Put Option Example and Problems

Options are financial derivatives that offer buyers the right, but not the obligation, to buy or sell underlying securities such as stocks, bonds etc at a predetermined price and date. These derivatives can be divided into call options or put options. Call options allow buyers to profit when the price of the security increases, while put options allow buyers to profit when the price of the security declines. In this article, we will discuss put option example, problems and how it works.

A put option contract will give the owner the right to sell a specific underlying security at a predetermined price known as the strike price. The investors don’t necessarily need to own the underlying stock to sell or buy a put. This contract is also valid within a certain period of time and thus has an elapsing time frame known as the maturity or expiration date. This is when the put option expires and is settled.

Each put option contract represents 100 shares of the underlying stock and the terms of the contract are set by the seller. In order to purchase this contract, the buyer pays the seller a pre-established fee per share known as a premium. An investor can lose the entire amount of the premium paid for a put option if the price of the underlying security does not trade below the strike price by option maturity.

Furthermore, put options are traded on various underlying assets such as stocks, bonds, currencies, futures, commodities, and indexes. A put option can be contrasted with a call option, which gives the holder the right to buy an underlying asset at a predetermined price before or on a specified date. Contrary to put options, the call option allows the holder to profit when the price of the underlying assets increases.

Types

There are two types of put options- long put and short put. A put option that is purchased is referred to as a long put while a put option that is sold is referred to as a short put.

The long put is the position wherein the investor buys a put option. This is a bearish position in the market. The put buyer or holder is short on the underlying security of the put option but long on the put option itself. That is, the holder wants the value of the put option to increase by a decline in the price of the underlying security below the strike price.

The short put, on the other hand, is the position wherein the trader opens an options trade by selling or writing a put option. The writer (seller) of a put is long on the underlying security and short on the put option itself. That is, the seller wants the option to become worthless by an increase in the price of the underlying security above the strike price.

Related: What are stock options? Types and examples

The seller of the put, on the other hand, is under the obligation to purchase the asset at the strike price if the holder eventually uses the right to sell the asset. If a holder of a put option uses the right to sell the underlying asset at the strike price; we say that the holder has exercised the put option. By exercising the put, the holder will sell the asset at the strike price specified even if the underlying asset is currently worthless.

Stocks and equities are the most widely traded put options, though they are traded on several other instruments like interest rates or commodities. Put options, and many other types of options, are traded through brokerages and some brokers usually have differentiated features and benefits for options traders. Puts may be combined with other derivatives as part of more complex investment strategies.

The terms for exercising a put option would differ depending on the option style. An American put option allows the holder to exercise at any time before expiration (early exercise) whereas a European put option allows the holder to exercise the put option on expiration. Holding a European put option is comparable to holding the corresponding call option and selling an appropriate forward contract; this equivalence is known as put-call parity.

Put option explained

How does a put option work? If the strike price is K, and at the time (t), the value of the underlying asset is S(t), then in an American option, the buyer can exercise the put option for a payout of K-S(t), at any time until the option’s expiration date (T). The put option will only yield a positive return if the underlying asset’s price falls below the strike price when the put option is exercised.

A European option can only be exercised at time T (i.e the expiration date) rather than at any time until T, while a Bermudan option can only be exercised on specific dates listed in the terms of the contract. Hence, if the put option is not exercised by expiration, the option expires worthless. Usually, the put option buyer/holder will not exercise the option at an allowable date if the price of the underlying asset is greater than K.

The most obvious essence of a put option is to serve as a type of insurance. What the investor does in the protective put strategy is to buy enough puts to cover their holdings of the underlying asset so that if the price of the underlying asset falls sharply, they can still sell it at the strike price. Another essence of the put option is speculation. An investor can take a short position (short sell) in the underlying stock without trading in it directly.

Short selling, also known as taking a short position is an investment technique in which an investor essentially does the opposite of what he would’ve done with a typical investment. For instance, rather than buying a stock at a low price and hoping to sell it at a higher price, the investor sells the stock at a high price and hopes to buy it later at a lower price.

A put option works differently from a call option. Put options tend to be more valuable as the price of the underlying stock or security decreases. Conversely, the value of a put option reduces as the price of the underlying stock increases. Hence, they are usually used for hedging purposes or to speculate on downside price action.

