Section 5: Put option basics

In this section we will cover put options – What they are and how to make profit calculations.

Subjects: Simple Put Option Example, PNL Calculations, Breakeven Points, Puts vs Selling Underlying, Buying vs Selling Puts, Maximum PNL, Live Trade Examples, Quiz

Total Lectures: 10

Lecture 5.1: Introduction to put options

As we covered in lecture 2.2, an option has 5 main parameters:
-The underlying asset
–The option type
-The expiry date
-The strike price
-The option price

In section 5 we will be focusing specifically on the put option type. A put option gives the option buyer the right to sell the underlying asset, at the strike price, on the expiry date. Be sure you understand that sentence in its entirety before moving on. It is the buyer of the put option that has the right to sell, meaning it is the buyer of the put option who benefits from the underlying price falling. Some traders who are brand new to options mistakenly believe that because they are betting on the underlying price going down, they must be executing a sell order. With put options this couldn’t be further from the truth, as you need to buy a put option to benefit from a decrease in price. The buyer of the put option is purchasing the right to execute a sell order on the underlying asset at a later date. On the other hand, the seller of a put option makes a loss when the underlying price decreases.

As a put option is the right to sell the asset, we will also look at how buying a put option compares to shorting (selling) the asset itself.

It is a common misconception among traders new to options that a put option is the opposite to being long a call option. This is not the case. As we discussed in previous sections, the opposite to being long a call option is being short a call option. While both being short a call option and being long a put option are both bearish trades, the risk and reward profiles of each are very different, and the rights and obligations are also different.

The buyer of a put option is purchasing the right to sell the underlying asset, at the strike price, on the expiry date. On the other side of the trade, the seller of the put option has an obligation to buy the underlying asset from the buyer, should the put option buyer choose to exercise their right.

In section 5 we will stick to put options in traditional markets, using examples where everything is denominated in US dollars. Then in section 6, we will move on to cryptocurrency put options. This will allow you to first learn the basic mechanics of put options without the added complexity that cryptocurrencies and inverse contracts bring. The differences are particularly important when calculating profit/loss and breakeven points.

So, let’s begin in the next lecture with a simple example of how a company might use a put option.

Lecture 5.2: Simple put option example

In this lecture we’ll look at how a company might use the purchase of a put option to make sure their business remains profitable.

Suppose a company, let’s call them DEF, is growing some corn. It’s currently April, but the corn won’t be ready for sale for another 6 months in October. DEF are worried that if the price of corn falls too much by October, that they won’t be able to sell the corn they have harvested for a price that makes them enough profit.

The current price of corn is $4.50 per bushel, which is a good price for DEF to sell at. The problem is they are not ready to sell the corn yet. After doing some calculations, DEF has estimated that the lowest price that would be acceptable for them to sell the corn at is $3.80/bushel.

What DEF would love is a way to guarantee a minimum price that they can sell their corn for in October when the corn is ready. This could take the form of a legal agreement with another company, let’s call this company UVW, that agrees to purchase the corn from DEF for a minimum of $4 on October 23rd. That is, even if the price of corn decreases to less than $4 per bushel, UVW will be obligated to buy corn from DEF at $4 per bushel.

You may be wondering what’s in it for UVW. Well, in exchange for this valuable agreement, DEF will pay a fee (or premium) to UVW. The fee could be something like $0.10 per bushel. This $0.10 fee per bushel is kept by UVW no matter what happens. So even if the price of corn remains higher than $4 in October, meaning DEF does not need to use the agreement to sell at $4, UVW will still get to keep their fee of $0.10 per bushel.

This agreement between DEF and UVW is essentially a put option. DEF has paid a fee to UVW, and in exchange UVW has given DEF the option to sell them corn at $4 per bushel in October. DEF does not have to sell the corn at $4 per bushel, they just have the option to.

In the previous lecture we listed again the 5 main parameters of an option contract:

-The underlying asset
-The option type
-The expiry date
-The strike price
-The option price

In this example, the underlying asset is corn. The option type is a put option, which is the right to sell the asset. The expiry date is October 23rd. The strike price is $4. And the option price (or premium) is $0.10 per bushel.

Buying a put option is very similar to buying insurance. With insurance you pay a premium to an insurance company in exchange for them covering your losses if the asset you’re insuring is damaged or destroyed. Here, DEF has paid a premium to UVW as insurance against the price of corn decreasing below $4. To DEF this is well worth the premium of $0.10 as it guarantees that they will be able to sell their produce at a price that makes them a profit.

Let’s have a look at what effect buying this put option will have for DEF, based on three different prices of corn on October 23rd.

Scenario 1:

The price of corn has increased to $5.50/bushel on October 23rd. DEF is now ready to sell their corn. The put option gives them the right to sell their corn to UVW for $4/bushel. However, because it’s possible to sell the corn at $5.50/bushel in the open market, there is no point in exercising that right.

DEF therefore sells their corn for $5.50/bushel in the open market. They also paid $0.10/bushel for the put option though, so the net amount they received is $5.40/bushel. This $5.40 is slightly less than they would have received if they had not purchased the put option, but is still much higher than the $3.80/bushel that they calculated as what they needed to make to be profitable.

So in scenario 1, where the price of corn has increased, DEF has a profitable outcome.

