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Rob's s1452 Notes

πŸ”Ž Solutions for all 8 Types of P/L Problems

There are four types of options: long call, short call, long put, short put.

Each of the four types can either be β€œin the money (In The Money)” or β€œout of the money (Out of The Money).” Therefore, there are 8 possible types of P/L problem.

This page includes practice problems with solutions for each. If you are trying to solve an option P/L problem, you can look up an example of the corresponding type here.

Long Call (Buy a Call)

Long Call (Out of The Money)

✏️ You have Bought a K=$100 Call. It is about to expire. Suppose S=$90 and Premium=$2.

  1. Will you exercise this option?
  2. What is your Per-Share Profit or Loss (P/L)?
    βœ” Click here to view answer

    Short Answer:

    1. Out of The Money, so WON'T be exercised.
    2. P/L = -$2.

    Full Explanation:

    This Long Call allows you to buy shares of stock worth S=$90 for K=$100.

    You could easily purchase the stock on the open market for $90, so exercising the option would mean overpaying by $10. We would think of this as a per-share $10 loss.

    Clearly, you won’t exercise the option, so it will just expire worthless. Because you can’t profitably exercise the option, we say the option is β€œOut of The Money (OTM)” and has no intrinsic value (IV=$0).

    The only impact on your P/L is the $2 premium you paid. In hindsight, this money was wasted. P/L = -$2 (per share). Better luck next time!

    Long Call (In The Money)

    ✏️ You have Bought a K=$100 Call. It is about to expire. Suppose S=$110 and Premium=$2.

    1. Will you exercise this option?
    2. What is your Per-Share Profit or Loss (P/L)?
      βœ” Click here to view answer

      Short Answer:

      1. In The Money, so WILL be exercised.
      2. P/L = $8.

      Full Explanation:

      This Long Call allows you to buy shares of stock worth S=$110 for K=$100. A mnemonic is that you can β€œCall” the shares to you and someone else (your counterparty) will have to sell them to you for K=$100.

      That is a discount of $10, so this option is β€œIn The Money (ITM)” and you will exercise it. When you exercise it, you will gain $10. This $10 is the option's intrinsic value.

      (If you don’t want to buy more shares, you could easily exercise the option to buy them for K=$100 and then turn around and sell them on the market for S=$110, netting a $10 profit. You could even take out a short-term loan to do this.)

      In addition to the $10 gain, you also paid a premium of $2. Therefore, your final P/L combines the $10 gain and the $2 loss: P/L = $10 - $2 = $8 (per share).

      Short Call (Sell/Write a Call)

      Short Call (Out of The Money)

      ✏️ You have Sold/Written a K=$100 Call. It is about to expire. Suppose S=$90 and Premium=$2.

      1. Will this option be exercised?
      2. What is your Per-Share Profit or Loss (P/L)?
        βœ” Click here to view answer

        Short Answer:

        1. Out of The Money, so WON'T be exercised.
        2. P/L = $2.

        Full Explanation:

        You have sold an option that obligates you to sell shares of stock worth S=$90 for K=$100 if requested.

        You can think of yourself as being matched with a β€œcounterparty” who purchased the option you wrote/sold. Just as you have a Short Call, they have a Long Call. They decide whether to exercise the Long Call they purchased. If they do, you must sell them 100 shares of the underlying stock for K=$100.

        From your counterparty's perspective, there is no way to make money by paying $100 for shares only worth $90. Therefore, we say this option is β€œOut of The Money (OTM)” and has no intrinsic value (IV=$0).

        Given this, your counterparty won’t exercise the option. The only impact on your P/L is the $2 premium your counterparty paid you. P/L = $2 (per share).

        Short Call (In The Money)

        ✏️ You have Sold/Written a K=$100 Call. It is about to expire. Suppose S=$110 and Premium=$2.

        1. Will this option be exercised?
        2. What is your Per-Share Profit or Loss (P/L)?
          βœ” Click here to view answer

          Short Answer:

          1. In The Money, so WILL be exercised.
          2. P/L = -$8.

          Full Explanation:

          You have sold an option that obligates you to sell shares of stock worth S=$110 for only K=$100 if requested.

          You can think of yourself as being matched with a β€œcounterparty” who purchased the option you wrote/sold. Just as you have a Short Call, they have a Long Call. They decide whether to exercise the Long Call they purchased. If they do, you must sell them 100 shares of the underlying stock for K=$100.

          By purchasing your shares worth $110 for only $100 (a discount of $10), your counterparty can make $10 per share. Therefore, we say the option is β€œIn The Money (ITM)” and has an Intrinsic Value of $10 for its owner.

          We’ll assume your counterparty will exercise the option. They will β€œCall” for your shares to purchase them for K=$100. This will cause a loss for you of $10. For example, if you own the shares, you will have to sell them for $10 less than you could get on the open market. Alternatively, if you don’t have the shares, you’ll have to buy them for $110 and sell them for $10 less. Either way, you are $10 poorer than you would be if your counterparty hadn't exercised the option. (Correspondingly, they are $10 richer. The IV of the option is both your loss and their gain.)

