Valuation of options

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In finance, the style or family of an option is the class into which the option falls, usually defined by the dates on which the option may be exercised. The vast majority of options are either European or American style options. These options—as well as others where the payoff is calculated similarly—are referred to as " vanilla options ".

Options where the payoff is calculated differently are categorized as " exotic options ". Exotic options can pose challenging problems in valuation and hedging. The key difference between American and European options relates to when the options can be exercised:. Where K is the strike price and S is the spot price of the underlying asset. Option option and future option trading wiki traded on futures exchanges are mainly American-style, whereas those traded option and future option trading wiki are mainly European.

Nearly all stock and equity options are American options, while indexes are generally represented by European options. Commodity options can be either style. Traditional monthly American options expire the third Saturday of every month. They are closed for trading the Friday prior. European options expire the Friday prior to the third Saturday of every month.

Therefore, they are closed for trading the Thursday prior to the third Saturday of every month. Assuming an arbitrage-free market, a partial option and future option trading wiki equation known as the Black-Scholes equation can be derived to describe the prices of derivative securities as a function of few parameters.

Under simplifying assumptions of the widely adopted Black modelthe Black-Scholes equation for European options has a closed-form solution known as the Black-Scholes formula. In general, no corresponding formula exist for American options, but a choice of methods to approximate the price are available for example Roll-Geske-Whaley, Barone-Adesi and Whaley, Bjerksund and Stensland, binomial options model by Cox-Ross-Rubinstein, Black's approximation and others; there is no consensus on which is preferable.

An investor holding an American-style option and seeking optimal value will only exercise it before maturity under certain circumstances. Owners who wish to realise the full value of their option will mostly prefer to sell it on, rather than exercise it immediately, sacrificing the time value.

Where an American and a European option are otherwise identical having the same strike priceetc. If it is worth more, then the difference is a guide to the likelihood of early exercise. In practice, one can calculate the Black—Scholes price of a European option that is equivalent to the American option except for the exercise dates of course.

The difference between the two prices can then be used to calibrate the more complex American option model. To option and future option trading wiki for the American's higher value there must be some situations in which it is optimal to exercise the American option before the expiration date.

This can arise in several ways, such as:. There are other, more unusual exercise styles in which the payoff value remains the same as a standard option as in the classic American and European options above but where early exercise occurs differently:. These options can be exercised either European style or American style; they differ from the plain vanilla option only in the calculation of their payoff value:. The following " exotic options " are still options, but have payoffs calculated quite differently from those above.

Although these instruments are far more unusual they can also vary in exercise style at least theoretically between European and American:. From Wikipedia, the free encyclopedia. Paul Option and future option trading wiki on Quantitative Finance. Energy derivative Freight derivative Inflation derivative Property derivative Weather derivative. Retrieved from " https: All articles with dead external links Articles with dead external links from March Articles with permanently dead external links All articles with unsourced statements Articles with unsourced statements from March Views Option and future option trading wiki Edit View history.

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In finance, a derivative is a contract that derives its value from the performance of an underlying entity. This underlying entity can be an asset , index , or interest rate , and is often simply called the " underlying ". In the United States , after the financial crisis of —, there has been increased pressure to move derivatives to trade on exchanges. Derivatives are one of the three main categories of financial instruments, the other two being stocks i.

Derivatives are contracts between two parties that specify conditions especially the dates, resulting values and definitions of the underlying variables, the parties' contractual obligations, and the notional amount under which payments are to be made between the parties. The components of a firm's capital structure, e. From the economic point of view, financial derivatives are cash flows, that are conditioned stochastically and discounted to present value. The market risk inherent in the underlying asset is attached to the financial derivative through contractual agreements and hence can be traded separately.

Derivatives therefore allow the breakup of ownership and participation in the market value of an asset. This also provides a considerable amount of freedom regarding the contract design. That contractual freedom allows to modify the participation in the performance of the underlying asset almost arbitrarily. Thus, the participation in the market value of the underlying can be effectively weaker, stronger leverage effect , or implemented as inverse.

Hence, specifically the market price risk of the underlying asset can be controlled in almost every situation. There are two groups of derivative contracts: Derivatives are more common in the modern era, but their origins trace back several centuries. One of the oldest derivatives is rice futures, which have been traded on the Dojima Rice Exchange since the eighteenth century.

Derivatives may broadly be categorized as "lock" or "option" products. Lock products such as swaps , futures , or forwards obligate the contractual parties to the terms over the life of the contract. Option products such as interest rate swaps provide the buyer the right, but not the obligation to enter the contract under the terms specified. Derivatives can be used either for risk management i.