Scenario 2:

The price of corn remains unchanged at $4.50/bushel on October 23rd. DEF is now ready to sell their corn. The put option gives them the right to sell their corn to UVW for $4/bushel. However, because it’s still possible to sell the corn at $4.50/bushel in the open market, there is no point in exercising that right.

DEF therefore sells their corn for $4.50/bushel in the open market. They also paid $0.10/bushel for the put option though, so the net amount they received is $4.40/bushel. This $4.40 is slightly less than they would have received if they had not purchased the put option, but is still much higher than the $3.80/bushel that they calculated as what they needed to make to be profitable.

So in scenario 2, where the price of corn has not changed, DEF has a profitable outcome.

Scenario 3:

The price of corn has decreased to $3/bushel on October 23rd. DEF is now ready to sell their corn. The put option gives them the right to sell their corn to UVW for $4/bushel. Because the price of corn is now $3/bushel, it is much more preferable for them to use the option to sell it to UVW for $4/bushel.

DEF therefore exercises the put option with a strike price of $4, which means they receive $4/bushel for the corn. They also paid $0.10/bushel for the put option though, so the net amount received is $3.90. Although the price of corn has fallen significantly, the put option has ensured the amount DEF receives does not fall below $3.90. As this is still above the $3.80 level that they set as an acceptable level, this means they have guaranteed they will make an acceptable profit.

Notice in this final scenario that if DEF had not purchased the $4 put option, the new price of corn of $3 would have meant they failed to get an acceptable price for their produce. This could have resulted in significant losses. In scenarios 1 and 2, the put option was not needed in the end, but it only added a small cost of $0.10/bushel, meaning the year was still profitable. In scenario 3 though, the put option was crucial to keeping DEF profitable, as it netted them an extra $0.90/bushel compared to not buying the put option.

So the put option only added a small cost in all 3 scenarios, but saved the year from catastrophe in scenario 3. This property of having a fixed cost, but having the potential to pay off big, is what makes the buying of options so attractive in certain circumstances.

This lecture has covered one hypothetical example where a put option would be useful, and we will cover many more examples, including live trades, throughout the rest of the course. In the next lecture though, we will study how to calculate the profit or loss of a put option.

Lecture 5.3: Profit/loss calculations for put options

In this lecture we will work through some examples of how to calculate the profit or loss of a put option position in dollars. For simplicity, for all of these examples, we will ignore any trading fees. Of course in practice to complete the calculation you would subtract whatever fees you have paid as well.

Profit/loss when closing a call option trade early

When an option position is not held to expiry, but closed early, the profit and loss calculation is very simple. Every trade involves a buy order and a sell order, so you simply subtract what you bought the option for from what you sold it for.

If you are long an option, closing the position would be done by selling the option back to another trader, reducing your net position to zero.

If you are short an option, closing the position would be done by buying back the option from another trader, reducing your net position to zero.

In both instances your profit is calculated by subtracting what you bought the option for from what you sold it for.

Example 1:

Let’s use a live price on Tastyworks for the example. Here we have the option chain for SLV, which is a silver ETF (exchange traded fund). The precise instrument we’re looking at here doesn’t matter too much for our profit/loss example, except to say that the contract multiplier for SLV is 100. That is, every 1 option contract represents 100 shares of SLV.

As usual we have strike prices down the centre column, with calls on the left, and puts on the right. We’re only interested in puts for today so we’ll only be looking at the right side of the option chain. Let’s use the put option which has a strike price of $21. The ask price, which is the price we can currently buy it for, is $1.54.

So, let’s assume we buy this put option for $1.54 today. How much profit will we make if the price of SLV moves down in the next few days, and as a result the price of this put option increases to say $4? Remember a put option is the right to sell an asset, so when the price of the asset decreases, all other things being equal, the value of put options for that asset will increase.

We’ve purchased this SLV $21 put option for $1.54, and a few days later it has increased in value to $4. We then decide to close the position before expiration by selling it for $4.

The total profit would then be:
$4 – $1.54 = $2.46

Remember though that the contract multiplier for SLV is 100. This calculation of $2.46 profit is per share. As the contract multiplier is 100, the total then is
$2.46 * 100 = $246.

When we say we bought the put for $1.54, that is per share. For 1 option contract, which represents 100 shares, that brings the total purchase price to $154. Similarly when we sell the contract for a price of $4, that is $4 per share. For 100 shares that is $400.

It’s relatively simple to see that if we bought something for $154, and then sold it for $400, we made a profit of $246. Which is calculated as $400 minus $154.

As we’ve closed the position early, all that matters is the price of our opening and closing orders. The price of SLV at expiry is no longer important to us as our position is now closed.

This is true for all option positions that you completely close early. Your profit is calculated as the price you sold the option for minus the price you bought the option for.

Options held to expiry

At expiration, all of the extrinsic value of an option resulting from volatility and time is gone. To calculate the value of an option when held to expiry we just need to know the strike price and the delivery price at expiration. This gives us the value of the option at expiration, then we simply adjust for the premium paid.

Let’s use the same $21 put option on SLV from example 1, but now we will assume we hold it until it expires.

When a put option has some value at expiration, i.e. when the underlying price at expiration is lower than the strike price, we can calculate the profit/loss of the option position at expiration using this formula:

(Strike Price – Price At Expiration – Premium Paid) * Contract Multiplier * Number Of Contracts

We can plot this formula for different values of ‘Price At Expiration’, which gives us this profit/loss payoff chart.

