Question

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

Answer 1

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