This distinction is important because the former is a prudent aspect of operations and financial management for many firms across many industries; the latter offers managers and investors a risky opportunity to increase profit, which may not be properly disclosed to stakeholders.

Along with many other financial products and services, derivatives reform is an element of the Dodd—Frank Wall Street Reform and Consumer Protection Act of The Act delegated many rule-making details of regulatory oversight to the Commodity Futures Trading Commission CFTC and those details are not finalized nor fully implemented as of late Still, even these scaled down figures represent huge amounts of money.

And for one type of derivative at least, Credit Default Swaps CDS , for which the inherent risk is considered high [ by whom? It was this type of derivative that investment magnate Warren Buffett referred to in his famous speech in which he warned against "financial weapons of mass destruction".

Lock products are theoretically valued at zero at the time of execution and thus do not typically require an up-front exchange between the parties. Based upon movements in the underlying asset over time, however, the value of the contract will fluctuate, and the derivative may be either an asset i. Importantly, either party is therefore exposed to the credit quality of its counterparty and is interested in protecting itself in an event of default.

Option products have immediate value at the outset because they provide specified protection intrinsic value over a given time period time value. One common form of option product familiar to many consumers is insurance for homes and automobiles. The insured would pay more for a policy with greater liability protections intrinsic value and one that extends for a year rather than six months time value.

Because of the immediate option value, the option purchaser typically pays an up front premium. Just like for lock products, movements in the underlying asset will cause the option's intrinsic value to change over time while its time value deteriorates steadily until the contract expires. An important difference between a lock product is that, after the initial exchange, the option purchaser has no further liability to its counterparty; upon maturity, the purchaser will execute the option if it has positive value i.

Derivatives allow risk related to the price of the underlying asset to be transferred from one party to another. For example, a wheat farmer and a miller could sign a futures contract to exchange a specified amount of cash for a specified amount of wheat in the future.

Both parties have reduced a future risk: However, there is still the risk that no wheat will be available because of events unspecified by the contract, such as the weather, or that one party will renege on the contract.

Although a third party, called a clearing house , insures a futures contract, not all derivatives are insured against counter-party risk. From another perspective, the farmer and the miller both reduce a risk and acquire a risk when they sign the futures contract: The miller, on the other hand, acquires the risk that the price of wheat will fall below the price specified in the contract thereby paying more in the future than he otherwise would have and reduces the risk that the price of wheat will rise above the price specified in the contract.

In this sense, one party is the insurer risk taker for one type of risk, and the counter-party is the insurer risk taker for another type of risk. Hedging also occurs when an individual or institution buys an asset such as a commodity, a bond that has coupon payments , a stock that pays dividends, and so on and sells it using a futures contract. The individual or institution has access to the asset for a specified amount of time, and can then sell it in the future at a specified price according to the futures contract.

Of course, this allows the individual or institution the benefit of holding the asset, while reducing the risk that the future selling price will deviate unexpectedly from the market's current assessment of the future value of the asset. Derivatives trading of this kind may serve the financial interests of certain particular businesses. The corporation is concerned that the rate of interest may be much higher in six months.

The corporation could buy a forward rate agreement FRA , which is a contract to pay a fixed rate of interest six months after purchases on a notional amount of money. If the rate is lower, the corporation will pay the difference to the seller. The purchase of the FRA serves to reduce the uncertainty concerning the rate increase and stabilize earnings.

Derivatives can be used to acquire risk, rather than to hedge against risk. Thus, some individuals and institutions will enter into a derivative contract to speculate on the value of the underlying asset, betting that the party seeking insurance will be wrong about the future value of the underlying asset. Speculators look to buy an asset in the future at a low price according to a derivative contract when the future market price is high, or to sell an asset in the future at a high price according to a derivative contract when the future market price is less.

Individuals and institutions may also look for arbitrage opportunities, as when the current buying price of an asset falls below the price specified in a futures contract to sell the asset. Speculative trading in derivatives gained a great deal of notoriety in when Nick Leeson , a trader at Barings Bank , made poor and unauthorized investments in futures contracts. The true proportion of derivatives contracts used for hedging purposes is unknown, [25] but it appears to be relatively small.

In broad terms, there are two groups of derivative contracts, which are distinguished by the way they are traded in the market:. According to the Bank for International Settlements , who first surveyed OTC derivatives in , [29] reported that the " gross market value , which represent the cost of replacing all open contracts at the prevailing market prices, Because OTC derivatives are not traded on an exchange, there is no central counter-party. Therefore, they are subject to counterparty risk , like an ordinary contract , since each counter-party relies on the other to perform.

