Question

Ms. Higden has been offered yet another incentive scheme. She will receive a bonus of $500,000 if the stock price at the end of the year is $120 or more; otherwise she will receive nothing. (Don’t ask why anyone should want to offer such an arrangement. Maybe there’s some tax angle.)

What combination of options would provide these payoffs? (Hint: You need to buy a large number of options with one exercise price and sell a similar number with a different exercise price.)

Please explain how you find the answer

Answer 1

Ms Higden will receive bonus of $500,000 if stock price at the end of the year is $120 or more.

In case of any downward movment in the stock- price, she stands to receive nothing.

Hence, Ms. Higden stands to benefit $500,000 in a Bullish scenario ($120 or above) and receives nothing in a Bearish scenario (lower than $120).

Also it may be noted that, the pay-off is fixed, in case stock stays at $120 or moves upwards. The pay-off will not vary with every tick in the movement of share price beyond $120.

The question requires us to replicate the pay-off using an option strategy where we have to "Buy a large number of options with one exercise price and sell a similar number with a different exercise price."

In order to replicate this position, we suggest Bull Put Spread or Bull Put Credit Spread Strategy.

The Strategy will involve Selling a Put Option with a Strike Price of $ 120, and then buying a Put Option having a Strike Price lower than $120, such that the difference in their premium is $500,000.

Let us examine this in more details:-

i) We sell / write Put Options with a Strike Price of $ 120 and pocket the Option Premium.

ii) We buy Put Options (which has a lower Strike Price than $120 but the same expiration period) such that the difference between their premiums is $500,000.

NOTE:- $500,000 will be received as the initial credit for this strategy, because the premium for the Strike Price of $ 120 will be higher than the Option having a lower Strike Price.

Pay-Off at Expiry:-

At the time of expiry, if Stock Price is at $120 or more, both the Put Options shall expire worth-less.

(Note: Put Options expire worthless if Stock Price closes at a level equal to or above their Strike Price).

Hence, we will be able to pocket the entire premium of $500,000.