Example of a put option to illustrate how it works

In order to have a better understanding of how a put option works, let’s look at a practical example. Let’s assume after some research, that Mr. Peter, an investor concludes that the shares of a tech company by the name Techbuddy will fall below $100 per share. Say, Techbuddy is currently trading at $100 per share and Mr. Peter decided to buy a put option for $5 (the premium) which gives him the right to sell 100 shares at the strike price of $100 per share.

Now, assuming, before the expiration of the put, Techbuddy‘s stock price drops to $80, Mr. Peter could exercise the put option and sell 100 shares at $100 per share which will result in a total profit of $1,500. To calculate the profit of the put option; you minus the $5 premium paid for the option from the $20 profit and then multiply by 100 shares. This gives Mr. Peter a total profit of $1,500. Also, if Mr. Peter happens to not own 100 shares of the company’s stock, he can choose to sell the option contract to another buyer. This practice is known as options trading.

Factors that affect the value of a put option

When it comes to selling put options, there are several factors to have in mind. It is best to understand the value and profitability of an option contract when considering a trade, if not, you risk the stock or underlying asset falling past the point of profitability.

Time plays a major role in the value of a put option. As the expiration date of a put option approaches, the value of the put option decreases due to the impact of time decay. As the option’s time to expiration draws closer, time decay accelerates because there is less time to realize a profit from the trade. As an option loses its time value, what is left off is the intrinsic value.

The intrinsic value of an option is equivalent to the difference between the strike price and the market price of the underlying security. For the put option, the intrinsic value is the strike price minus the market price of the underlying security. If a put option has intrinsic value it is said to be in the money (ITM). Put options are said to be in the money when the price of the underlying security is below the strike price at expiration.

Conversely, when the price of the underlying security is above the strike price, the put option is said to be out of the money (OTM). A put option that is at the money (ATM) has a strike price that is equivalent to the current price of the underlying security. At-the-money (ATM) and out-of-the-money (OTM) put options have no intrinsic value. This is because there is no benefit in exercising the option.

OTM doesn’t have intrinsic value but only possesses extrinsic or time value. However, being out of the money doesn’t mean a trader can’t make a profit on the put option. Rather than exercising an out-of-the-money put option at an undesirable strike price, the trader has the option of short selling the stock at the current higher market price. Though outside of a bear market, short selling is usually riskier than buying put options.

Before exercise, an option has a time value (extrinsic value) apart from its intrinsic value. The time value of a put option is reduced by factors such as the shortening of the time to expire, a decrease in the volatility of the underlying security, and an increase in interest rates. This time value is reflected in the premium of the option. For instance, if $20 is the strike price of a put option and the underlying stock is currently trading at $19, the intrinsic value of the option is $1 and the put option may trade for a premium of $1.35. The extra $0.35 is the time value because the price of the underlying stock could change before the option matures.

See also: Nonqualified stock options

When to buy a put option

Knowing the right time to buy an option can be dicey. For a call option, it is best to buy it when you think the price of the underlying security will rise. However, the reverse is the case for a put option. It is best to buy a put option when you think the price of the underlying security will decrease. This will let you sell the underlying security at a markup.

Have in mind that buying options is less risky than selling them. When buying options, the risk is equivalent to the premium paid. So, you should sell puts, if you expect that the price of the underlying security will rise. This will enable you to pocket the premium without worrying about the buyer exercising the contract. however, there are unlimited risks that options sellers face.

Generally, investors tend to buy a put option when they are concerned that the stock market will fall. This is because the put grants them the right to sell the underlying security at a fixed price through a predetermined period of time. The put option will typically increase in value when the price of the underlying security goes down. Hence, the investors benefit from a down market either as an investor hedging loss against a long position or as a short speculator. Therefore, one can benefit from buying a put option whether they own a portfolio of stock or simply want to bet that the market will go down.

Related: Equity Options Examples and Problems

Exercising a put option examples

Exercising a put option is when a holder of a put option uses the right to sell the underlying asset at the strike price. The terms for exercising a put option would differ depending on the option style. An American put option gives its holder the right to exercise at any time before expiration whereas a European put option gives its holder the right to exercise the put option on expiration.

