Option Maximum loss/gain

CFA Level I Derivatives
#1

Any trick to remember what is maximum loss/gain to option writer and buyer?

It seems i can answer the questions but its so time consuming. Would be good to remember somehow or a trick to solve it quickly.

#2

If you think of the worst-case scenario in each situation, it’s pretty easy:

  • Maximum loss for the buyer is the total option premium paid: the worst case is that the option expires worthless.
  • Maximum loss for the writer of a call option is infinite: the worst case is that the price of the underlying skyrockets.
  • Maximum loss for the writer of a put option is (X – premium received): the worst case is that the price of the underlying goes to zero.

As with so many other ideas in the curriculum, if you draw a picture of the payoff on the option, then adjust it by the premium (up for the writer, down for the buyer), the picture will tell you the answer.

#3

Thanks! I was confused about remembering the payoffs as well! Is there a difference between option payoff and option profit/loss? I think i read somewhere that there is a subtle difference.

#4

The payoff doesn’t incorporate the option premium; the profit does.

For example:

  • Suppose that you buy a call option with a strike price of $100; you pay $5.45 for the option. At expiration, the price of the underlying is $110. The payoff is $10 (= $110 – $100); the profit is $4.55 (= $10 – $5.45).
  • Suppose that you sell a put option with a strike price of $50; you receive $8.15 for the option. At expiration, the price of the underlying is $45. The payoff is -$5 (= $45 – $50); the profit is $3.15 (= $8.15 – $5).

If you draw payoff diagrams, the horizontal part will be at zero (when the option expires worthless). When you draw profit diagrams, the horizontal part will be below zero for long positions (you had to pay to buy the option) and above zero for short positions (you were paid to sell the option); to get the profit diagram, you start with the corresponding payoff diagram and move it down (long) or up (short) by the amount of the option premium.

#5

thanks so much!!

#6

You’re welcome.