p)/R

P = R-d/ u-d where P represents probability to get upside price

u = upper possible rate / current stock price = 150/102 = 1.47

d = lower possible rate / current stock price = 82/102 = 0.80

p= 1.08-0.80/1.47-0.80 = 0.42

1-p = 0.52

value of put = payoff upside* P + payoff downside *(1-p)/ R

= 0*0.42 + (102-82)*0.58/1.08

= 10.74

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