Introduction to Options

What are call and put options?

1. A call option - The option to buy, but which comes with a choice at the end, for the owner of the option, of whether or not to go through with the settlement of the forward trade. The buyer of the call option has the option to settle the long forward trade - they are long the call option.
2. A put option - The option to sell

Using the figure below, when will the option be exercised?

Let’s assume the put option costs $50 per ounce.

• Now we see that if the platinum price ends up above $1000 an ounce, they lose $50 per share. In this case the option is “out of the money”.
• The put is “in the money” when the price of the underlying platinum ends up below the $1000 per ounce level - the “strike” of the option. And if the price ends up even lower, below $950, then they make back the premium plus more.

$950 is the breakeven on the 1000-strike put option, bought for $50 per ounce.

Using the figure below, how do these options look from the sellers perspective?

The seller takes in the premium and then becomes short the option - they take in the premium of $50 per ounce.

• If the platinum price ends up below $1000, then the option will be left to expire worthless by the buyer. The value of the position ends up at $50 - to the seller.
• However, if the platinum price ends up above $1000, then the buyer of the option will exercise the option. As this is a call option, when the buyer exercises, they will buy for the strike price of $1000 per ounce. This means that the seller of the option will be selling platinum at $1000 an ounce, even though the price is higher, and therefore is effectively losing money.

For example, if the price of platinum ends up at $1500, then the seller of the option will sell platinum for $1000, effectively losing $500 per ounce, however, this is offset by the $50 of the premium, giving a loss of $450.

What are the similarities between the break-even graphs?

If we add together the breakeven graph for the long call position and the breakeven graph for the short call position at every possible value for the platinum price at the end, we get zero. They are mirror images of each other - when one side gains, the other loses.

What do the long call/put and short call/put graphs tell us?

We can use these pictures to think about whether the option position gives you a long or short position in the underlying. We can see that both the long call and short call put give long positions in the underlying. Similarly, the long put and the short call give a short position in the underlying.

What are asymmetric/symmetric payoffs?

One key feature of options that we can see from the simple break-even graphs is that they give rise to asymmetric payoffs. The payoff on the forward trade is symmetric.

1. Symmetric Example:

The position that arises from buying platinum 3-mo forward at 1000 is symmetric - if the platinum price goes to 1100, the buyer makes $100. If the price goes to 900, the buyer loses $100. The probabilities offset each other. The greater volatility does not change the fair forward price, it just means that the potential gains and losses get greater.

2. Asymmetric Example:

However, in the above instance of a long call position, if the platinum price goes to 1100, the 1000 strike call option is in the money and worth $100. If the price goes to 900, the option is out of the money and worth zero. The payoffs are not symmetric - the buyer has to pay a premium.

What is a straddle trade?

A long straddle position is created by buying the call and put options at the same strike, on the same underlying, with the same expiration date. For example, an options trader buys both the 3-mo 1000 strike call and the 3-mo 1000 strike out on platinum. They cost $50 each, so the straddle costs $100.

What do the breakevens on the straddle tell us?

The breakevens on the straddle are at 900 and 1100. The options trader makes money in both directions. By buying the straddle, they are expressing a view that the market will move in one direction or the other, not a view on the direction. The buyer becomes long volatility, the more the straddle costs, the more volatility is priced in.

How does it look to sell the straddle?

The seller of the straddle receives the premium. As it is for the case above, they want the market to stay right where it is. The best outcome for the straddle seller is that the platinum price ends up at 1000. They want no volatility as it will cause the position to lose value for them - they are short volatility.