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# Payoff profiles

## Introduction

There are 8 possibilities in terms of profit and/or losses when the price of the underlying asset changes (simple assumption: strike price = price of underlying). They are as shown in Table 1.

These payoff/loss profiles may be depicted as follows, but first we provide the assumptions:

Underlying commodity = platinum

Contract = 100 ounces

Strike price = see diagrams below

Premium (option price) = USD 10 per ounce (i.e. total of USD 1 000)

Option type = European.

 Position Change in price of underlying asset Profit or loss Call option - buy (long call) Fall Loss: premium only Rise Profit: unlimited Call option - sell (write) (short call) Fall Gain: premium only Rise Loss: unlimited Put option - buy (long put) Fall Profit: unlimited Rise Loss: premium only Put option - sell (write) (short put) Fall Loss: unlimited* Rise Gain: premium only Note: these profiles only apply if strike price = price of underlying on deal day. * = unlimited up to the point where the underlying has no value.

Table 1: Payoff profiles of writer and buyer

## Call option: buy (long call) at expiry

The long call option is depicted in Figure 344. If the price of platinum remains at USD 450 (per ounce45) or falls below USD 450 for the term of the option contract, the buyer will not exercise the option, because it is not profitable to do so. The option will lapse, and the buyer loses the premium amount USD 10 per ounce, i.e. USD 1 000 (USD 10 x 100). He cannot lose more than this amount.

If the price moves upwards to say USD 455 at the end of the life of the option, the holder will exercise the option because he will recover part of the premium paid, i.e. USD 500 (USD 5 x 100). The total loss of the holder of the option will be half the premium, i.e. USD 500.

It should be clear that the exercising of the option means that the writer delivers 100 ounces of platinum to the buyer for which the buyer pays USD 450 x 100 = USD 45 000. The total cost to the buyer / holder of the option now is USD 46 000 (USD 45 000 plus the USD 1 000 premium). The buyer / holder of the platinum now sells the platinum in the spot market at the spot market price of USD 455 and receives USD 45 500 (USD 455 x 100). The total loss is USD 500 (USD 46 000 - USD 45 500). If the holder does not exercise the option the loss is USD 1 000 (the premium).

Figure 3: long call option

There are two other "options" for the buyer / holder in this regard:

• The holder could sell the option contract in the secondary market that exists for this paper. The value of the contract will be close to the market price of the underlying asset (pricing is discussed in some detail below).

• If the market is cash settled and the holder exercises, the writer pays the relevant amount to the holder (i.e. USD 500), and the writer's profit is USD 500.

If the spot platinum price moves to USD 460 (i.e. the strike price plus the premium) at the end of the life of the option, it also pays the holder to exercise the option because he will recover the premium paid. The option holder pays the writer USD 450 x 100 = USD 45 000, and sells the 100 ounces at the spot price of USD 460, i.e. for USD 460 x 100 = USD 46 000. The difference is USD 1 000 (USD 46 000 - USD 45 000), which is equal to the premium paid.

At any price above USD 460, there are 3 possibilities (that apply every day until expiry):

• Exercise the option.

• Sell the option.

• Keep the option (to expiry and exercise on expiry).

It will be apparent that the profit potential of the holder is unlimited. If say the platinum price moves to USD 600 and the holder exercises, the profit is:

Amount paid = 100 x USD 450 = USD 45 000

Premium paid = 100 x USD 10 = USD 1 000

Total cost = USD 46 000

Amount sold for = 100 x USD 600 = USD 60 000

Profit = USD 60 000 - USD 46 000 = USD 14 000.

## Call option: sell (write) (short call) at expiry

The short call option payoff profile is depicted in Figure 4. The payoff profile of the seller/writer of the call option is the reverse of that of the buyer. The maximum the seller can earn is USD 1 000, and the loss potential is unlimited. Thus, if the price at expiry is USD 450 or lower, he makes a profit of USD 1 000. At USD 460, the writer makes nothing, and at any price above USD 460, the writer makes a loss.

Figure 4: short call option

Some of the jargon referred to earlier is pertinent here. An uncovered or naked short call is where the writer does not have a position in the underlying instrument, i.e. is not holding the underlying instrument in portfolio (in this case 100 ounces of platinum). Where the writer does have a matching position in the underlying asset, he is covered, i.e. has a covered short call.

## Put option: buy (long put) at expiry

The long put option payoff profile is depicted in Figure 5.

A put option is where the buyer has the right to "put" (sell to) the writer the underlying asset at a pre-specified price. In this example, the strike price is USD 470, and the buyer pays a premium of USD 1 000 (remember, USD 10 per ounce).

This is the mirror image of buying a call, i.e. the buyer is hoping for a fall in the price to make a profit. At a spot price of USD 470 or higher the buyer will allow the put option to lapse. At USD 460, the buyer breaks even and he will exercise the option before or at expiry in order to break even. At any price lower than USD 460 the buyer will make a profit.

Figure 5: long put option

## Put option: sell (write) (short put) at expiry

The short put option payoff profile is depicted in Figure 6.

At a spot platinum price of USD 470 or higher, the writer of a put option with a strike price of USD 470 will make a profit of USD 1 000 (i.e. the premium). At say USD 465 the profit will be halved because the buyer will exercise at expiry date). At any platinum price lower than USD 460, the writer's potential loss is unlimited (up to point where platinum price = 0).

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