Option payoff diagrams, Epitrain by Epitrain Pte Ltd

Payoff Diagrams Ok boys and girls, let's walk thru this thing again. Long Futures Let's say we're trading some instrument. It can be anything - DBS shares, USD's (viewed as a commodity, paid for in SGD), whatever. The concepts remain the same. Let's assume the instrument trades in incremental values of $1 Let's assume we are long the underlying instrument at the price of $5, and that's the only position we have. Our P&L profile will look like this: Current Price of Underlying Instrument

$10

Long at $5

-$4

-$3

-$2

-$1

At the price of $5, our P&L is zero (assuming no transaction costs). As prices of the underlying rise above $5, we start making money. As they fall below $5, we start losing money.

Long at $5 Profit $6

Long at $5

$4 $2 $0 -$2

-$4

current price

-$6 Loss

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Short Futures Ok, so we have seen what a Long position's P&L looks like. What will a Short position's P&L Graph look like? The P&L in a tabular form will be as follows: Current Price of Underlying Instrument

$10

Short at $5

-$1

-$2

-$3

-$4

-$5

At the price of $1, you will be making a profit of $4 since you are short at the price of $5, and so on. Graphically represented, it will look like this:

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Long Call Now as we have discussed, the buyer of a CALL has the RIGHT but not the OBLIGATION to buy the underlying instrument, at a given price (Strike Price), for a specific time. To obtain this call, the buyer will have to pay a premium for it. Let's say the premium paid is $1. Let's say the Strike Price is at $5. What will the P&L table look like? Current Price of Underlying Instrument

$10

Long Call, strike $5, premium $1

-$1

Let's say some time after you buy the option, the market price of the underlying instrument moves to $5 (from wherever it was when you bought the option). It makes no difference if you exercise your option to buy or not, because you can get the underlying instrument either from the option (at the strike price of $5) or from the current open market at the same price of $5. The premium of $1 that you paid still has to be accounted for in the P&L table as that cost has already been incurred by you, at the time you purchased the option. Hence your P&L when the market price is $5 will be -$1 (the cost of your premium). At the price of $6, your P&L will be zero. Intrinsically, your P&L should be $1 (the strike price is at $5 enabling you to be long the underlying instrument at a price of $5 by exercising the option. The current market price is $6, so you can sell the underlying you receive from the option at $6, and make a profit of $1. But in truth, you have already paid $1 for the premium of the option at the start, so you net P&L is zero. As we move up the price scale, you will make progressively more money as you obtain the underlying instrument at a price of $5 by exercising the option, and selling it at the (higher) current market value. Of course you will need to take out the $1 you paid as premium. As we move below the price of $5, you will not want to obtain the underlying instrument via exercising the option. Obviously you won't want to do this - why would you want to obtain the underlying instrument at the strike price of $5 when you can get it from the current open market at a price of $4, or $3, or $2 etc....... That is the whole objective of buying options you will have the RIGHT, but not the OBLIGATION. However, your P&L will still have to account for the premium of $1 you paid for the option. Hence as we go below the strike price of $5, you will not exercise the option and hence not face any intrinsic losses from the option, but you will still incur a $1 loss.

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Hence the P&L graph will look like this:

As we can see from the graph, our losses are limited to $1 (the part of the line below Zero on the vertical axis) whilst our profits grow continuously as the price of the underlying instrument in the current open market rises. Hence we have UNLIMITED PROFIT POTENTIAL while facing only LIMITED LOSS (as we have discussed, that is the risk profile of a buyer of options)

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Long Put Ok, moving onto Long Puts. Let's say we buy a PUT (which gives us the RIGHT, but not the OBLIGATION to sell the underlying instrument at a given price, let's say strike of $6, for a specified time). The premium we pay for this PUT option is, say, $1 Current Price of Underlying Instrument

$10

Long Put, Strike $6, premium $1

-$1

As in the case of the Call we examined earlier, when the current market price for the underlying instrument is $6, it will be immaterial whether we sell the underlying instrument in the open market or exercise our right to sell at $6 (which we have because we bought the Put). It will only make a difference if the current open market price for the underlying instrument were below the strike price, say at $3. If the current market price was $3, then we would exercise our Put option, and sell at the strike price of $6. That would give us an implied profit of $3 (we get to sell at $6 instead of the current market price of $3, so that gives us an implied profit of $3). Of course we need to take out $1 from the implied profit to account for the premium we paid for the option. Hence we see in the table above that at the current market price of $3, we have a profit of $2 If the current market price is above $6, we would definitely not want to exercise our Put option, instead choosing to sell the underlying instrument in the current market (why would you want to sell at the strike price of $6 when you can instead sell at the current market is at $10 ?) The premium we paid is of course not recoverable, and hence we see in the table above that at the current market price of $10, our P&L is -$1.

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Hence graphically our P&L will looks like this:

Once again, as the buyer of the option, we have LIMITED RISK, but UNLIMITED PROFIT POTENTIAL, which we can see in the graph - our profits (the vertical axis) rise as the market price falls (the further the market price falls, the greater our implied profit). Our losses however, are always limited to the premium we paid.