          Offsetting the $10 loss from selling the shares, you also received a premium of $2. Your final per-share premium is P/L = $2 - $10 = -$8.

          (For comparison, your counterparty's final P/L is $8. As always, one party's gain is the other party's loss.)

          Long Put (Buy a Put)

          Long Put (Out of The Money)

          ✏️ You have Bought a K=$100 Put. It is about to expire. Suppose S=$110 and Premium=$2.

          1. Will you exercise this option?
          2. What is your Per-Share Profit or Loss (P/L)?
            βœ” Click here to view answer

            Short Answer:

            1. Out of The Money, so WON'T be exercised.
            2. P/L = -$2.

            Full Explanation:

            This Long Put allows you to sell shares of stock worth S=$110 for K=$100.

            There is no way to make money by selling something worth S=$110 for only K=$100. Because you can’t exercise the option to make money, we say the option is β€œOut of The Money (OTM)” and has no intrinsic value (IV=$0).

            If you had shares you wanted to sell, you could easily sell them on the open market for $110. Exercising the option would mean being underpaid by $10, which we would think of as a $10 loss.

            Clearly, you won’t exercise the option, so it will just expire unexercised.

            The only impact on your P/L is the $2 premium you paid. In hindsight, this money was wasted. P/L = -$2 (per share). Better luck next time!

            Long Put (In The Money)

            ✏️ You have Bought a K=$100 Put. It is about to expire. Suppose S=$90 and Premium=$2.

            1. Will you exercise this option?
            2. What is your Per-Share Profit or Loss (P/L)?
              βœ” Click here to view answer

              Short Answer:

              1. In The Money, so WILL be exercised.
              2. P/L = $8.

              Full Explanation:

              This Long Put allows you to sell shares of stock worth S=$90 for K=$100. $100 is a great price for something only worth $90. It's a $10 premium.

              A mnemonic is that you can β€œPut” the shares out on the market and someone else (your counterparty) will have to buy them for K=$100.

              If you have shares you want to sell, you can exercise the option to sell them for $10 extra. If you don’t have shares you want to sell, you could easily borrow money and buy the shares for $90 on the open market. You then exercise your option to sell the same shares for $100, pocketing a $10 profit.

              Either way, the option β€œIn The Money (ITM)”. You will exercise it to gain the option’s intrinsic value of $10.

              In addition to the $10 gain, you also paid a premium of $2. Therefore, your final P/L combines the $10 gain and the $2 loss: P/L = $10 - $2 = $8 (per share).

              Short Put (Sell/Write a Put)

              Short Put (Out of The Money)

              ✏️ You have Sold/Written a K=$100 Put. It is about to expire. Suppose S=$110 and Premium=$2.

              1. Will this option be exercised?
              2. What is your Per-Share Profit or Loss (P/L)?
                βœ” Click here to view answer

                Short Answer:

                1. Out of The Money, so WON'T be exercised.
                2. P/L = $2.

                Full Explanation:

                You have sold an option that obligates you to buy shares of stock worth S=$110 for K=$100 if requested.

                You can think of yourself as being matched with a β€œcounterparty” who purchased the option you wrote/sold. Just as you have a Short Put, they have a Long Put. They decide whether to exercise the Long Put they purchased. If they do, you must buy 100 shares of the underlying stock from them for K=$100.

                There is no way for your counterparty to make money by selling you shares worth $110 for only $100. Therefore, we say this option is β€œOut of The Money (OTM)” and has no intrinsic value (IV=$0).

                Given this, your counterparty won’t exercise the option. The only impact on your P/L is the $2 premium your counterparty paid you. P/L = $2 (per share).

                Short Put (In The Money)

                ✏️ You have Sold/Written a K=$100 Put. It is about to expire. Suppose S=$90 and Premium=$2.

                1. Will this option be exercised?
                2. What is your Per-Share Profit or Loss (P/L)?
                  βœ” Click here to view answer

                  Short Answer:

                  1. In The Money, so WILL be exercised.
                  2. P/L = -$8.

                  Full Explanation:

                  You have sold an option that obligates you to buy shares of stock worth S=$90 for K=$100 if requested.

                  You can think of yourself as being matched with a β€œcounterparty” who purchased the option you wrote/sold. Just as you have a Short Put, they have a Long Put. They decide whether to exercise the Long Put they purchased. If they do, you must buy 100 shares of the underlying stock from them for K=$100.

                  By selling shares worth $90 for $100 (a premium of $10), your counterparty can make $10 per share (at your expense). Therefore, we say the option is β€œIn The Money (ITM)” and has an Intrinsic Value of $10 for its owner.

                  We’ll assume your counterparty will exercise the option. Your counterparty will β€œPut” the shares out there and you will have to buy them for $100. The shares are only worth $90, so you will overpay by $10. Just as your counterparty gains $10, you lose $10. The IV of the option is both their gain and your loss.

                  Offsetting your $10 loss from selling the shares, you have also already received a premium of $2 from your counterparty. Your final per-share premium is P/L = $2 - $10 = -$8.

                  (For comparison, your counterparty's final P/L is $8. As always, one party's gain is the other party's loss.)