A put option is considered to have intrinsic value when the underlying security has a market price (S) below the option’s strike price (K). This means the put option is in the money (ITM). Therefore, upon exercise, the option is valued at K-S. Anything other than ITM, its value is zero.

A put buyer or holder wants the value of the put option to increase by a decline in the price of the underlying security below the strike price. Whereas, a writer (seller) of a put wants the option to become worthless by an increase in the price of the underlying security above the strike price.

We will look at some put options examples below to explain buying and selling a put option as well as an example of put option in-the-money.

Buying a put option example

A buyer of a put option thinks the price of a stock will decrease. So, the buyer pays a premium that he will never get back unless the put is sold before it expires. The put option gives the buyer the right to sell the underlying asset at the strike price. The put holder/buyer either believes that the price of the underlying asset will fall by the exercise date or hopes to protect a long position in it.

The upside of buying a put is that the option owner’s risk of loss is limited to the premium paid for it. Moreso, the put buyer’s prospect (risk) of gain is limited to the option’s strike price minus the underlying’s market price and the premium/fee paid for it. That is, the maximum loss on the option position is limited to the premium that the put option buyer paid for the put. While the maximum gain on the option position would occur if the price of the underlying assets fell to zero.

Buying a put option calculation example

Assume an investor, Mrs. Mary, buys one put option on the SPDR S&P 500 ETF (SPY), in March 2022 which was trading at $445. Say, the put option has a strike price of $425 expiring in one month. For this put option, she paid a premium of $2.80 ( i.e $2.80 × 100 shares or units= $280).

Now, if the units of SPY drop to $415 before expiration, the $425 put will be in the money and will trade at a minimum of $10, which is the put option’s intrinsic value.

Option’s intrinsic value: $425 – $415= $10.

In regard to this, the exact price for the put would be nothing less than $10. More so, the put’s price would depend on some factors, of which the time remaining to expiration is the most important factor. So, let’s assume that the $425 put is trading at $10.50.

Since the put option is now ITM, Mrs. Mary has to decide whether to exercise the option, which would give her the right to sell 100 shares of SPY at the strike price of $425; or to just sell the put option and pocket the profit.

We will consider three cases:

1. Mrs. Mary already holds 100 units of SPY
2. Mrs. Mary does not hold any SPY units
3. Mrs. Mary sells the put option

Note that in order to keep things simple and very comprehensible, we’ll ignore commission costs in the put option calculation example below:

Mrs. Mary already holds 100 units of the underlying security and exercises the put option

Let’s say Mrs. Mary exercises the put option and she already holds 100 units of SPY in her portfolio. It is fair to say that she purchased the put option to hedge downside risk. That is the put option was purchased as a protective put. Let’s assume she purchased the shares at $400 as of then. Now, upon exercising her put option, her broker would sell the 100 SPY shares at the strike price of $425.

We can calculate profit on the put option as:

[(SPY sell price – SPY purchase price) – (Put option purchase price)] × Number of shares or units

Profit = [($425 – $400) – $2.80)] × 100 = $2,220

This means Mrs. Mary will make a profit of $2,220 from exercising her put option and selling the 100 units of SPY in her portfolio.

Mrs. Mary does not hold any units of the underlying security but exercises the put option

In a situation whereby Mrs. Mary does not own the SPY units, it is evident that the put option was purchased purely as a speculative trade. In such a situation, exercising the put option would result in a short sale of 100 SPY units at the $425 strike price. That is, Mrs. Mary could buy back the 100 SPY units at the current market price of $415 to close out the short position.

We can calculate the net profit on this trade as:

[(SPY short sell price – SPY purchase price) – (Put option purchase price)] × Number of shares or units

Profit = [($425 – $415) – $2.80)] × 100 = $720

This means that Mary will make a profit of $720 from exercising her put option and short selling.

Mrs. Mary sells the put option

From the preceding scenario, it can be seen that exercising the put option, short selling the shares and then buying them back sounds like a fairly complicated attempt. Also, there could be added costs in the form of commissions due to multiple transactions as well as margin interest (for the short sale).

In order to avoid that, Mrs. Mary can actually go for an easier option which is to just simply sell the put option at its current price and make a profit.

Remember that since the units of SPY dropped to $415 before expiration, the $425 put will be in the money and trade at a minimum of $10 ($425 – $415), which is the put option’s intrinsic value. Let’s assume that the $425 put is trading at $10.50.

