Put Call Profit

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Call and Put Options Definitions and Examples

The Balance 2020

Call and put options are derivative investments, meaning their price movements are based on the price movements of another financial product, which is often called the underlying.

  • A call option is bought if the trader expects the price of the underlying to rise within a certain time frame.
  • A put option is bought if the trader expects the price of the underlying to fall within a certain time frame.

Puts and calls can also be written/sold, which generates income but gives up certain rights to the buyer of the option. 

Breaking Down the Call Option

For U.S.-style options, a call is an options contract that gives the buyer the right to buy the underlying asset at a set price at any time up to the expiration date. Buyers of European-style options may exercise the option—buy the underlying—only on the expiration date. 

Strike Price

The strike price is the predetermined price at which a call buyer can buy the underlying asset. For example, the buyer of a stock call option with a strike price of 10 can use the option to buy that stock at $10 before the option expires. 

Options expirations vary and can be short-term or long-term. It is worthwhile for the call buyer to exercise their option, and require the call writer/seller to sell them the stock at the strike price, only if the current price of the underlying is above the strike price. For example, if the stock is trading at $9 on the stock market, it is not worthwhile for the call option buyer to exercise their option to buy the stock at $10 because they can buy it for a lower price on the market.

What the Call Buyer Gets

The call buyer has the right to buy a stock at the strike price for a set amount of time. For that right, the call buyer pays a premium. If the price of the underlying moves above the strike price, the option will be worth money (will have intrinsic value). The buyer can sell the option for a profit (this is what most call buyers do) or exercise the option at expiry (receive the shares). 

What the Call Seller Gets

The call writer/seller receives the premium. Writing call options is a way to generate income. However, the income from writing a call option is limited to the premium, while a call buyer has theoretically unlimited profit potential. 

Calculating the Call Option’s Cost

One stock call option contract actually represents 100 shares of the underlying stock. Stock call prices are typically quoted per share. Therefore, to calculate how much buying the contract will cost, take the price of the option and multiply it by 100. 

  • In the money means the underlying asset price is above the call strike price.
  • Out of the money means the underlying price is below the strike price.
  • At the money means the underlying price and the strike price are the same. 

You can buy a call in any of those three phases. Your premium will be larger for an in the money option, because it already has intrinsic value.

Breaking Down the Put Option

For U.S.-style options, a put is an options contract that gives the buyer the right to sell the underlying asset at a set price at any time up to the expiration date. Buyers of European-style options may exercise the option—sell the underlying—only on the expiration date.

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Strike Price

The strike price is the predetermined price at which a put buyer can sell the underlying asset. For example, the buyer of a stock put option with a strike price of $10 can use the option to sell that stock at $10 before the option expires. 

It is worthwhile for the put buyer to exercise their option, and require the put writer/seller to buy the stock from them at the strike price, only if the current price of the underlying is below the strike price. For example, if the stock is trading at $11 on the stock market, it is not worthwhile for the put option buyer to exercise their option to sell the stock at $10 because they can sell it for a higher price on the market.

What the Put Buyer Gets

The put buyer has the right to sell a stock at the strike price for a set amount of time. For that right, the put buyer pays a premium. If the price of the underlying moves below the strike price, the option will be worth money (will have intrinsic value). The buyer can sell the option for a profit (what most put buyers do) or exercise the option at expiry (sell the shares). 

What the Put Seller Gets

The put seller/writer receives the premium. Writing put options is a way to generate income. However, the income from writing a put option is limited to the premium, while a put buyer’s maximum profit potential occurs if the stock goes to zero.

Calculating the Put Option’s Cost

Put contracts represent 100 shares of the underlying stock, just like call option contracts. To find the price of the contract, multiply the underlying’s share price by 100.

Put options can be in, at, or out of the money, just like call options.

  • In the money means the underlying asset price is below the put strike price.
  • Out of the money means the underlying price is above the strike price.
  • At the money means the underlying price and the strike price are the same. 

Just as with a call option you can buy a put option in any of those three phases. Your premium will be larger for an in the money option, because it already has intrinsic value.

Put Option

What Is a Put Option?

A put option is a contract giving the owner the right, but not the obligation, to sell, or sell short, a specified amount of an underlying security at a pre-determined price within a specified time frame. The pre-determined price the put option buyer can sell at is called the strike price.

Put options are traded on various underlying assets, including stocks, currencies, bonds, commodities, futures, and indexes. A put can be contrasted with a call option, which gives the holder to buy the underlying at a specified price on or before expiration. They are key to understanding when choosing whether to perform a straddle or a strangle.

