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?

please give me a detailed and elaborated answer for 10 marks I have the short answer. Also mention what do we do with the put option premium.

Answer 1

Put Option

A put option is a type of option contract, which protects against downside risk i.e. if the price goes below the strike price then option gets exercised otherwise it will lapse.

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 (This will be subtracted from expected profit as this is a cost incurred to buy the option and hence must be subtracted.)

Hence

Profit in first scenario = max((130-125),0) = $5

Profit in second scenario = max((130-60),0) = $70

The probabilities are equal, therefore

Expected profits = (50% * $5 + 50% * $70 ) - Premium

= $37.5 - $7

= $30.5

Hence Profit from put option will be $30.5.

If you have any doubts please let me know in comments.