# Definition put option wikipedia

In financial mathematicsput—call parity defines a relationship between the price of a European call option and European put optionboth with the identical strike price and expiry, namely that a portfolio of a long call option and a short put option is equivalent to and hence has the same value as a single forward contract at this strike price and expiry.

This is because if the price at expiry is above the strike price, the call will be exercised, while if it is below, the put will be exercised, and thus in either case one unit of the asset will be purchased for the strike price, exactly as in a forward contract. The validity of this relationship requires that certain assumptions be satisfied; these are specified and the relationship is derived below. In practice transaction costs and financing costs leverage mean this relationship will not exactly hold, but in liquid markets the relationship is close to exact.

Put—call parity is a static replicationand thus requires minimal assumptions, namely the existence of a forward contract. In the absence **definition put option wikipedia** traded forward contracts, the forward contract can be replaced indeed, itself replicated by the definition put option wikipedia to buy the underlying asset and finance this by borrowing for fixed term e.

These assumptions do not require any transactions between the initial date and expiry, and are thus significantly weaker than those of the Black—Scholes modelwhich requires dynamic replication and continual transaction in the definition put option wikipedia.

Replication assumes one can enter into derivative transactions, which requires leverage and capital costs to back thisand buying and selling entails transaction costsnotably the bid-ask spread. The relationship thus only holds exactly in an ideal frictionless market with unlimited liquidity.

However, real world markets may be sufficiently liquid that the relationship is close to exact, most significantly FX markets in major currencies or major stock indices, in the absence of market turbulence.

The left side corresponds to a portfolio of long a call and short a put, while the right side corresponds to a forward contract. The assets C and P on the left side are given in current values, definition put option wikipedia the assets F and K are given definition put option wikipedia future values forward price of asset, and strike price paid at expirywhich the discount factor D converts to present values.

In this case the left-hand side is a fiduciary callwhich is long a call and enough cash or bonds to pay the strike price if the call is exercised, while the right-hand side is a protective putwhich is long a put and the asset, so the asset can be sold for the strike price if the spot is below strike at expiry. Both sides have payoff max S TK at expiry i. Note that the right-hand side of the equation is also the price of buying a forward contract on the stock with delivery price K.

Thus one way to read the equation is that a portfolio that is long a call and short a put is the same as being long a forward. In particular, if the underlying is not tradeable but there exists forwards on it, we can replace the right-hand-side expression by the price of definition put option wikipedia forward.

However, one should take care with the approximation, especially with larger rates and larger time periods. When valuing European options written on stocks with known dividends that will be paid out during the life of the option, the formula becomes:. We can rewrite the equation as:. We will suppose that the put and call options are on traded stocks, but the underlying can be any other tradeable asset.

The ability to buy and sell the underlying is crucial to the "no arbitrage" argument below. First, note that under the assumption that there are no arbitrage opportunities the prices are arbitrage-freetwo portfolios that always have the same payoff at time T must have the same value at any prior time.

To prove this suppose that, at some time t before Tone portfolio were definition put option wikipedia than the other. Then one could purchase go long the cheaper portfolio and sell go short the more expensive. At time Tour overall portfolio would, for any value of the share price, have zero value all the assets and liabilities have canceled out.

The profit we made at time t is thus a riskless profit, but this violates our assumption of no arbitrage. We will derive the put-call parity relation by creating two portfolios with the same payoffs static replication and invoking the above principle rational pricing. Consider a call option and a put option with the same strike K for expiry at the same date T on some stock Swhich pays no dividend. We assume the existence of a bond that pays 1 dollar at maturity time T. The bond price may be random like the stock but must equal 1 at maturity.

Let the price of S be S t at time t. Now assemble a portfolio by buying a call option C and selling definition put option wikipedia put option P of the same maturity T and strike K. The **definition put option wikipedia** for this portfolio is S T - K.

Now assemble a second portfolio by buying one share and borrowing K bonds. Note the payoff of the latter portfolio definition put option wikipedia also S T - K at time Tdefinition put option wikipedia our share bought for S t will be worth S T and the borrowed bonds will be worth K.

Thus given no arbitrage opportunities, the above relationship, which is known as put-call parityholds, and for any three prices of the call, put, bond and stock one can compute the implied price of the fourth.

In the case of dividends, the modified formula can be **definition put option wikipedia** in similar manner to above, but with the modification that one portfolio consists of going long a call, going short a put, and D T bonds that each pay 1 dollar at maturity T the bonds will be worth D t at time t ; the other portfolio is the same as before - long one share of stock, short K bonds that each pay 1 dollar at T.