As you can see, for this put option at expiration, the risk is fixed to $1.54 if the price of SLV is anywhere above $21. The profit then increases continuously for any SLV price below $21. Let’s look at some specific examples.

Example 2:

So, this time we’ve purchased the $21 SLV put option for $1.54. Let’s assume that the price of SLV at expiration is $15.
This means we have:
-A price at expiration of $15
-A strike price of $21
-A premium paid of $1.54
-A contract multiplier of 100, and
-A number of contracts of 1

Substituting all these values into the formula, we get:

(21 – 15 – 1.54) * 100 * 1

=4.46 * 100 = $446

That’s $4.46 per share, multiplied by 100 shares. This long put option position has therefore made a profit of $446.

Example 3:

Using the same option still, what if the price at expiration was $20 instead.

We would then have:
-A price at expiration of $20
-A strike price of $21
-A premium paid of $1.54
-A contract multiplier of 100, and
-A number of contracts of 1

Substituting all these values into the formula, we get:

(21 – 20 – 1.54) * 100 * 1

= -0.54 * 100 = -$54

That’s negative $0.54 per share, meaning this long put option position has made a loss of $54. Notice how the price at expiration of $20 is below the strike price of $21. This means the put option did have some value at expiration, $1 per share. However, because we paid $1.54 per share for the option, the value at expiration was not enough to make up for the premium paid, leading to a small loss.

Example 4:

Sticking with the same option, let’s finally see what happens if the price moves in completely the wrong direction, and assume the price at expiration is $30.

We would then have:
-A price at expiration of $30
-A strike price of $21
-A premium paid of $1.54
-A contract multiplier of 100, and
-A number of contracts of 1

This time though, we don’t need to use the formula because the put option has no value at expiry. This is because the price at expiration is above the strike price.

The loss is simply what was paid for the option, which is:

Premium Paid * Contract Multiplier * Number Of Contracts

1.54 * 100 * 1 = $154

Even though the price of SLV increased way above the strike price $21, the loss of the long put option position is limited to the price paid for the option. Even if the price of SLV had increased even further, to say $100, the loss would still only have been the same $154. We’ve mentioned it previously but it’s worth repeating, this fixed risk is one of the most attractive features of buying options.

In summary

Buying a put option has a fixed risk. The maximum loss is limited to the premium paid for the put option. This maximum loss will occur when the option is held to expiration, and the underlying price fails to fall below the strike price by this time.

When closed early, the profit/loss of a long put option is equal to the price it was sold for minus the price paid for the option.

When the call option is held to expiry, and the underlying price is less than the strike price, we can use this formula to calculate the profit/loss precisely:
(Strike Price – Price At Expiration – Premium Paid) * Contract Multiplier * Number Of Contracts

The further below the strike price the underlying price has moved, the more profit a long put option will make.

Lecture 5.4: Breakeven points for put options

When a trader buys a put option, they are hoping that the underlying price falls, and specifically that it falls below their strike price. The strike price though, is not the price at which the trader will breakeven at expiration. This is because the option was not free, a premium was paid. This premium must be taken into account to calculate where the option will break even if held to expiry.

In example 3 in the previous lecture, you may remember we bought an SLV put option with a strike price of $21, and then it expired with the price of SLV at $20, which is below our strike price. This means the option had an intrinsic value of $1. However, because we paid a $1.54 premium for the option, we lost $0.54 per share on the trade overall.

It is useful when buying put options, particularly if you’re planning to hold them to expiry, to know what price the underlying needs to reach for your trade to break even. Thankfully this is a very simple calculation.

In that example where the strike price of the put option was $21, and the premium paid was $1.54, the breakeven point is simply

$21 – $1.54 = $19.46

This means that if the price of SLV is exactly $19.46 when the put option expires, the trade will have made precisely $0. No profit, but no loss either.

General formula

More generally, the breakeven point of a put option can be calculated as:

Breakeven Point = Strike Price – Premium Paid

It’s important to remember that it’s the premium paid per share that you need to use when making this calculation. You’ll remember that the contract multiplier for SLV was 100, so when we purchased the put option, the total premium paid was actually $154. It is the per share price of $1.54 though, that we use when making the breakeven calculations.

More examples

As the calculation is simple when only considering one put option at a time, it’s possible to do this calculation on the fly while looking over the option chain.

For example, a $20 put option with an ask price of $1.12. If we were to purchase this put for $1.12 and hold it until expiration, our breakeven point would be the strike price of $20 minus the premium paid of $1.12, which equals $18.88.

For a $17 put option with a current ask price of $0.35. If we were to purchase this put for $0.35 now and hold it until expiration, our breakeven point would be $17 minus $0.35, which equals $16.65.

We will be moving on to the differences between buying and selling a put option later in the section. It’s worth mentioning briefly now though, that the breakeven point for the seller of the put option is exactly the same as the breakeven point for the buyer of the put option. 

In summary

The breakeven point of a put option can be calculated as the strike price minus the premium paid for the option.
Remember to use the per share value for the premium paid, not the total premium.