Key Takeaways

  • Puts give holders of the option the right, but not the obligation, to sell a specified amount of an underlying security at a specified price within a specified time frame.
  • Put options are available on a wide range of assets, including stocks, indexes, commodities, and currencies.
  • Put option prices are affected by the underlying asset price and time decay. They increase in value as the underlying asset falls in price, and lose value as time to expiration nears.

Put Option Basics

How Do Put Options Work?

A put option becomes more valuable as the price of the underlying stock decreases. Conversely, a put option loses its value as the underlying stock increases. Because put options, when exercised, provide a short position in the underlying asset, they are used for hedging purposes or to speculate on downside price action.

Investors often use put options in a risk-management strategy known as a protective put. This strategy is used as a form of investment insurance to ensure that losses in the underlying asset do not exceed a certain amount, namely the strike price.

In general, the value of a put option decreases as its time to expiration approaches due to time decay, because the probability of the stock falling below the specified strike price decreases. When an option loses its time value, the intrinsic value is left over, which is equivalent to the difference between the strike price less the underlying stock price. If an option has intrinsic value, it is in the money (ITM).

Out of the money (OTM) and at the money (ATM) put options have no intrinsic value because there would be no benefit of exercising the option. Investors could short sell the stock at the current higher market price, rather than exercising an out of the money put option at an undesirable strike price.

Time value, or extrinsic value, is reflected in the premium of the option. If the strike price of a put option is $20, and the underlying is stock is currently trading at $19, there is $1 of intrinsic value in the option. But the put option may trade for $1.35. The extra $0.35 is time value, since the underlying stock price could change before the option expires. Different put options on the same underlying asset may be combined to form put spreads.

The payoff of a put option at expiration is depicted in the image below:

Where to Trade Options

Put options, as well as many other types of options, are traded through brokerages. Some brokers have specialized features and benefits for options traders. Those who have an interest in options trading can check out Investopedia’s list of best brokers for options trading. There you can get an idea of which brokers may fit your investment needs.

Alternatives to Exercising a Put Option

The put seller, known as the “writer”, does not need to hold an option until expiration, and neither does the option buyer. As the underlying stock price moves, the premium of the option will change to reflect the recent underlying price movements. The option buyer can sell their option and either minimize loss or realize a profit depending on how the price of the option has changed since they bought it.

Similarly, the option writer can do the same thing. If the underlying’s price is above the strike price they may do nothing because the option may expire worthless and they can keep the whole premium. But if the underlying’s price is approaching or dropping below the strike price, to avoid a big loss the option writer may simply buy the option back, getting them out of the position. The profit or loss is the difference between the premium collected and premium paid to get out of the position.

Real World Examples of Put Options

Assume an investor owns one put option on the SPDR S&P 500 ETF (SPY)—currently trading at $277.00—with a strike price of $260 expiring in one month. For this option they paid a premium of $0.72, or $72 ($0.72 x 100 shares).

The investor has the right to sell 100 shares of XYZ at a price of $260 until the expiration date in one month, which is usually the third Friday of the month, though it can be weekly.

If shares of SPY fall to $250 and the investor exercises the option, the investor could establish a short sell position in SPY as if it were initiated from a price of $260 per share. Alternatively, the investor could purchase 100 shares of SPY for $250 in the market and sell the shares to the option’s writer for $260 each. Consequently, the investor would make $1,000 (100 x ($260-$250)) on the put option, less the $72 cost they paid for the option. Net profit is $1,000 – $72 = $928, less any commission costs. The maximum loss on the trade is limited to the premium paid, or $72. The maximum profit is attained if SPY falls to $0.

Contrary to a long put option, a short or written put option obligates an investor to take delivery, or purchase shares, of the underlying stock.

Assume an investor is bullish on SPY, which is currently trading at $277, and does not believe it will fall below $260 over the next two months. The investor could collect a premium of $0.72 (x 100 shares) by writing one put option on SPY with a strike price of $260.

The option writer would collect a total of $72 ($0.72 x 100). If SPY stays above the $260 strike price, the investor would keep the premium collected since the options would expire out of the money and be worthless. This is the maximum profit on the trade: $72, or the premium collected.

Conversely, if SPY moves below $260, the investor is on on the hook for purchasing 100 shares at $260, even if the stock falls to $250, or $200, or lower. No matter how far the stock falls, the put option writer is liable for purchasing shares at $260, meaning they face theoretical risk of $260 per share, or $26,000 per contract ($260 x 100 shares) if the underlying stock falls to zero.

Put-Call Parity

What Is Put-Call Parity?

