Data: So = 100:X= 110; 1 + r= 1.10. The two possibilities for STare 130 and 80.
ID: 2790719 • Letter: D
Question
Data: So = 100:X= 110; 1 + r= 1.10. The two possibilities for STare 130 and 80. a-1. The range of S is 50 while that of C is 20 across the two states. What is the hedge ratio of the call? (Round your answer to 1 decimal place.) Hedge ratio a-2. Calculate the value of a call option on the stock with an exercise price of 110. (Do not use continuous compounding to calculate the present value of X in this example because we are using a two-state model here with discrete periods, not a continuous-time Black-Scholes model.) (Round your answer to 2 decimal places.) Call valueExplanation / Answer
a. Computation of Hedge ratio:
H = (Cu - Cd) / (uS0 - dS0)
= (20-0) / (130-80) = 0.4
Therefore, Hedge ratio = 0.4
b. Calculation of Value of a call option:
Portfolio cost = 2S-5C = 200-5C
Now let us calculate the value of the portfolio:
Present value of portfolio = (80*2shares) / 1+r = 160/ 1.10 = 145.455
Therefore, put call parity relationship :
200-5C = 145.455
C = $10.91 is the call value.
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