Question

The price of an asset will either rise by 25% or fall by 40% in 1 year, with equal probability. A European put option on this asset matures after 1 year. Assume the following: • Price of the asset today: 100 • Strike price of the put option: 130 • Put option premium: 7 What is the expected profit for this asset?

I need a detailed answer for 10 marks

Answer 1

Answer:

Expected profit = ∑Xi ∗ Pi

Where:
Xi = profit in scenario i
Pi = probability of scenario i

The profit from put option = Payoff - Premium

Payoff from put option = max((K - S),0)

• where
• K = strike price = $130
• S = underlying price at maturity
  if price moves up then S = 100 * 1.25 =$ 125
  if price moves down then S = 100 * (1-0.40) =$ 60

Premium = $7

Hence,
Profit in first option = max((130-125),0) = $5
Profit in second option = max((130-60),0) = $70

Therefore, expected profits = (50% * 5) + (50% *70) = $37.5