Lecture 5.5: Buying a put vs selling the underlying

Buying a put option gives the holder the right to sell the underlying asset, at the strike price, on the expiry date. The option buyer pays a premium for this right, so why not just sell (or short) the underlying directly in the first place?

The main reason is the fixed risk feature of being long a put option. It can also require less capital than shorting the asset (depending on margin requirements). Put options can also be a useful way to hedge downside risk, while maintaining a long position in the underlying asset.

Fixed risk

As we’ve mentioned a few times already, buying a put option has a fixed risk. The maximum amount the trader can lose is the premium they pay for the option.

Let’s take a look at how the profit/loss of a put option compares to shorting the underlying asset. By doing this we can deduce some of the pros and cons of each.

Suppose a stock is trading at $100, and there is a put option for this stock with a strike price also of $100. This put option has a price of $5 per share. This chart shows the profit and loss of the put option at expiration (in blue), and of shorting 100 shares of the underlying (in red). 

Shorting (or selling) the stock leads to this straight line (in red) which continues all the way back to an underlying price of zero to the downside, and off to infinity to the upside. If you short 100 shares, every dollar decrease in the underlying price will give you a profit of $100. The only cap on this is if the price falls to zero, which would result in you gaining the full value of the shares you shorted. In this instance as you sold 100 shares at $100 each, if the shares become worthless, you will have gained the full $10,000 you sold them for. Conversely though, every dollar increase in the underlying price will give you a $100 loss, and this is not capped! This means your potential losses when shorting are unlimited.

Let’s compare this to the put option in blue. As you can see, to the downside, the payoff is very similar to shorting the 100 shares. The difference being that as $500 of premium was paid for the option, the profit is $500 less at every point below the $100 strike price. So far it’s not looking favourable for the put option, but now look at what happens when the underlying price increases instead. The losses of the put option position are limited to the $500 premium paid, no matter what happens to the underlying price. Even if the price goes significantly higher to say $300 per share, the loss is still only $500. Compare that to the $20,000 potential loss of shorting the stock outright and price moving to $300, and it’s a clear advantage for the put option.

The point at which these two lines intersect is $105. This can be calculated as the current stock price of $100, plus the premium per share of $5 paid for the option. It’s at this point that the put option would have exactly the same profit/loss as owning the shares. For any point to the right of this, it would be much more beneficial to have the put option rather than the shares. For any point to the left of this, it is a little more profitable to have shorted the shares, but both gain from all further price decreases.

In other words, by opting for the put option instead of shorting the shares initially, you’re sacrificing a small fixed amount of your potential profit, for the guarantee that you can’t lose more than the amount you pay for the option.

Potentially lower cost

How much you require in your account to short something will depend on the margin requirements of whatever platform and asset you are trading. Unless using very high leverage though the capital required to open the short will be higher than the amount required to purchase the option.

Even if high leverage is available, if the price moves against you, you would quickly need to add more funds to keep the short position open. This is not the case for the put option, as the most you will ever need is the amount paid for the option.

This means that by purchasing the put option, you can gain very similar exposure to a decrease in the price of the asset, but without tying up as much capital, and without the risk of needing to add more.

Hedging downside risk

Put options also offer an alternative to closing a long position in the underlying. Imagine for example, if you purchased 100 shares at $60 each, and the price has increased to $100 a share. This leaves you with a nice profit that you would like to protect and so are considering selling the shares. However, what if you still think there is a chance it could continue to increase up to $150? 

Selling the shares now to realise your gain of $40 per share would mean you don’t benefit from any further increase in price. If you buy a put option with a strike price of $100 instead, you will still be able to sell the shares at $100 each if the price decreases, but you will also still benefit if the price does indeed continue to increase to $150.

You will of course need to pay the premium to purchase the put option, but if you believe the price is worth paying, the put option may be a superior way of locking in most of your unrealised profit from owning the shares.

The effect of time

As well as the premium that is paid for the put option, there is one major disadvantage worth mentioning, and that’s the inherent time limit that an option has. If the expiry date is reached and price has failed to decrease, the option will expire worthless and result in a loss for the put option trader. To regain exposure to price decreases they would need to buy another put option, whereas a trader who had shorted the shares instead could simply continue to hold the position.

So when purchasing a put option, there is more pressure to be correct about the timing of the move as well, not just the direction.

In summary

Shorting an asset can require a lot of capital, and even if the capital requirements are lowered using leverage, this still means that more capital will need to be added if price increases. Shorting also has the potential for large losses if the price of the asset increases significantly.

Buying a put option will usually require less capital. The maximum loss of a long put option position is also fixed to the premium paid. 

These properties make put options ideal for traders who want to limit their risk, while still participating in almost all of any decreases in the underlying price.

The costs of gaining these attractive properties are the premium paid for the option, and the inherent time limit the option trade has to work.

Lecture 5.6: Buying vs selling a put option

Every option trade has a buyer and a seller. Selling an option is also sometimes referred to as writing an option. So far we have focused on put options from the buyers side, but it’s also important to understand the transaction from the sellers point of view.

Apart from any trading fees, an option contract is a zero sum game. Any profit made by a put option buyer will result in an equal loss made by the put option seller. Conversely any loss made by a put option buyer will result in an equal profit made by the put option seller.

This relationship means the profit/loss chart for the put option seller is similar to the profit/loss chart for the put option buyer, but flipped along the x-axis. Here we can see the same put option we looked at in the previous lecture, with a strike price of $100, and a premium of $5 per share.

