We will derive put option value using the binomial option pricing model in this

Question

We will derive put option value using the binomial option pricing model in this problem. Data: S_0=250; X=260; 1+r=1.1. The two possibilities for S_T are 280 and 180. The range of S is 100 while that of P is 80 across the two states. What is the hedge ratio of the put? (Negative value should be indicated by a minus sign. Round answer to 2 decimal places.) Form a portfolio of 4 shares of stock and 5 puts. What is the (nonrandom) payoff to this portfolio? (Round your answer to 2 decimal places.) What is the present value of the portfolio? (Round your answer to 2 decimal places.) Given that the stock is currently selling at 250, calculate the put value. (Round your answer to 2 decimal places.)

Explanation / Answer

a. when ST =$280 P =0 when ST =$180 P =$80

Hedge Ratio = 0-$80/ $280-$180 = -$0/$100 = -/10 or - 0.08

b-1 and b-2

c. The portfolio cost is 4S+5P = 4($250)+5P = $1000+5P

The value of portfolio is $1018.182.

Therefore $1000+5P =  $1018.182.

P = $18.182. / 5 = $ 3.6364

Riskless Portfolio ST=$180 ST= $280 Buy 4 shares 720 1120 Buy 5 puts 400 0 ($80*4) ($0*4) Total 1120 1120 Present value = $1120/1.10 =1018.182

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