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
Expected profit = ∑Xi ∗ Pi
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)
Premium = $7
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
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