In the case of selling the put option at its current price, we can calculate the net profit as:

(Put sell price – Put purchase price) × Number of shares or units

Profit= (10.50 – $2.80) × 100 = $770

From the calculation done, it can be seen that selling the option actually results in a profit of $770 compared to going through the complicated process of option exercise in the preceding example, which resulted in $720.

Selling the option gave $50 more than the $720 made by exercising the option. This is because selling the put option allows the time value of $0.50 per share ( i.e $0.50 × 100 shares = $50) to be captured as well. This is the reason why most long-option positions that have value before expiration are sold rather than exercised.

Writing/selling a put option example

The put ‘writer’ or ‘seller’ believes that the price of the underlying security will rise, and not fall. So, the writer sells the put to collect the premium. The total potential loss of the put seller/writer is limited to the put’s strike price minus the market price and premium already received. Put options can also be used to limit the writer’s portfolio risk and may be part of an options spread.

The maximum gain for a put writer/ seller is limited to the premium collected, whereas the maximum loss would occur if the underlying stock price fell to zero. Therefore, the gain/loss profiles for the put buyer and put writer are thus diametrically opposite. The put writer or seller receives a premium from the buyer. This premium is the profit the put writer makes if the buyer doesn’t exercise the put option. However, if the buyer exercises the put option, the put writer/seller will buy the stock at the strike price.

Furthermore, put writing is an advanced options strategy meant for experienced traders and investors. Strategies such as writing cash-secured puts need a significant amount of capital. Hence, if you’re new to options and have limited capital, put writing would be a risky attempt and is not recommended for you.

In the previous examples, we looked at put options from the buyer’s perspective or an investor who has a long put position. Now, in this section, we will turn our attention to the put option seller or the put option writer, who has a short put position. We will be looking at the other side of the options trade; a short-put position. A short or written put option is contrary to a long put option. The short put option will obligate an investor to take delivery or purchase shares, of the underlying security at the strike price specified in the option contract.

Writing a put option example

Assume an investor, Mr. Peter is positive and hopeful on SPY, which is currently trading at $445. He is bullish and does not believe the price will fall below $430 over the next month. Mr. Peter could write one put option on SPY with a strike price of $430 and collect a premium of $3.45 per share (i.e $3.45×100 shares= $345).

Mr. Peter would keep the premium collected ($345) if SPY stays above the $430 strike price over the next month. Because the options would expire out of the money and be worthless. The $345 is the premium collected or maximum profit that Mr. Peter can make on the trade.

On the flip side, if SPY moves below $430 before the expiration of the option in one month, Mr. Peter is obligated to purchase 100 shares at $430, even if SPY falls to $400, or $350, or even lower. That is, the put option writer, Mr. Peter is liable for purchasing the shares at the strike price of $430 no matter how far the stock falls. This means he faces a theoretical risk of $430 per share or $43,000 per contract ($430 × 100 shares) if the underlying stock falls to zero.

Sell put option example

Assume Trader X (put buyer) purchases a put option contract to sell 100 shares of Company ABC to Trader Z (put seller/writer) for $50 per share. Say, the current price of the stock is $50 per share and Trader X pays a premium of $5 per share.

Now, if Company ABC’s stock price falls to $40 per share before expiration, then Trader X can exercise the put option by buying 100 shares for a total of $4,000 from the stock market, and then selling them to Trader Z for $5,000.

• The sale of the 100 shares of ABC stock at a strike price of $50 to Trader Z is calculated as $5,000
• The purchase of 100 shares of ABC stock at $40 is calculated as $4,000
• The put option premium paid to Trader Z for buying the contract of 100 shares at $5 per share, excluding commissions is calculated as $500

Therefore, Trader X’s net profit can be calculated as:

($5,000 − $4,000) − $500

=$500

That is, Trader X makes a profit of $500 if the put option is exercised.

On the flip side, if the share price never drops below the strike price of $50, then Trader X would not exercise the option because selling the shares to Trader Z at $50 would cost Trader X more than that to buy it. Trader X’s option would be worthless and he would have lost the whole investment, including the premium of $500 ($5 per share, 100 shares per contract) paid for the options contract.