An "asset-backed security" is used as an umbrella term for a type of security backed by a pool of assets—including collateralized debt obligations and mortgage-backed securities Example: An empirical analysis" PDF. Retrieved July 13, Asset-backed securities, called ABS, are bonds or notes backed by financial assets. Typically these assets consist of receivables other than mortgage loans, such as credit card receivables, auto loans, manufactured-housing contracts and home-equity loans.

The CDO is "sliced" into "tranches" , which "catch" the cash flow of interest and principal payments in sequence based on seniority. The last to lose payment from default are the safest, most senior tranches.

As an example, a CDO might issue the following tranches in order of safeness: Separate special-purpose entities —rather than the parent investment bank —issue the CDOs and pay interest to investors. CDO collateral became dominated not by loans, but by lower level BBB or A tranches recycled from other asset-backed securities, whose assets were usually non-prime mortgages.

A credit default swap CDS is a financial swap agreement that the seller of the CDS will compensate the buyer the creditor of the reference loan in the event of a loan default by the debtor or other credit event.

The buyer of the CDS makes a series of payments the CDS "fee" or "spread" to the seller and, in exchange, receives a payoff if the loan defaults. In the event of default the buyer of the CDS receives compensation usually the face value of the loan , and the seller of the CDS takes possession of the defaulted loan.

If there are more CDS contracts outstanding than bonds in existence, a protocol exists to hold a credit event auction ; the payment received is usually substantially less than the face value of the loan. CDSs are not traded on an exchange and there is no required reporting of transactions to a government agency. In addition to corporations and governments, the reference entity can include a special-purpose vehicle issuing asset-backed securities.

In finance, a forward contract or simply a forward is a non-standardized contract between two parties to buy or to sell an asset at a specified future time at a price agreed upon today, making it a type of derivative instrument. The party agreeing to buy the underlying asset in the future assumes a long position , and the party agreeing to sell the asset in the future assumes a short position.

The price agreed upon is called the delivery price , which is equal to the forward price at the time the contract is entered into. The price of the underlying instrument, in whatever form, is paid before control of the instrument changes. The forward price of such a contract is commonly contrasted with the spot price , which is the price at which the asset changes hands on the spot date. The difference between the spot and the forward price is the forward premium or forward discount, generally considered in the form of a profit , or loss, by the purchasing party.

Forwards, like other derivative securities, can be used to hedge risk typically currency or exchange rate risk , as a means of speculation , or to allow a party to take advantage of a quality of the underlying instrument which is time-sensitive. A closely related contract is a futures contract ; they differ in certain respects. Forward contracts are very similar to futures contracts, except they are not exchange-traded, or defined on standardized assets.

However, being traded over the counter OTC , forward contracts specification can be customized and may include mark-to-market and daily margin calls. Hence, a forward contract arrangement might call for the loss party to pledge collateral or additional collateral to better secure the party at gain.

In finance , a 'futures contract' more colloquially, futures is a standardized contract between two parties to buy or sell a specified asset of standardized quantity and quality for a price agreed upon today the futures price with delivery and payment occurring at a specified future date, the delivery date , making it a derivative product i.

The contracts are negotiated at a futures exchange , which acts as an intermediary between buyer and seller. The party agreeing to buy the underlying asset in the future, the "buyer" of the contract, is said to be " long ", and the party agreeing to sell the asset in the future, the "seller" of the contract, is said to be " short ".

While the futures contract specifies a trade taking place in the future, the purpose of the futures exchange is to act as intermediary and mitigate the risk of default by either party in the intervening period. For this reason, the futures exchange requires both parties to put up an initial amount of cash performance bond , the margin.

Margins, sometimes set as a percentage of the value of the futures contract, need to be proportionally maintained at all times during the life of the contract to underpin this mitigation because the price of the contract will vary in keeping with supply and demand and will change daily and thus one party or the other will theoretically be making or losing money. To mitigate risk and the possibility of default by either party, the product is marked to market on a daily basis whereby the difference between the prior agreed-upon price and the actual daily futures price is settled on a daily basis.

This is sometimes known as the variation margin where the futures exchange will draw money out of the losing party's margin account and put it into the other party's thus ensuring that the correct daily loss or profit is reflected in the respective account. If the margin account goes below a certain value set by the Exchange, then a margin call is made and the account owner must replenish the margin account.

This process is known as "marking to market". Thus on the delivery date, the amount exchanged is not the specified price on the contract but the spot value i.