Fly by Night stock price is expected to go up by 20% or down by 15% over the next year. You own a one-year put option on the stock. The interest rate is 12%, and current stock price of Fly by Night is $75. What exercise price leaves you indifferent between holding the put and exercise it now?
A. |
$27.342 |
|
B. |
$121.332 |
|
C. |
$14.452 |
|
D. |
$62.349 |
|
E. |
$77.907 |
|
F. |
$34.521 |
|
G. |
$88.437 |
|
H. |
$49.508 |
Expected return = (Probability of rise * change in price) + (1 - probability of risk)
0.12 = ( P * 0.20) + (1 - P) * (-0.15)
0.12 = 0.20P + 0.15P - 0.15
0.12 + 0.15 = 0.35P
0.27 = 0.35P
P = 0.27 / 0.35
P = 0.7714
Probable next year stock prices:
$75 * 1.20 = $90
$75 * (1 - 0.15) = $63.75
X - 75 = ((P * $0) + (1 - P) * (X - 63.75)) / (1+r)
X - 75 = ((0.7714 * $0) + (1 - 0.7714) * (X - 63.75)) / 1.12
(X - 75) * 1.12= (0 + 0.22857X - 14.5714)
1.12X - 0.22857X = 84 - 14.5714
0.89143X= 69.4286
X = 69.4286 / 0.89143
X = $77.907
Break even excise price = $77.907
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