The profit/loss of the put option buyer is shown in blue, and in red we can see the profit/loss of the put option seller. At each level of underlying price, the PNL lines for buyer and seller are an equal distance away from the x-axis, but on opposite sides of course, one positive and one negative.

Where both lines cross the x-axis represents the breakeven point, i.e. the point at which $0 profit or loss is made. The buyer and seller of the option share the same breakeven point as well (again, this is ignoring any trading fees).

Fixed profit

When the underlying price is above the strike price at expiry, you will remember the put option buyer has a fixed risk. For the put option seller, this means they have a fixed profit when the underlying price is above the strike price at expiry.

The seller has a cap on their profit, and that is the premium they collected for the option. In this case $5 per share for a total of $500. No matter how high the price moves, the seller can make $500 at most.

(Almost) unlimited risk

When the underlying price decreases below the strike price, the potential profit for the put option buyer is limited only by the share price reaching zero. This means the potential loss for the put option seller is also only limited by the share price reaching zero.

This is a key point because, even though there is technically a cap, it means the put option seller can still lose far more than they collected in premium, and even potentially lose everything in their trading account. For this reason it is extremely important for new traders to make themselves fully aware of the risks before selling options.

The effect of time

As the put option seller’s potential profit is capped to the premium collected, but their potential loss is limited only by price hitting zero, you may be asking yourself why a trader would choose to sell a put option in the first place.

Remember from the previous lecture that there is an inherent time limit on an option. For the buyer of the put option this represents a need for the underlying price to decrease sufficiently before the expiry date. So time is against the buyer.

For the seller though, the passage of time helps them. Every day that passes, the option will lose a little bit of it’s value. The more time that passes without the underlying price decreasing, the more value the option will lose, and the more profit the put option seller will be making.

Put another way, if the price moves down this is bad for the put option seller, however if the price moves up or if the price does not move at all, then this is good for the put option seller. So if nothing happens, the seller is benefiting.

Margin

When buying an option, this will normally require the buyer to pay the entire premium up front to open the position. As the maximum the long put option can lose is the premium paid, this is the only capital the buyer needs to use.

In contrast the maximum loss for selling a put option is the strike price minus the premium collected, a figure that will be considerably larger. The seller may not be required to hold enough in their trading account to cover their maximum loss, but they will be asked to keep a certain amount in their trading account to support the position. This amount is called margin. Margin is an amount the broker has deemed appropriate for the trader to keep in their account to support their positions.

As the losses of selling a put could exceed this amount if the price decreases significantly enough, this could leave the seller in a position where they need to add more funds to their trading account, or face having the position forcibly closed by their broker at a loss.

Once you’re experienced with options, the margin system of the trading platform you are using will be second nature to you. However, this added complexity and risk means it is advisable to stick to buying options, or at least avoid selling naked options when you’re first starting out. That is until you’re comfortable with how the margin system works and what risk is involved with selling options.

Selling a naked option means you have sold the option with no other position covering it at all. In other words there is nothing else in your account hedging that undefined risk.

It is possible to turn a short option position into a risk defined position by adding a long option to the position, converting it to a vertical spread. We will cover this later in the course.

In summary

Selling a put option is the complete opposite of buying a put option. Both the risk and reward are reversed. Any profit for the seller is a loss for the buyer, and vice versa.

Buying a put is a bet that the underlying price will decrease, and selling a put therefore is a bet that the underlying price will not decrease. Or at least not decrease beyond the strike price.

The seller of a put option has a limited profit potential. Their maximum profit is the premium they collected for the put.

The seller also has a risk only limited by the asset reaching a price of zero, meaning they could lose far more than they initially collected if the price decreases significantly. As they have undefined risk they will also need to be aware of the margin system of the site they are using.

When you’re brand new to options, it’s best to wait until you’re confident you have sufficient knowledge of the risks before selling naked options.

Lecture 5.7: Maximum profit/loss of put options

In this lecture we will cover the maximum profit or loss of a put option, for both the buyer and the seller. As with any trade, it is important to be aware of the risk you’re taking before placing the trade.

Firstly, this table shows how to calculate the profit or loss of a put option position for either the buyer or seller. For now, to keep things simple, we’ve left out the position size i.e. the contract multiplier and number of contracts.

What we are doing here to calculate the profit/loss, is calculating the value of the put option at expiry, then adjusting for the premium to give the final profit/loss. The value of a put option that expires in the money is the strike price minus the underlying price at expiry. So we could write this as:
Put Value = Strike – Price

To calculate the buyers profit/loss we then just need to subtract the premium they paid from the value of their put option at expiry. This leads to us calculating:
Put Buyer’s PNL = Put Value – Premium

As we just covered, when the put expires in the money, the put value is ‘Strike – Price’, so we can write as:
=Strike – Price – Premium

So you can see how the formula for the buyer’s PNL is derived. 

The seller’s PNL is of course just the negative of this, i.e. multiplied by minus one. So the seller’s PNL can be calculated as:
Put Seller’s PNL = (Put Value – Premium) * -1

= Premium – Put Value
= Premium – (Strike – Price)
= Premium + Price – Strike

So you can see how the formula for the seller’s PNL is derived.