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Short Call Ok time for some confusionâ&#x20AC;Ś. So we have covered what the Long Call and Long Put look like. What if we are short a Call? Let's use the same details as the Long Call example: Strike $5, premium $1 Letâ&#x20AC;&#x2122;s think about this first from the buyer's perspective. If the current market is below the strike price of $5, then buyer of the option would not want to exercise his option, preferring to buy the underlying instrument from the current open market at a price lower than $5. Since the buyer will not be exercising his option, then we as the Sellers (in this example) would be able to pocket the premium and not have to do anything more. Since the premium is $1, our profit will be $1. If the current market price is $5, it does not matter whether the Buyer of the Option exercises his option against us or not. If he does not, we simply pocket the $1 he paid in premium. If he does exercise against us, we are OBLIGATED to sell to him at the strike price of $5, but since the current market price is also $5, we will have no problems covering the resultant Short position we get landed with, without incurring any losses. So at a current market price of $5, our profit (as the seller of the option), will still be $1 (the premium paid). As the current market price rises above the strike price, then the buyer of the option would definitely want to exercise his option (he of course would want to, since he has the RIGHT to buy the underlying instrument from us at $5, the strike price). So if the current market price is $6, we are OBLIGATED to sell to him at the strike of $5. We will be faced with covering our Short position at the current market price of $6. That means we will have sold the underlying at $5 (the strike price), and will buy the underlying at $6 - that means a loss of $1 for us. Since we collected $1 previously in the form of premium, we will have a net P&L of Zero (as you can see in the table below). As the current market price continues to rise above $6, we will be facing increasing losses as we have to cover our Short position at higher and higher prices, but still being obligated to sell at $5 to our counterparty. Our losses will be lessened by the premium we collected, but that is constant at $1.

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Hence we end up with the following P&L Table: Current Price of Underlying Instrument Short call, Strike $5, Premium $1

$10

-$1

-$2

-$3

-$4

So graphically, the P&L for a Short Call position will be:

Hence we can see that our profit is always limited to $1, but our losses grow continuously as the current market price rises above the strike price. We have LIMITED PROFIT, but face UNLIMITED LOSSES, which is the risk profile of a Seller of Options The seller's P&L profile should be the mirror-image of the buyer's profile (due to the zero-sum nature of markets). Looking at the Buyer's P&L table (conveniently copied onto this page in brown for you), we can see that it is indeed so Buyer's P&L Profile Current Price of Underlying Instrument Long Call, strike $5, premium $1 Short call, Strike $5, Premium $1

$10

-$1

-$2

-$3

-$4

Seller's P&L Profile

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Short Put Ok, so this is pretty much the same as in the case of a Short Call, so don’t panic. Let's use the same details as the Long Put example: Strike $6, Premium $1 The P&L table will look like this: Current Price of Underlying Instrument

$10

Short Put, Strike $6, premium $1

-$4

-$3

-$2

-$1

Once again think about the logic at each price level. If the current market price is the same as the Strike price ($6), then it makes no difference if the buyer of the option (that is our counterparty) exercises the option or not. If he does not, then we just pocket the premium we collected. If he does exercise (since this is a PUT option, our counterparty has the RIGHT to sell to us. we have the OBLIGATION to buy from him at the strike price), he will be selling the underlying to us at the strike price of $6. Hence we will be long the underlying at $6. But we have no problem throwing out this resultant underlying position into the current market at the same price of $6 (the current market price), so we face no losses, and still retain the premium as profit. If the current market price is above the strike price, our counterparty would not exercise his option to sell to us, instead he would prefer to sell at a higher price (than the strike price) in the current market. Only if the current market price is below the strike price, will our counterparty want to exercise his RIGHT to sell the underlying instrument to us at the Strike Price. We, as the seller of the option, have the OBLIGATION to buy from our counterparty at $6. If the current market price is $2, having been obligated to buy the underlying instrument from our counterparty at $6, we will have an implied loss of $4. This is offset against the premium we collected at the start. Hence our net loss is $3 …. and so on…..

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Graphically represented:

Once again we can see that as a seller of an option, we have LIMITED PROFIT POTENTIAL, but UNLIMITED LOSS. Comparing our P&L table with that of the Long Put (in pink below) we see that it is indeed a mirror-image. Buyer's P&L Profile Current Price

$10

Long Put, Strike $6, premium $1

-$1

Short Put, Strike $6, premium $1

-$4

-$3

-$2

-$1

Seller's P&L Profile

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Option Strategies Following the same logical approach we have been using over the last pages, let's look at some common Option Strategies (the P&L Profiles of the strategies are in Green).

