We will derive a two-state put option value in this problem. Data: S_0 = 150; X=

Question

We will derive a two-state put option value in this problem. Data: S_0 = 150; X= 160; 1 + r = 1.1. The two possibilities for S_t are 180 and 100. The range of S is 80 while that of P is 20 across the two states. What is the hedge ratio of the call? (Round your answer to 2 decimal places.) Calculate the value of a call option on the stock with an exercise price of 160. (Do not use continuous compounding to calculate the present value of X in this example, because the interest rate is quoted as an effective per-period rate.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Explanation / Answer

We have provided that,

So ( Current Stock Price) =150

X ( exercise price) =160

1+r =1.1

The two possibility of stock

S1=180

S2 =100

Now we will calculate the Hedge ratio for call as follow

The hedge ratio for the call is

  =H =Cu -Cd / uSo -dSo

     = 20-0 /180-100

   =20 /80

=1/4

B

We have given that excersie price is 160 and we need to calculate the value of call option

It is as follow

Present value

= $160/1.10

= $145.455

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