When the put option has no value at expiry, because the price expires above the strike, you can substitute in zero for the ‘Put Value’ to give:
Put Buyer’s PNL = Put Value – Premium
= 0 – Premium
= -Premium

And:
Put Seller’s PNL = Premium – Put Value
= Premium – 0
= Premium

PNL example

As a quick example, assume a trader buys a put option with a strike price of $40, and pays a premium of $5 per share.

What is the profit and loss for the buyer and seller if the price at expiry is $25?
We have a:
Price of $25
Strike of $40
Premium of $5

As the price at expiry of $25 is below the strike price of $40, the put has some value at expiry, so we will use the bottom row of formulas.

The buyer of the put option has a profit/loss of:
= Strike – Price – Premium
= 40 – 25 – 5
=$10

So the put option buyer has a profit of $10.

The seller of the put option has a profit/loss of:
= Premium + Price – Strike
= 5 + 25 – 40
= -$10

So the seller of the put option has a loss of $10.

Max profit/loss

As well as just being able to calculate the profit or loss for a specific value, it’s also useful to know the maximum profit or loss of any option position you’re thinking of opening.

For example, if we use the previous example with a:
Price of $25
Strike of $40
Premium of $5

The maximum profit for the buyer is $35. This is calculated as:
= Strike – Premium
= 40 – 5
= $35

The maximum loss for the seller is of course also $35, calculated in the same way.

For the put option buyer, their profit continues to increase for every dollar decrease in the underlying price. Remember the put option buyer’s profit is calculated as: = Strike – Price – Premium
So if we assume a minimum price of $0, this means their maximum profit is limited to:
=Strike – Premium

When the put option buyer has their maximum profit, the put option seller has their maximum loss of the same amount.

The put option buyer suffers their maximum loss when the underlying price at expiry is above the strike price, rendering the put option worthless. When this is the case they lose the premium they paid for the option, but nothing more.

Similarly for the put option seller, they make their maximum profit when the underlying price at expiry is above the strike price of the put option. The seller gets to keep the premium they collected, and does not have to pay anything out. Their maximum profit is equal to the premium collected.

Note: It is extremely rare, but it is technically possible for an asset price to become negative, which could increase a put option buyer’s profit, and increase a put option seller’s loss past the maximum we’ve listed here.
This can happen for physically settled contracts for assets that cost a lot to take delivery of and store. For example this happened in April 2020 with a WTI Oil contract. With the Covid-19 crisis greatly decreasing demand for oil, oil storage facilities were running very low on storage capacity. Due to this, many people who were left holding the physically settled contract coming into expiry did not want to take physical delivery of the oil, and so were even willing to pay other parties up to $37.63 a barrel to take the contracts off their hands. A quick google search will give you more details on this event if you want to study it in more detail.

In summary

The buyer of a put option has a fixed risk, and a profit that is only limited by the underlying price reaching zero.
The seller of a put option has a risk only limited by the underlying price reaching zero, and a fixed maximum profit.

Whether trading call options or put options, or a combination of both, it is always wise to be aware of where your risk lies. It is also important to be aware of the potential magnitude of that risk in a worst case scenario, i.e. your maximum loss.

Lecture 5.8: Trade example – Put option long (buy)

Now we’ve covered the basics of put options, it’s time to put some of this theory into practice with our first live put trade example. These next two live trades will largely follow the same format as the call examples in lectures 3.8 and 3.9, except this time of course we’ll be trading a put option each time.

In today’s example, we’re going to buy a put option live on Tastyworks. We will then look at what our potential profit will be at expiration, taking into account the premium we pay and the strike price, and we will then let the option expire. Once the option has expired we will analyse how the position performed and calculate how much profit/loss was made.

As with the call examples in section 3, we will use the SLV silver ETF for the next two examples. This is a deliberate choice to keep most parameters the same, except the fact we are using puts. This should give you a good understanding of what differences arise specifically because of the difference between puts and calls, rather than confusing the situation by also trading a different asset. In later sections though, we will of course place trades on different products as well.

First let’s take a look at the current price of SLV on a chart I’ve pulled from Trading View.

Today is Wednesday 9th December 2020, and SLV is currently trading at around $22.34. This is a one hour chart of the price of SLV, meaning each candle represents one hour.

You can see that the price gapped down at the start of today’s session. Let’s say we have a view that the price of SLV is going to continue to decrease for the rest of the week, so we want to buy a put option to take advantage of this. We’re going to buy the put option that expires on Friday (which is December 11th), with a strike price of $22. Let’s head over to the Tastyworks software to check out the prices and place the trade.

Here we have the option chain for SLV. As you can see in the top left, I’ve expanded the December 11th expiry date, so every option on the screen expires on Friday.

We’re interested in the $22 strike price, which we can find in the middle column. And we want the put, so we head right from here.

The bid is what we could currently sell this option for immediately, which is 15 cents in this case. The ask is what we could currently buy this option for immediately, which is 16 cents in this case. As we are buying this put today, it’s the ask price that we are interested in.

To populate the order form with an order to buy the put, we can click on the ask price of 16 cents. For this example, instead of just buying straight into the ask price of 16 cents, we’re going to set a limit price at 15 cents. This will mean we aren’t guaranteed to get filled, but if we do get filled, we will have purchased the option for a slightly cheaper price.