Put-call parity is a principle that defines the relationship between the price of European put options and European call options of the same class, that is, with the same underlying asset, strike price, and expiration date.

Put-call parity states that simultaneously holding a short European put and long European call of the same class will deliver the same return as holding one forward contract on the same underlying asset, with the same expiration, and a forward price equal to the option’s strike price. If the prices of the put and call options diverge so that this relationship does not hold, an arbitrage opportunity exists, meaning that sophisticated traders can theoretically earn a risk-free profit. Such opportunities are uncommon and short-lived in liquid markets.

The put/call parity concept was introduced by economist Hans R. Stoll in his Dec. 1969 paper “The Relationship Between Put and Call Option Prices,” published in The Journal of Finance.

The equation expressing put-call parity is:

C = price of the European call option

PV(x) = the present value of the strike price (x), discounted from the value on the expiration date at the risk-free rate

P = price of the European put

S = spot price or the current market value of the underlying asset

Put-Call Parity

Understanding Put-Call Parity

Put-call parity applies only to European options, which can only be exercised on the expiration date, and not American options, which can be exercised before.

Say that you purchase a European call option for TCKR stock. The expiration date is one year from now, the strike price is $15, and purchasing the call costs you $5. This contract gives you the right—but not the obligation—to purchase TCKR stock on the expiration date for $15, whatever the market price might be. If one year from now, TCKR is trading at $10, you will not exercise the option. If, on the other hand, TCKR is trading at $20 per share, you will exercise the option, buy TCKR at $15 and break even, since you paid $5 for the option initially. Any amount TCKR goes above $20 is pure profit, assuming zero transaction fees.

Say you also sell (or “write” or “short”) a European put option for TCKR stock. The expiration date, strike price, and cost of the option are the same. You receive $5 from writing the option, and it is not up to you to exercise or not exercise the option since you don’t own it. The buyer has purchased the right, but not the obligation, to sell you TCKR stock at the strike price; you are obligated to take that deal, whatever TCKR’s market share price. So if TCKR trades at $10 a year from now, the buyer will sell you the stock at $15, and you will both break even: you already made $5 from selling the put, making up your shortfall, while the buyer already spent $5 to buy it, eating up his or her gain. If TCKR trades at $15 or above, you have made $5 and only $5, since the other party will not exercise the option. If TCKR trades below $10, you will lose money—up to $10, if TCKR goes to zero.

The profit or loss on these positions for different TCKR stock prices is graphed below. Notice that if you add the profit or loss on the long call to that of the short put, you make or lose exactly what you would have if you had simply signed a forward contract for TCKR stock at $15, expiring in one year. If shares are going for less than $15, you lose money. If they are going for more, you gain. Again, this scenario ignores all transaction fees.

Key Takeaways

  • Put/call parity shows the relationship that has to exist between European put and call options that have the same underlying asset, expiration, and strike prices.
  • Put/call parity says the price of a call option implies a certain fair price for the corresponding put option with the same strike price and expiration (and vice versa).
  • When the prices of put and call options diverge, an opportunity for arbitrage exists, enabling some traders to earn a risk-free profit.

How Put-Call Parity Works

Another way to imagine put-call parity is to compare the performance of a protective put and a fiduciary call of the same class. A protective put is a long stock position combined with a long put, which acts to limit the downside of holding the stock. A fiduciary call is a long call combined with cash equal to the present value (adjusted for the discount rate) of the strike price; this ensures that the investor has enough cash to exercise the option on the expiration date. Before, we said that TCKR puts and calls with a strike price of $15 expiring in one year both traded at $5, but let’s assume for a second that they trade for free:

Put-Call Parity And Arbitrage

In the two graphs above, the y-axis represents the value of the portfolio, not the profit or loss, because we’re assuming that traders are giving options away. They are not, however, and the prices of European put and call options are ultimately governed by put-call parity. In a theoretical, perfectly efficient market, the prices for European put and call options would be governed by the equation:

C + PV(x) = P + S

Let’s say that the risk-free rate is 4% and that TCKR stock is currently trading at $10. Let’s continue to ignore transaction fees and assume that TCKR does not pay a dividend. For TCKR options expiring in one year with a strike price of $15 we have:

C + (15 ÷ 1.04) = P + 10

In this hypothetical market, TCKR puts should be trading at a $4.42 premium to their corresponding calls. This makes intuitive sense: with TCKR trading at just 67% of the strike price, the bullish call seems to have the longer odds. Let’s say this is not the case, though, for whatever reason, the puts are trading at $12, the calls at $7.

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