Payoff diagrams

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There are two types of options - calls and puts. Also, for long put option payoff diagram these payoff diagrams I have ignored option premiums so long put option payoff diagram can focus on the payout. Option premiums can be considered constants that move the entire graph up or down, without changing its shape which is what we are interested in.

The payoff for a stock position is linear. The payoff increases or decreases linearly with price, depending upon whether it is a long or a short position. A long position in a call option has a zero pay off till the exercise price, after which its payoff is identical to that of the stock. Here is a simple trick that some may find useful to remember what option payoff diagrams look like. The one pay-off diagram you will need to remember is the long call. Recall that this looks as follows:.

To get the short call pay-off diagram, assume there is an imaginary mirror placed on the x-axis. This applies to every option position, or complex set of positions. To get the long put position from the long call, imagine there is a mirror along the y-axis this time.

You get the pay-off from a long put position. Given this, you can visualize the payoff from a short put position too. Complex options positions can long put option payoff diagram understood by combining payoff diagrams. Next, we will combine payoff diagrams to understand the put-call parity.

Imagine an options portfolio with a long call and a short put position, both with the same exercise price. This will have the following payoff:. Compare the resulting payoff — the diagram on the right hand side. This looks just like the payoff for the stock, except that the line is a bit lower. And it is lower by exactly the amount of the exercise price, present valued to today. By combining a long call with a short put, we end up with a linear payoff, just like for the stock.

This linear payoff, combined with a bank deposit, has a payoff identical to a stock:. This is the put-call parity.

Notice the right hand side of this equation. The exercise price is a constant, and so is the spot price. So at any point in time, RHS is fixed. Therefore if call prices rise, put prices would rise need long put option payoff diagram rise too in order to maintain the parity. The minus sign indicates a short position. Payoff for a stock position The payoff for a stock position is linear.

The payoff from a short stock position is just the opposite: The payoffs for a short call, a long put and a short put are given below: How to remember what different payoff diagrams look like: Recall that this looks as follows: Long put option payoff diagram payoffs Complex options positions can be understood by combining payoff diagrams.

Understanding put-call parity Imagine an options portfolio with a long call and a short put position, both with the same exercise price. This will have the following payoff: This linear payoff, combined with a bank deposit, has a payoff identical to a stock: Combining the two, we get: This can also be written as: So we can write the put call parity long put option payoff diagram Introduction to vanilla options. Payoff diagrams There are two types of options - calls and puts.

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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 underlying , at a specified price the strike , by 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 K , and at time t the value of the underlying is S t , then 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 T , and 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: Puts 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 parity , a 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 time right before expiration, while an American put option allows exercise at any time before expiration.

The put buyer either believes that the 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, in 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 price 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 option to increase by a decline in the price of the underlying asset below the strike price. The writer seller 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 put , also called an uncovered put , is a put option whose writer the 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 the 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 bankruptcy , his 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 selling the option: During the option's lifetime, if the stock moves lower, the option's premium may increase depending on how far the stock falls and how much time passes.

If it does, it becomes more costly to close the position repurchase the put, sold earlier , resulting in a loss. If the stock 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 price. The writer receives a premium from the buyer. If the buyer exercises his 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 value.

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 dependence 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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