So here I’ve lowered the limit price of the order to 15 cents, and will send this into the market to wait for a fill. Once SEND ORDER is clicked, the pop up tells us the order has been sent correctly and is working in the market. Now we just wait and hope someone decides to sell into our buy order. Don’t worry I’ll cut out the waiting part if it takes very long.

There is a pop up notification letting us know that the order has been filled. That only took a few seconds thankfully. It can take much longer, or even not be filled at all, but it’s worth knowing that you don’t have to take the ask price when buying, or the bid price when selling. You can set a limit order at whatever price you like. These SLV options we’re looking at have very tight spreads anyway, but this knowledge can be particularly useful if you’re trading an instrument with wider spreads. We’ll touch on this in other lectures as well.
We’ve now purchased the $22 put option that expires in 2 days. Before skipping ahead to see what happened, let’s look at what could happen with this position depending on what happens to the price of SLV in the next two days. We can use the knowledge gained in the other section 5 lectures to calculate our potential profit, potential loss, and where the breakeven point on this trade is. 

What could happen

Let’s remind ourselves of the option parameters we have for this position.
-The underlying asset is shares of SLV
-The option type is put
-The expiry date is 11th December 2020
-The strike price is $22
-The option price (or premium) is $0.15 per share

As this is a real world example we will also include the fees in our calculations.

The total fees and commission for our order were $1.14. As the contract multiplier for SLV is 100, each option contract represents 100 shares of SLV. We bought 1 contract, representing 100 shares, so this total fee of $1.14 equates to a fee per share of $0.0114, or a little over 1 cent. This per share amount will help us in some of our calculations.

PNL chart

Given all the parameters we just covered, this is the PNL chart at expiry for this option position.

For any price of SLV above the strike price of $22, we will make the maximum possible loss. This maximum loss is limited to the premium we paid, plus the fees. We paid a premium of $0.15 per share, and the fees were $0.0114 per share. This gives us a total cost per share of $0.1614. As the contract multiplier is 100 and we purchased 1 contract, this equates to a total maximum loss of $16.14. And indeed this amount is what was shown as the total cost when we placed the order on tastyworks.

If SLV is any price below our strike price of $22 at expiry, we can calculate our profit or loss using the formula from lecture 5.3:

(Strike Price – Price At Expiration – Premium Paid) * Contract Multiplier * Number Of Contracts

Except instead of just using the premium paid per share, we can use the total cost per share, which includes the fees. So $0.1614 per share.

The profit/loss line increasing to the left of our strike price is this same formula plotted for each underlying price of SLV at expiry.

As an example, if the price of SLV at expiration is $20.50, we can calculate our profit as:

(22 – 20.5 – 0.1614) * 100 * 1 = $133.86

If the price of SLV at expiration has decreased to $20.50, our option to sell SLV at $22 is clearly worth $1.50 per share, for a total of $150. As this option cost us $16.14 in total, this gives us our profit of $133.86.

Breakeven

In lecture 5.4, we gave the formula for the breakeven point of a put option as:

Breakeven Point = Strike Price – Premium Paid

As with the profit calculations, instead of using just the premium paid, we will use the total cost including fees, which is $0.1614 per share. The breakeven point is then calculated as:

$22 – $0.1614 = $21.8386

This is the point at which the profit/loss line crosses the x axis.

What actually happened

Now we’ve studied what could happen, let’s jump forward and find out what actually did happen. Here we have the same 1 hour price chart of SLV we looked at just before placing the trade. Except now of course, it’s the end of Friday 11th December, so the option has expired.

We can see the point in time we bought the put option 2 days ago on the 9th. Later on the 9th, the price did continue to decrease, even past our strike price of $22. However, by today’s session the price had bounced back above $22, finishing the day at a price of $22.26. This is above the strike price of $22, so the put option has expired worthless, resulting in the maximum possible loss for this trade of $16.14.

The price of SLV did decrease over the life of the trade, but only by 8 cents in the end. As this was still above the strike price of the put option, this resulted in us making the maximum loss of the premium we paid plus fees.

Underlying position comparison

We began with a bearish bias, and bought the put option. This resulted in a loss, but how does this loss compare to a position in the underlying? In other words, what if we had just shorted 100 shares of SLV instead?

The price of SLV was $22.34 when we purchased the put, so we could have sold 100 shares for $2,234 instead. At the end of Friday the price had decreased slightly to $22.26, meaning we could buy back the 100 shares for $2,226. This means selling the shares instead would have resulted in a small gain of $8 (minus a little for fees).

Selling the shares would have required a lot more capital than purchasing the put option, but in this instance, selling the shares would have resulted in a better profit outcome.

Lecture 5.9: Trade example – Put option sell (short)

In this second put example we’re going to sell a put option live on Tastyworks. As with the example in the previous lecture, we will then look at what our potential profit will be at expiration, taking into account the premium we pay and the strike price, and we will then let the option expire. Once the option has expired we will analyse how the position performed and calculate how much profit/loss was made.

We’re using SLV again, so let’s take a quick look at the current price of SLV on a chart I’ve pulled from Trading View.

Today is Monday 14th December 2020, and SLV is currently trading at around $22.20. As with the previous SLV examples, this is a one hour chart of the price, meaning each candle represents one hour. 