The difference is that at time Tthe stock is not only worth S T but has paid out D T in dividends. Forms of definition put option wikipedia parity appeared in practice as early as medieval ages, and was formally described by a number of authors in the early 20th century. The Early History of Regulatory Arbitragedescribes the important role that put-call parity played in developing the equity of redemptionthe defining characteristic of a modern mortgage, in Medieval England.

In the 19th century, financier Russell Sage used put-call parity to create synthetic loans, which had higher interest rates than the usury laws of the time would have normally allowed. Nelson, an option arbitrage trader in New York, published a book: His book was re-discovered by Espen Gaarder Haug in the early s and many references from Nelson's book are given in Haug's book "Derivatives Models on Models".

Engham Wilson but in less detail than Nelson Mathematics professor Vinzenz Bronzin also derives the put-call parity in and uses it as part of his arbitrage argument to develop a series of mathematical option models under a series of different distributions. The work of professor Bronzin was just recently rediscovered by professor Wolfgang Hafner and professor Heinz Zimmermann. The original work of Bronzin is a book written in German and is now translated and definition put option wikipedia in English in an edited work by Hafner and Zimmermann "Vinzenz Bronzin's option pricing models", Springer Verlag.

Its first description in the modern academic literature appears to be by Hans R. Definition put option wikipedia in the Journal of Finance. From Wikipedia, the free encyclopedia. Options, Futures and Other Derivatives 5th ed. Energy derivative Freight derivative Inflation derivative Property derivative Weather derivative. Retrieved from " https: Finance theories Mathematical finance Options finance.

All articles with unsourced definition put option wikipedia Articles with unsourced statements from June Articles with unsourced statements from July Views Read Definition put option wikipedia View history. This page was last edited on 4 Aprilat By using this site, you agree to the Terms of Use and Privacy Policy.

Can't someone write a proper layman's definition of a put option? Even the 'example' given uses specialist terminologies. Aren't the only likely people who visit this article people who do NOT know what a put option is suxh as myselfnor are they likely to be familiar with it's terminologies. Whereas this article was written by an expert FOR an expert.

This article is unnecessarily complicated, especially since put options definition put option wikipedia pretty simple concepts see [1] — Preceding unsigned comment added by Hey why can't you give some numerical explanation or examples for put option definition put option wikipedia a layman to understand.

Though I obviously feel that this is a very simple theory, the unnecessary complecated, ambiguous language in the article, makes this seem extremely difficult to understand. I have no idea how to interpret the graphs, and I pretty much understand how a put option works.

I liked the graphs and found them very helpful in understanding how options work. Different people use different ways to learn. Can you please restore the graphs? 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 payed for it, whereas the asset short seller's risk of loss definition put option wikipedia unlimited its price can rise greatly, theoretically, infinitely, all the short seller's loss.

Rgeards, Shitij Malik —Preceding unsigned comment added by This article is mixing up the writer with the buyer in the first and second paragraphs. However, if the strike price is lower, then the writer seller has less risk since a given stock is less likely to drop more significantly. And yet, the writer would be paid a higher premium? Higher premium for less risk? Again, this makes no sense.

I believe to calculate the premium paid to the seller for a given puts contract is a very complex financial formula. I looked up puts after reading about them on a blog an hour ago, so I am new to this, but I am pretty sure the current calculation given for the premium is wrong. Additionally, the article definition put option wikipedia no mention of the importance of the duration of the put contract. A contract with a longer duration is of course more risky for the seller as the stock has a better chance of dipping below the strike price, and thus the seller will be paid a higher premium the longer the contract.

The first paragraph left my very non-financial head spinning. I've noted the confusing points with asterisks:. Here, the buyer is selling and the seller is buying. Was this a series of mistakes, or is finance-o-speak typically written backwards like this? If it is, wow! Thanks for clarifying this arcane process for **definition put option wikipedia** less market savvy types. I would rewrite but I have no financial knowledge. And from reading this, I still have none: A "put" or "put option" is an option to sell an item at a preset price at some time in the future.

That is it is a contract between two parties where one party the buyer of the put has the option, but not the obligation, to sell an item, typically a commodity or financial instrument such as a stock, to the other party the seller of the put at future date and definition put option wikipedia a predetermined price the strike price lower than the current market price.

If the price of the specified item does not drop below the strike price within the time period specified by the contract neither party has any further obligation and the definition put option wikipedia is complete. If the price does drop below the strike price, the seller of the put has an obligation to buy the definition put option wikipedia from the other party at the strike price, so the seller or writer of the put has a maximum exposure set definition put option wikipedia the strike price should the market price of the item being optioned drop to zero.

