value 1.25 points We will derive a two-state put option value in this problem. D

Question

value 1.25 points We will derive a two-state put option value in this problem. Data. So-230; X-240; 1 + r: 1.1. The two possibilities for Sr are 260 and 180 a. The range of S is 80 while that of P is 60 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.) Hedge ratico b-1. Form a portfolio of 3 shares of stock and 4 puts. What is the (nonrandom) payoff to this portfolio? (Round your answer to 2 decimal places.) Nonrandom payoff b-2. What is the present value of the portfolio? (Round your answer to 2 decimal places.) Present value c. Given that the stock currently is selling at 230, calculate the put value. (Round your answer to 2 decimal places.) Put valueS

Explanation / Answer

1A) The Hedge ratio (HR) can be found as:

HR= Pu-Pd/Su-Sd

Where Su= Stock price in upmove

             Sd=Stock Price in downmove

            Pu= Put Price in upmove

            Pd=Put Price in downmove

                                                                            HR=(0-60)/(260-180)

                                                                                  =-60/80

                                                                                  =-0.75

1b-1) the payoff for the Put Option strike price (X) 240 in two scenarios is given as:

Max(0,X-S)

       When stock price(S) 260 the put payoff is: Max(0,240-260)=Max(0,-20)=0

       When stock price(S) 180 the put payoff is: Max(0,240-180)=Max(0,80)=80

Now with the given information the payoff for portfolio with 3 shares and 4 Puts can be found in the given table:

S=260

S=180

3 Shares (3*S)

780

540

4 Puts (4*Payoff)

0

240

Sum

780

780

     

Conclusion: Hence the non-random payoff of this portfolio is $ 780.

1b-2) The present value of portfolio is:

                                                                        Non Random Payoff/(1+r)

=780/1.10

=$ 709.09

1c) We know from question 1b that the present value of the portfolio of 3Shares and 4 Puts is $ 709.09. So I can write an equation as:

3S+4P=709.09

Now we are also told that the stock is currently trading at $ 230. Therefore,

3×230+4P=709.09

4P=709.09-690

4P=19.09

P=4.77

Conclusion: When the stock price is $ 230 put value will be $ 4.77.

S=260

S=180

3 Shares (3*S)

780

540

4 Puts (4*Payoff)

0

240

Sum

780

780

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