Calculate the value of a call option using the binomial model. Data: S0 = 100; X
ID: 2634864 • Letter: C
Question
Calculate the value of a call option using the binomial model. Data: S0 = 100; X = 110; 1 + r = 1.10. The two possibilities for ST are 130 and 80.
What is the hedge ratio of the call?
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=r, because the interest rate is quoted as an effective per period rate. In other words, use standard discount formula: PV=FV/(1+r) (Round your answer to 2 decimal places. Omit the "$" sign in your response.)
(a)What is the hedge ratio of the call?
(b)Calculate the value of a call option on the stock with an exercise price of 110. (Do not use continuous compounding to calculate the present value of X in this example=r, because the interest rate is quoted as an effective per period rate. In other words, use standard discount formula: PV=FV/(1+r) (Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Explanation / Answer
(a)
S0 = 100, X = 110, r = 0.1 , Su = 130, Sd = 80
Cu = max(Su-X, 0) = max(130-110,0) = 20
Cd = max(Sd-X, 0) = max(80-110,0) = 0
hedge ratio(H) = (Cu-Cd)/(Su-Sd) = (20-0)/(130-80) = 0.4
(b)
purchase stock = H*S0 = 0.4*100 = 40
borrow = (Sd*H - Cd)/(1+r) = (80*0.4 - 0)/1.10 = 29.09
call value = 40 - 29.09 = 10.91
The answer is $10.91
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