Let’s say we have a view that the price will finish this week above last week’s low of $21.93, so we decide to sell the $21.50 strike put option that expires this Friday (which is December 18th). Let’s head over to the tastyworks software to check out the prices and place the trade.

Here we have the option chain for SLV. As you can see in the top left here, I’ve expanded the December 18th expiry date, so every option on the screen here expires on Friday.

We’re interested in the $21.50 strike price, which we can find in the middle column. And we want the put, so we head right from here.

The bid is what we could currently sell this option for immediately, which is 15 cents in this case. The ask is what we could currently buy this option for immediately, which is 16 cents in this case. As we are selling this put today, it’s the bid price that we are interested in.
To populate the order form with an order to sell the put, we can click on the bid price of 15 cents. As in the previous example, instead of just selling straight into the bid price of 15 cents, we’re going to set a limit order with a price of 16 cents. This will mean we aren’t guaranteed to get filled, but if we do get filled, we will have sold the option for a slightly higher price.

After populating the form, I’ve increased the limit price of the order to 16 cents, and will send this into the market to wait for a fill. Once SEND ORDER is clicked, the pop up tells us the order has been sent correctly and is working in the market. Now we just wait to see if someone is willing to buy into our sell order.

It took about 3 minutes to fill this time. We’ve now sold the $21.50 put option that expires in 4 days, and we’ve sold it for $0.16 a share. Before skipping ahead to see what happened, let’s look at what could happen with this position depending on what happens to the price of SLV in the next four days. 

What could happen

Let’s remind ourselves of the option parameters we have for this position.
-The underlying asset is shares of SLV
-The option type is put
-The expiry date is 18th December 2020
-The strike price is $21.50
-The option price (or premium) is $0.16 per share
As this is a real world example we will also include the fees in our calculations.

The total fees and commission for our order were $1.15. As the contract multiplier for SLV is 100, each option contract represents 100 shares of SLV. We sold 1 contract, representing 100 shares, so this total fee of $1.15 equates to a fee per share of $0.0115. Again, this per share amount will help us in some of our calculations.

PNL chart

Given all the parameters we just covered, this is the PNL chart at expiry for this option position.

For any price of SLV above the strike price of $21.50, we will make the maximum possible profit. This maximum profit is limited to the premium we collected, minus the fees. We collected a premium of $0.16 per share, and the fees were $0.0115 per share. This gives us a total credit per share of $0.1485. As the contract multiplier is 100 and we sold 1 contract, this equates to a total maximum profit of $14.85. And as usual this amount is what was shown as the total credit when we placed the order on Tastyworks.

If SLV is any price below our strike price of $21.50 at expiry, we can calculate our profit or loss using this formula:

(Premium + Price At Expiration – Strike Price) * Contract Multiplier * Number Of Contracts

This is similar to the formula we gave in lecture 5.3, except because we are the seller it has been multiplied by negative one.

Instead of just using the premium collected per share of $0.16, we can use the total collected per share, which includes the fees. So $0.1485 per share.

The profit/loss line decreasing to the left of our strike price is this same formula plotted for each underlying price of SLV at expiry.

As an example, if the price of SLV at expiration is $20.90, we can calculate our profit as:

(0.1485 + 20.90 – 21.50) * 100 * 1 = -$45.15

If the price of SLV at expiration has decreased to $20.90, the option to sell SLV at $21.50 is clearly worth $0.60 per share, for a total of $60. As we are the seller of this contract this represents a loss for us. As we also collected $14.85 in total for this option, this gives us our total loss of $45.15.

Breakeven

You may remember, the formula for the breakeven point of a put option is:

Breakeven Point = Strike Price – Premium Paid

As with the profit calculations, instead of using just the premium collected, we will use the total credit including fees, which is $0.1485 per share. The breakeven point is then calculated as:

$21.50 – $0.1485 = $21.3515

This is the point at which the profit/loss line crosses the x axis.

What actually happened

Now we’ve studied what could happen, let’s jump forward and find out what actually did happen. Here we have the same 1 hour price chart of SLV we looked at just before placing the trade. Except now of course, it’s the end of Friday 18th December, so the option has expired.

We can see the point in time we sold the put option 4 days ago on the 14th. Since then the price has increased significantly, and finished the Friday session at $23.96. This is well above the strike price of $21.50, so the put option has expired worthless, resulting in the maximum possible profit for this trade of $14.85.

Underlying position comparison

We began with a view that the price would not decrease below last week’s low, and sold the option. This resulted in a maximum profit of $14.85, but how does this profit compare to a position in the underlying? What if we had just bought 100 shares of SLV instead?

The price of SLV was $22.20 when we sold the put option, so we could have purchased 100 shares for $2,220 instead. At the end of Friday the price had increased to $23.96, meaning we could have sold the 100 shares for $2,396. This means that purchasing the shares instead would have resulted in a profit of $176 (minus a few cents in fees).

Due to how far the price rallied higher this week, buying the shares therefore would have resulted in a significantly larger profit than selling the put. By selling the put we capped our potential profit at the premium collected minus fees.

Continue your learning: Proceed to Section 6

Remember: Options trading involves risk. Never invest more than you can afford to lose. This educational content does not constitute financial advice. Always practice with paper trading before using real capital.

Ready to apply what you’ve learned? Start trading options on Deribit