Question

You are considering buying a three month put option on Wing and a Prayer Construction stock. The company's stock currently trades for $10 per share and its price will either rise to $15 or fall to $7 in three months. The risk-free rate for three months is 2%. What is the appropriate price for a put option with a strike price of $9?

Answer 1

u = Su/S0 = 15 / 10 = 1.5

d = Sd/S0 = 7/10 = 0.7

Pu = max (K - Su, 0) = max (9 - 15, 0) = 0

Pd = max (K - Sd, 0) = max (9 - 7, 0) = 2

Risk neutral probabiity of an up state = p = (1 + r - d) / (u - d) = (1 + 2% - 0.7) / (1.5 - 0.7) = 40.00%

Hence, the appropriate price for a put option with a strike price of $9

= [p x Pu + (1 - p) x Pd] / (1 + r)

= [40% x 0 + (1 - 40%) x 2] / (1 + 2%)

= $ 1.18