Straddles Long Straddles consist of a Long Call and a Long Put, both with the same Strike Prices. The holder of such a strategy would have Unlimited Profit potential and only Limited Losses. Current Price of Underlying Instrument

$10

Long Call, strike $5, premium $1

-$1.00

$0.00

$1.00

$2.00

$3.00

$4.00

Long Put, Strike $5, premium $1.1

$2.90

$1.90

$0.90

-$0.10

-$1.10

NET P&L

$1.90

$0.90

-$0.10

-$1.10

-$2.10

-$1.10

-$0.10

$0.90

$1.90

$2.90

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Short Straddles Short Straddles are made up of a Short Call and a Short Put, both with the same strike. Writers of Straddles will be faced with Unlimited Loss and Limited Profit potential. Current Price of Underlying Instrument

$10

Short Call, strike $5, premium $1

$1.00

$0.00

-$1.00

-$2.00

-$3.00

-$4.00

Short Put, Strike $5, premium $1.1

-$2.90

-$1.90

-$0.90

$0.10

$1.10

NET P&L

-$1.90

-$0.90

$0.10

$1.10

$2.10

$1.10

$0.10

-$0.90

-$1.90

-$2.90

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Strangles Long Strangles are made up of a Long Call and a Long Put, with different strike prices. Current Price of Underlying Instrument

$10

Long Call, strike $6, premium $1

-$1.00

$0.00

$1.00

$2.00

$3.00

Long Put, Strike $4, premium $1

$2.00

$1.00

$0.00

-$1.00

NET P&L

$1.00

$0.00

-$1.00

-$2.00

-$1.00

$0.00

$1.00

$2.00

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Short Strangles Short Strangles are made up of a Short Call and a Short Put, both with different strikes. Writers of Strangles will be faced with Unlimited Loss and Limited Profit potential. Current Price of Underlying Instrument

$10

Short Call, strike $6, premium $1

$1.00

$0.00

-$1.00

-$2.00

-$3.00

Short Put, Strike $4, premium $1

-$2.00

-$1.00

$0.00

$1.00

NET P&L

-$1.00

$0.00

$1.00

$2.00

$1.00

$0.00

-$1.00

-$2.00

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Synthetics Finally, on the issue of Synthetics. Sometimes we may not be able to buy or sell the particular option we desire because of a lack of liquidity in the market, or the prices quoted for our desired option might not represent "fair value". In such cases, we can use a combination of Futures contracts and other available options to replicate the P&L profile of our desired option. Let's see how this works.

Synthetic Long Call The P&L Table for a Long position, we have seen, is as follows: Current Price of Underlying Instrument

$10

Long at$ 5

-$4

-$3

-$2

-$1

The P&L Table for a Long Put is as follows: Current Price of Underlying Instrument

$10

Long Put, Strike $6, premium $1

-$1

Hence if we combine the two P&L tables we get the following: Current Price of Underlying Instrument

$10

Long at $5

-$4

-$3

-$2

-$1

Long Put, Strike $6, premium $1

-$1

NET P&L

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If we graphically represent the above, we get the following graph:

The blue line is the simple Long Futures (where we just buy the underlying at a price of $5). The pink line is the Long Put. If we look at the green line, which is the net P&L profile of the simple Long Futures position and the Long Put position, we see that our P&L remains constant as the current market price of the underlying instrument falls, but our profits rise steadily as the current market price of the underlying instrument rise. This is the same P&L profile as that of a Long Call. Hence we see that by putting together a simple Long Futures position and a Long Put position, we can achieve the same P&L profile as a Long Call position. The importance of knowing this is that sometimes, when we want to buy a call, we might not be able to find a seller for it. This is especially so in illiquid currencies or markets. If we however are able to find someone willing to sell a Put, we can still synthetically assemble a call for ourselves. Another application of synthetics is that sometimes, the premium for the Put might be cheaper than the Call, such that putting together a Synthetic Call would give you the same protection profile as buying a call directly, but at a lower premium (there are other factors affecting cost and effective protection levels, but that I am not going into that aspect of things at this time). So letâ&#x20AC;&#x2122;s run thru some other synthetic combinationsâ&#x20AC;Ś. I will just use the same P&L tables from the other pages. The Green line in the following graphs are the Synthetics

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Synthetic Long Put Consists of a Short Futures, and a Long Call: Current Price of Underlying Instrument

$10

Short at $5

-$1

-$2

-$3

-$4

-$5

Long Call, strike $5, premium $1

-$1

NET P&L

-$1

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Synthetic Short Call Consists of Short Futures, and a Short Put: Current Price of Underlying Instrument

$10

Short at $5

-$1

-$2

-$3

-$4

-$5

Short Put, Strike $6, premium $1

-$4

-$3

-$2

-$1

NET P&L

-$1

-$2

-$3

-$4

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Synthetic Short Put Consists of Long Futures, Short Call Current Price of Underlying Instrument

$10

Long at $5

-$4

-$3

-$2

-$1

Short call, Strike $5, Premium $1

-$1

-$2

-$3

-$4

NET P&L

-$3

-$2

-$1

By varying the price at which we buy or sell Futures, and the strike prices of the Puts or Calls, we can create Synthetic Puts or Calls with different strikes.

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