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Skip to 0 minutes and 13 secondsPayoff diagrams for options are more complicated than those of a futures contract. This is because the payoff structure of an options contract does not only depend on investors' long or short position in the options market, but also depends on the type of the option, ie, whether it is a call option or a put option. Call options give the investor the right to buy the underlying asset on the expiration date, whereas a put option provides the investor with the right to sell the underlying asset on the expiration date. So payoff diagrams for an options contract will have four possible variations - the long call, the short call, the long put and finally, the short put.

Skip to 1 minute and 19 secondsIn this video, we will study payoff diagrams by using a call option. The first graph we will look at is the payoff diagram for a long call option. In this example, the investor bought a call option that allows him to buy firm A's stock at the price of 30 on the expiration date. The premium to purchase the call was 5. The horizontal axis indicates the market price of the underlying asset, which changes along with the market condition, whereas the vertical axis represents the option payoff and the overall profit.

Skip to 2 minutes and 15 secondsBecause this is a long call option gives the investor the right to buy the underlying asset at the exercise price, 30, the investor will gain if the market price of the underlying asset is higher than 30 on the expiration date. On that day, the investor will call the options seller to buy stocks from him at 30, after which the investor can sell those stocks on the market at a higher price. However, if the market price is lower than 30, then this long call option has no value. It will not be exercised and the payoff zero. It is worth noting that the upper line in the graph indicates the payoff from the options contact.

Skip to 3 minutes and 18 secondsThe lower line, in red, shows profit and losses once we take into account the option premium. We can see that the lower line is obtained by moving the upper line down by the magnitude of the option premium, which is 5 per share. Therefore, including the cost of buying the option in the picture, we see that the market price should be higher than 35 for the investor to make a net profit. For a market price between 35 and 30 the investor will make a small overall loss - the gain from exercising the option offsets some, but not all of the option premium. In this case, the option seller makes the profit. Now, what about the payoff for a short call option?

Skip to 4 minutes and 28 secondsLet's look at the next diagram. The investor sold a call option, which gives the option holder the right to buy the underlying asset at the exercise price of 30. If the market price on the expiration date is higher than 30, say 40, then the option seller is making a loss, because in this case the option holder will call the seller, asking them to sell the option holder the shares at a price of 30. The option seller has to buy the underlying asset from the market at a higher price of 40, and then sell those shares to the option holder at the exercise price of 30.

Skip to 5 minutes and 29 secondsOn the other hand, if the market price is lower than the exercise price of 30, then the option holder will not exercise this option. Hence, the option seller will make a small profit equal to the option premium they received. Notice how the profit line, in red, is above the option payoff line for the seller of the call option. We have added two further examples below showing payoff diagrams for a long put option and a short put option. Have a look and share your thoughts on those with your fellow learners. Remember, a long put involves purchasing the right to sell the asset at the exercise price, labelled E.

Skip to 6 minutes and 33 secondsAnd a short put involves selling the right to sell the asset at the exercise price.

How to read payoff diagrams for options contracts

Payoff diagrams for options are more complicated than those of a futures contract.

In this video, Dr Hong Bo expains how the payoff structure of an options contract does not only depend on investors’ long or short position in the options market, but also depends on the type of the option, ie, whether it is a call option or a put option.

Use the diagrams in the downloads section to work through all the options in your own time: a long call, short call, long put and short put.

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This video is from the free online course:

Risk Management in the Global Economy

SOAS University of London

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