Question

Consider a European put option on a share of a company. The strike price is 50. The investors pays an option premium of 10. If the payoff for the investor (not taking into account the option premium) is 10, then what is the profit of the option writer (taking everything into account)?

Answer 1

option type = European PUT

Strike price = 50

Option premium received by the WRITER = 10

Option premium paid by the INVESTOR = (10)

Pay off (excluding Premium paid) = 10

A put option is a financial contract between the buyer and seller of a securities option providing the buyer, a right sell the security at a predetermined price (Strike price)

A put option is bought if the trader expects the price of the underlying to fall within a certain time frame.if the market price falls below the strike price, as expected, the buyer can decide to exercise his or her right to sell at that price and the writer of the option contract has the obligation to buy the security at the strike price. With the exercise of the put, the investor makes the difference between the cost of the security in the market (i.e. a lower price than the option strike price) and the sale of the option to the put writer (i.e. at the strike price).

As given here, that the pay off of the investor is 10 (excluding premium), this implies that the current price of the stock is 20 points below the strike price.

Explanation:

Current market price = 50 = Strike price

If the stock goes 10 points below the strike price, the profit made by the investor is 10. HOWEVER, the investor has already paid a premium of 10, so it doesn't matters if the investor chooses to exercise hi option or buys the stock from the market. This is a breakeven point for investor. Any price movement below this price (i.e.40) should give investor a net profit.

In this case investor has gained 10, that means the market price of the stock is further 10 points below the 40 (i.e. at 30).

Noe the investor will choose to buy the security from the option writer at a pre-determined price (strike price). That means, the market price is 30, but option buyer has the right to sell the security at strike price of 50.

So, option seller will have to buy the securities from the market, at 30, and sell it to the option buyer (who has chosen to exercise his option) at 50. Which causes a loss of 20 for every security. HOWEVER, writer has got 10 from the investor as premium, so net loss for the option writer is 10. (i.e. Strike price - Spot Price - Premium Received) = 50-30 -10 = 10

So, if the investor has bought 1 option, then the writer will have a payoff of -10.

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