Although neither party has to own the item being optioned at the time the contract is written, the prototypical case is where the buyer of the put does already own the item and wants to reduce their risk should its market price drop. Whereas the seller of the put does not own the object but is willing to accept future risk in exchange for immediate compensation. The perceived risk effectively determines the price of the put. In this transaction, the buyer of the put is paying money upfront in order to reduce potential loss should the market price of the item drop.

Therefore the buyer believes the market price will rise, but also recognizes a possibility that the price will drop and wants to set a floor on definition put option wikipedia future potential losses. The seller of the put is being paid to take on that risk should the market price drop and definition put option wikipedia they also beleive the price will rise but are able to tolerate more risk than the seller. The existing article is pretty definition put option wikipedia.

I tried to start simple and also explain motivations, but I will leave it to someone else to change the article. The only definition put option wikipedia it would have any value at all is if the exercise date was a long way off in the future I'm new to this and maybe I've just got confused, but that's what I thought when Definition put option wikipedia read it.

I don't understand, why definition put option wikipedia anyone write a put? This article suggests that unless the stock price definition put option wikipedia drop, the person who wrote the put loses money. Nothing wrong with the answers so far, per se, but they all kind of miss the point of the original question posed. Big institutions can write puts because they have the ability to hedge efficiently.

The option premium they charge covers the expected cost of hedging plus a little extra their expected profit. The existence of hedging strategies means the put seller doesn't have to worry about the upward or downward drift of the underlying's price.

In fact, it's even better than that for these big guys I would disagree with folding the section on "Naked Puts" into the "Put Options" page. Of course the two should be linked, but whereas the underlying concept is the same, the ethical aspect is not. Selling what you do not have may have been fine during the previous decade's tumultuous, but rising, market. However, with the advent of this recent global financial crisis, chinks in the armor of the financial system have begun to show.

One of those faults has been the growing inability for unsophisticated investors who have overextended themselves to meet their obligations, as well as the increasingly apparent problem of the very complex web of trades that are not formally registered with any sort of clearing authority. The latter problem is supposedly being dealt with, in the Definition put option wikipedia.

Sorry not to have gotten back to this sooner, but my definition put option wikipedia schedule does not permit me to do much. Allow me to explain what I mean by an ethical issue. We would not very well combine the "investment" and "gambling" pages would we? Even though there are clearly elements of gambling in investment, and vice versa, we still hold, as a society, to the idea that investment involves the provision of capital by investors to the business community in hopes of developing some sort of viable operation that would contribute to the economy.

Yes, modern punters, on the whole, look more at how the market moves than how they can participate in profiting from the market's development; and, statistically, one has about the same chance of selecting winners by tossing a dart as through complex modeling.

Business ethics is a course taught in every business school today, though few seem to adhere to the principles they learn. Selling something one does not have, and could not guarantee he would be able to lay hands on, is fraud. At the very least such an action, as demonstrated in the recent VW-Porsche debacle, might be considered malpractice on the definition put option wikipedia of the professionals who are supposed to be acting on our behalf. In the introduction it is written: Taking a short position in general means selling an option, not, as stated above, buying an definition put option wikipedia.

For the sentence to be true, "short" should be replaced by "long". It can be checked here: Hull 2nd definition put option wikipediapage 7. The buyer of the put option acquires a short position by purchasing the right to buy the underlying instrument from the seller of the option for a specified price the strike price during a specified period of time.

If the option buyer exercises his right, the seller is obligated to sell the underlying instrument to him at the agreed-upon strike price, regardless of the current market price. In exchange for having this definition put option wikipedia, the buyer pays the seller or option writer a fee the option premium.

Put options offer insurance against excessive loss by providing a guaranteed buyer and price for an underlying instrument. In addition, the seller of put options can profit by selling put options that are not utilised. Such is the case when the ongoing market value of the underlying instrument makes the option useless, usually when the current market price of the underlying instrument remains above the strike price.

Holders of put options may also profit from the potential to sell the underlying instrument at a price greater than current market value and could then repurchase the underlying instrument at the definition put option wikipedia price to gain a profit. I find the graphs of poor quality. They do not show the intersection of the payoff function with the vertical axis, which is important to see in order to see the limited upside in the case of a buyer or limited downside in the case of a seller.

In addition, I really don't get the funny jagged bumps. What is the point of them? I **definition put option wikipedia** when talking about the payoff it is necessary to include the multiplier!! The payoff as it is currently treated in the article has to be multiplied by this multiplier. Have a look at this site http: From Wikipedia, the free encyclopedia. Put option received a peer review by Wikipedia editors, which is now archived.

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