question archive The current price of a non-dividend paying stock is $30
The current price of a non-dividend paying stock is $30
Subject:FinancePrice:2.87 Bought7
The current price of a non-dividend paying stock is $30. Use a two-step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months. Each step is 3 months, the risk free rate is 8% per annum with continuous compounding. What si the option price when u -1.1 and d 0.9.
A. $1.29
B. $1.49
C. $1.69
D. $1.89
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Answer:
|
American option: |
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|
Particulars |
# |
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Stock price = S = |
30.00 |
|
Exercise price = X = |
32.00 |
|
Interest rate = r = |
8.00% |
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Standard deviation = s = |
|
|
Total time = T |
0.5 |
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Number of steps = |
2 |
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Each time step = t = |
0.25 |
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U = |
1.100 |
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D = |
0.900 |
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U = Exp(r*t+s*t^0.5) = |
1.1000 |
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D = Exp(r*t-s*t^0.5) = |
0.9000 |
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Pu = Probability of up-move = (Exp(r*t)-D)/(U-D) |
0.6010 |
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Du = Probability of down-move = 1-Pu = |
0.3990 |
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Price of call option at CU1 = Max((CU2*Pu + CN2*Du)/Exp(r*t), SU1-X) = |
2.53 |
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Price of call option at CD1 = MAX((CN2*Pu + CD2*Du)/Exp(r*t), SD1-X) = |
0.00 |
| Value of Call working =4.3*EXP(-8%*0.25)*0.601*EXP(-8%*0.25)*0.601 = 1.49 | |
|
Current price of call option = C0 = (CU1*Pu + CD1*Du)/Exp(r*t) = |
1.49 |
Stock price $36.30 SU2 $33.00 SU1 $29.70 SN2 $30 SO $27.00 SD1 $24.30 SD2 Call option price $4.30 CU2 $2.53 CU1 $1.49 CO $0.00 CN2 $0.00 CD1 $0.00 CD2
PFA