Therefore, Trader X’s (put buyer) total loss is limited to the cost of the put premium plus the sales commission to buy it. Whereas, the maximum gain for Trader Z (put seller) is limited to the premium collected.

In the money put option example

Let’s have a look at an example of a put option in the money to know how it works.

Assuming that an investor has a put option for shares in a telecommunication company. Say, this put option contract gives the investor the right to sell 100 shares of the company at a strike price of $100. Assume he purchased the put option at a premium of $10 with the hope that the stock price of the company would drop before the option’s expiration date.

Luckily, the investor’s hunch proved to be right at the expiration date and the stock price falls to $75 per share. This scenario renders the put option in the money (ITM) because the price of the stock is below the strike price at expiration. The investor could exercise the option and net himself a profit of $15 per share, which is the difference between the strike price ($100) and the actual price of the stock ($75) minus the premium the investor paid ($25 – $10). The profit of $15 per share multiplied by the 100 shares, then gives a total profit of $1,500 that the investor gets.

In the money vs out of the money put option

An out-of-the-money (OTM) put option is the reverse of the preceding example. Put options are said to be ITM when the price of the underlying security is below the strike price at expiration. Wheres, a put option is said to be OTM when the price of the underlying security is above the strike price.

Assuming, the stock of the telecommunication company in the preceding example is trading at $100 and the investor purchases a put option that gives him the right to sell 100 shares of the company at a strike price of $100 with the hope that the stock price of the company would drop before the option’s expiration date.

An out-of-the-money put option example would be a scenario whereby, the investor’s hunch is proved to be wrong at the expiration date and the stock price rises to $120 per share. This scenario renders the put option out of the money because the price of the stock is above the strike price at expiration.

Whether one should buy an in-the-money or out-of-the-money puts would really depend on factors like the investor’s amount of capital, trading objective, risk appetite, etc. The dollar outlay for an in-the-money put option is higher than that for an out-of-the-money put option. This is because the ITM put option gives you the right to sell the underlying security at a higher price.

However, the lower price for OTM puts is offset by the fact that they also have a lower probability of being profitable by expiration. Therefore, OTM put options may be a good choice if the investor doesn’t want to spend too much on protective puts and is willing to accept the risk of a modest decline in his portfolio.

Related: Exercising stock options and taxes

Buying a put option vs short selling

Buying puts and short selling are both bearish strategies. Nevertheless, there are some differences between these two strategies. The maximum loss associated with buying a put option is limited to the premium that the put buyer paid for the put. Also, buying puts does not need a margin account and can be done with limited amounts of capital.

Short selling, on the other hand, risk of loss is unlimited and is significantly more expensive. This is because of expenses such as stock borrowing charges and margin interest. Generally, short selling requires a margin account. Hence, it is considered to be much riskier than buying a put option.

Bull spread put option

Investors use the bull put spread as an options strategy when they expect a moderate rise in the price of the underlying asset. The bull put spread strategy is also known as a credit put spread and a short put spread. The strategy profits with bullish, or rising stock prices, hence, the term bull put spread. The term credit put spread makes reference to the fact that the strategy is created for a net credit, or net amount received. Finally, the term short put spread makes reference to the fact that this strategy involves the net selling of options, that is; it is established for a net credit.

The bull put spread strategy engages two put options to form a range that consists of a low strike price and a high strike price. So, the investor gets a net credit from the difference between the premiums of the two options. A bull put spread consists of one long put with a lower strike price and one short put with a higher strike price. The two puts have the same underlying asset and the same expiration date.

So, the bull put spread is established for a net credit and profits from either time erosion or a rising stock price, or both. The potential profit is limited to the net premium received minus commissions. While the potential loss is limited to when the price of the underlying assets falls below the strike price of the long put.

Bull spread put option example

Let’s say an investor, Mr. Peter is bullish on a tech company, Techbuddy over the next month. Assume the stock of Techbuddy currently trades at $275 per share. In order to implement a bull put spread, Mr. Peter would do the following:

• Buy one put option for $2 with a strike of $270 expiring in one month
• Sell one put option for $8.50 with a strike of $280 expiring in one month

Mr. Peter would earn a net credit of $6.50 for the two options ($8.50 credit – $2 premium paid). Therefore, the total credit received is $650 because one options contract equals 100 shares of the underlying asset.

