Options Pricing: Profit and Loss Diagrams

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In finance, a put or put option is a stock market device which gives the owner of a put the right, but not the obligation, to sell an asset the underlyingat a specified price the strikeby a predetermined date the expiry or maturity to a given party the seller of the put. The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying.

Put options are most commonly used in the stock market to protect against the decline of the price of a stock below a specified price. In this way the buyer of the put will receive at least the strike price specified, even if the asset is currently worthless. If the strike is Kand at time t the value of the underlying is S tthen in an American option the buyer can exercise the put for a payout of K-S t any time until the option's maturity time T.

The put yields a positive return only if the security price falls below the strike when the option is exercised. A European option can only be exercised at time T rather than any time until Tand a Bermudan option can be exercised only on specific dates listed in the terms of the contract. If the option is not exercised by maturity, it expires worthless. The buyer will not exercise the option at an allowable date if the price of the underlying is greater than K.

The most obvious use of a put is as a type of insurance. In the protective put strategy, the investor buys enough puts to cover his holdings of the underlying so that if a drastic downward movement of the underlying's price occurs, he has the option to sell the holdings at the strike price. Another use is for speculation: Buy put option graph may also be combined with other derivatives as part of more complex investment strategies, and in particular, may be useful for hedging.

By put-call paritya European put can be replaced by buying the appropriate call option and selling an appropriate forward contract. The terms for exercising the option's right to sell it differ depending on option style.

A European put option allows the holder to exercise the put option for a short period of buy put option graph right before expiration, while buy put option graph American put option allows exercise at any time before expiration.

The put buyer either believes that buy put option graph underlying asset's price will fall by the exercise date or hopes to protect a long position in it.

The advantage of buying a put over short selling the asset is that the option owner's risk of loss is limited to the premium paid for it, whereas the asset short seller's risk of loss is unlimited its price can rise greatly, buy put option graph fact, in theory it can rise infinitely, and such a rise is the short seller's loss.

The put writer believes that the underlying security's buy put option graph will rise, not fall. The writer sells the put to collect the premium. The put writer's total potential loss is limited to the put's strike price less the spot and premium already received. Puts can be used also to limit the writer's portfolio risk and may be part of an option spread. That is, the buyer wants the value of the put buy put option graph to increase by a decline in the price of the underlying asset below the strike price.

The writer buy put option graph of a put is long on the underlying asset 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 asset above the strike price.

Generally, a put option that is purchased is referred to as a long put and a put option that is sold is referred to as a short put. A naked putalso called an uncovered putis a put option whose writer buy put option graph seller does not have a position in the underlying stock or other instrument.

This strategy is best used by investors who want to accumulate a position in the underlying stock, but only if the price is low enough. If the buyer fails to exercise the options, then the writer keeps buy put option graph option premium as a "gift" for playing the game. If the underlying stock's market price is below the option's strike price when expiration arrives, the option owner buyer can exercise the put option, forcing the writer to buy the underlying stock at the strike price.

That allows the exerciser buyer to profit from the difference between the stock's market price and the option's strike price. But if the stock's market price is above the option's strike price at the end of expiration day, the option expires worthless, and the owner's loss is limited to the premium fee paid for it the writer's profit.

The seller's potential loss on a naked put can be substantial. If the stock falls all the way to zero bankruptcyhis loss is equal to the strike price at which he must buy the stock to cover the option minus the premium received.

The potential upside is the premium received when buy put option graph the option: During the option's lifetime, if the stock moves lower, the option's premium may increase depending on how far the stock buy put option graph and how much time passes. If it does, it becomes more costly to close the position repurchase the put, sold earlierresulting in buy put option graph loss.

If the buy put option graph price completely collapses before the put position is closed, the put writer potentially can face catastrophic loss. In order to protect the put buyer from default, the put writer is required to post margin. The put buyer does not need to post margin because the buyer would not exercise the option if it had a negative payoff. A buyer thinks the price of a stock will decrease. He pays a premium which he will never get back, unless it is sold before it expires.

