We will derive a two-state put option value in this problem. Data: S 0 = 120; X

Question

We will derive a two-state put option value in this problem. Data: S0 = 120; X = 130; 1 + r = 1.1. The two possibilities for ST are 140 and 90.

The range of S is 50 while that of P is 40 across the two states. What is the hedge ratio of the put?(Negative value should be indicated by a minus sign. Round your 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.)

Given that the stock currently is selling at 120, calculate the put value. (Round your answer to 2 decimal places.)

We will derive a two-state put option value in this problem. Data: S0 = 120; X = 130; 1 + r = 1.1. The two possibilities for ST are 140 and 90.

Explanation / Answer

Solution:

uS 0 = 140 P u = 0

dS 0 = 90 P d = 40

The hedge ratio is: Pu - Pd/(uSo-dSo)

=0-40/140-90 = -40/50

Hence the hedge ratio of put = -4/5

b. Riskless Portfolio S T = 90 S T = 140

   Buy 4 shares             360          560

   Buy 5 puts                200    0

   Total                         560 560

   Present value = $560/1.10 = $509.09

C.The portfolio cost is: 4S + 5P = 120*4 + 5P

    Hence The value of the portfolio is: $509.09 calculated above

    Therefore: 480 + 5P = $509.09

    P = $29.09/5 = $5.818

    Thank you.

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