Let’s look at two scenarios that depict maximum profit and maximum loss.

Scenario 1- maximum profit

Assuming Techbuddy rises and trades at $300 at expiry. The maximum profit achieved is $650 ($8.50 – $2 = $6.50 x 100 shares). The bull put spread strategy ceases to earn any additional profit once the stock rises above the upper strike price.

This means that with the bull put spread, the potential profit is limited to the net premium received minus commissions. The profit is only realized if the stock price is at or above the strike price of the short put (higher strike) at expiration and both puts expire worthlessly.

Scenario 2- maximum loss

Assuming Techbuddy trades at $200 per share or below the low strike, the maximum loss is realized. However, the loss is rounded off at $350:

i.e $280 put – $270 put – ($8.50 – $2) x 100 shares

=$350

The maximum risk of the bull put spread is equal to the difference between the strike prices minus the net credit received including commissions. This is realized if the stock price is at or below the strike price of the long put at expiration.

Naked put

Naked put also known as an uncovered put, is a put option whose writer (seller) does not have a position in the underlying security. This strategy is best used by investors who want to build up a position in the underlying security, but only if the price is low enough.

So, if the buyer fails to exercise the options, the writer keeps the option premium. But if the market price of the underlying security is below the option’s strike price at expiration, the option owner (buyer) can exercise the put option, compelling the writer to buy the underlying security at the strike price. Hence, the put buyer profits from the difference between the market price of the underlying security and the option’s strike price.

On a naked put, the seller’s potential loss can be substantial. If the market price of the underlying security falls all the way to zero, the loss is equal to the strike price (at which the seller must buy the underlying security to cover the option) minus the premium received. The potential profit is the premium received when selling the option; that is if the market price of the underlying security is above the strike price at expiration; the option seller keeps the premium, and the option expires worthless.

Alternatives to exercising a put option

A put buyer does not need to hold an option until expiration. As the price of the underlying security or stock rises, the premium of the option will change to reflect the recent underlying price movements. In order to minimize loss or realize a profit, the option buyer can sell their option, depending on how the price of the option has changed since they purchased it.

Similarly, the put writer can do the same thing. If the price of the underlying asset is above the strike price, put writers may do nothing. This is because the option may expire at no value, thus, allowing them to keep the whole premium. However, if the price of the underlying asset is approaching or dropping below the strike price, then the option writer may simply buy the option back to avoid a big loss.

See also: Stock options vs equity

Benefits

Investors usually use put options in a risk management strategy called a protective put. The protective put is used as a form of investment insurance or hedge to ensure that losses in the underlying asset do not exceed a certain amount. In this risk management strategy, the investor purchases a put option to hedge downside risk in a stock held in the portfolio. If the option is eventually exercised, the investor would sell the stock at the put option’s strike price. However, if the investor does not hold the underlying stock and exercises a put option, a short position in the stock would be created.

Put options allow investors to trade in options to sell 100 shares of a particular stock at some point in the future. This allows them to take either a positive or negative position on a stock for a relatively small price. It allows the holder to sell a security or stock at a guaranteed price, even if the market price for that security has fallen lower.

The advantage of selling puts is that you receive cash upfront (premium paid) and may not ever have to buy the stock at the strike price. That is, if the stock rises above the strike price by expiration, you’ll make money. The main upside of buying put options is the chance to speculate on securities that investors feel may be headed for a fall in price.

It serves as a form of insurance against a stock decline. Put options are inherently less risky compared to shorting a stock. This is because the premium paid is the most that one can lose for the put, while the short seller is exposed to considerable risk as the stock moves higher.

Put option problems

The major put option problem is the fact that there could be a substantial loss if the price of the underlying security moves in the opposite direction of where the investor anticipates it to go.

A put buyer wants the value of the put option to increase by a decline in the price of the underlying security below the strike price. Whereas, a put seller wants the option to become worthless by an increase in the price of the underlying security above the strike price. Should things happen otherwise for either party, there could be a loss.

Put options can do damage if the price goes in the opposite direction from what the investor anticipated. The damage could be more for those who are selling these options. The put buyers are only at risk for the premium paid for the put option, whereas, put sellers/writers, can suffer limitless losses.

See also: ISO stock options, tax and requirements

Last Updated on November 8, 2023 by Nansel Nanzip Bongdap