The buyer has the right to sell the stock at the strike buy put option graph. The writer receives a premium from the buyer. If the buyer exercises buy put option graph option, the writer will buy the stock at the strike price. If the buyer does not exercise his option, the writer's profit is the premium. A put option is said to have intrinsic value when the underlying instrument has a spot price S below the option's strike price K.

Upon exercise, a put option is valued at K-S if it is " in-the-money ", otherwise its value is zero. Prior to exercise, an option has time value apart from its intrinsic buy put option graph. The following factors reduce the time value of a put option: Option pricing is a central problem of financial mathematics. Trading options involves a constant monitoring of the option value, which is affected by changes in the base asset price, volatility and time decay.

Moreover, the buy put option graph of the put option value to those factors is not linear — which makes the analysis even more complex. The graphs clearly shows the non-linear dependence of the option value to the base asset price.

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If you have seen the page explaining call option payoff , you will find the overall logic is very similar with puts; there are just a few differences which we will point out. While a call option gives you the right to buy the underlying security, a put option represents the right but not obligation to sell the underlying at the given strike price. When holding a put option, you want the underlying price go down, because the lower it gets relative to the strike price, the more valuable your put option becomes.

A long put option position is therefore a bearish trade — makes money when underlying price goes down and loses when it goes up.

You can see the payoff graph below. Of course, it also depends on your position size 1 contract representing shares in this example.

The relationships is linear and the slope depends on position size. For example, if underlying price is You can immediately buy it back on the market for Above the strike, the put option has zero value, because there is no point exercising the right to sell the underlying at strike price when you can sell it for a higher price without the option. The first component is equal to the difference between strike price and underlying price.

The lower underlying price gets relative to strike price, the higher your cash gain at expiration. However, this only applies when underlying price is below strike price. When it gets above, the result would be negative you would be losing money by exercising the option. Because a put option gives you the right but not obligation to sell, if underlying price is above strike price, you choose to not exercise the option and therefore cash flow at expiration is zero.

Taking all scenarios into consideration, a long put option cash flow at expiration is therefore the higher of:. The above is per share. To get the total dollar amount, you need to multiply it by number of contracts and contract multiplier number of shares per contract. Initial cost is of course the same under all scenarios. Therefore the formula for long put option payoff is:. It is very easy to calculate the payoff in Excel.

The key part is the MAX function; the rest is basic arithmetics. You can see all the formulas in the screenshot below. Besides the strike price, another important point on the payoff diagram is the break-even point, which is the underlying price where the position turns from losing to profitable or vice-versa. Calculating the exact break-even price is very useful when evaluating potential option trades.

The formula for put option break-even point is actually very simple:. If you don't agree with any part of this Agreement, please leave the website now. All information is for educational purposes only and may be inaccurate, incomplete, outdated or plain wrong. Macroption is not liable for any damages resulting from using the content.

No financial, investment or trading advice is given at any time. Home Calculators Tutorials About Contact. Tutorial 1 Tutorial 2 Tutorial 3 Tutorial 4. Put Option Payoff Diagram and Formula. This page explains put option payoff. We will look at: Long Put Option Position is Bearish While a call option gives you the right to buy the underlying security, a put option represents the right but not obligation to sell the underlying at the given strike price. Put Option Payoff Diagram You can see the payoff graph below.

Put Option Scenarios and Profit or Loss 1. What you can get when exercising the option What you have paid for the option in the beginning The first component is equal to the difference between strike price and underlying price. Taking all scenarios into consideration, a long put option cash flow at expiration is therefore the higher of: Therefore the formula for long put option payoff is: Put Option Break-Even Point Calculation Besides the strike price, another important point on the payoff diagram is the break-even point, which is the underlying price where the position turns from losing to profitable or vice-versa.

The formula for put option break-even point is actually very simple: Long Put Option Payoff Summary A long put option position is bearish, with limited risk and limited but usually very high potential profit. Maximum possible loss is equal to initial cost of the option and applies for underlying price higher than or equal to the strike price.

With underlying price below the strike, the payoff rises in proportion with underlying price. The position turns profitable at break-even underlying price equal to strike price minus initial option price. Maximum theoretical profit which would apply if the underlying price dropped to zero is per share equal to the break-even price.