# Futures et options : principes fondamentaux

The actual market price of the option may vary depending on a number of factors, such as a significant option holder may need to sell the option as the expiry date is approaching and does not have the financial resources to exercise the option, or a buyer in the market is trying to amass a large option holding.

## What are 'Options On Futures'

Also referred to as performance bond margin. Initial margin is the equity required to initiate a futures position.

This is a type of performance bond. The maximum exposure is not limited to the amount of the initial margin, however the initial margin requirement is calculated based on the maximum estimated change in contract value within a trading day. Initial margin is set by the exchange. If a position involves an exchange-traded product, the amount or percentage of initial margin is set by the exchange concerned. In case of loss or if the value of the initial margin is being eroded, the broker will make a margin call in order to restore the amount of initial margin available.

Calls for margin are usually expected to be paid and received on the same day. If not, the broker has the right to close sufficient positions to meet the amount called by way of margin.

The Initial Margin requirement is established by the Futures exchange, in contrast to other securities' Initial Margin which is set by the Federal Reserve in the U. A futures account is marked to market daily. If the margin drops below the margin maintenance requirement established by the exchange listing the futures, a margin call will be issued to bring the account back up to the required level. Maintenance margin A set minimum margin per outstanding futures contract that a customer must maintain in their margin account.

Margin-equity ratio is a term used by speculators , representing the amount of their trading capital that is being held as margin at any particular time.

The low margin requirements of futures results in substantial leverage of the investment. However, the exchanges require a minimum amount that varies depending on the contract and the trader. The broker may set the requirement higher, but may not set it lower. A trader, of course, can set it above that, if he does not want to be subject to margin calls. Performance bond margin The amount of money deposited by both a buyer and seller of a futures contract or an options seller to ensure performance of the term of the contract.

Margin in commodities is not a payment of equity or down payment on the commodity itself, but rather it is a security deposit. Settlement is the act of consummating the contract, and can be done in one of two ways, as specified per type of futures contract:. Expiry or Expiration in the U. For many equity index and Interest rate future contracts as well as for most equity options , this happens on the third Friday of certain trading months.

This is an exciting time for arbitrage desks, which try to make quick profits during the short period perhaps 30 minutes during which the underlying cash price and the futures price sometimes struggle to converge. At this moment the futures and the underlying assets are extremely liquid and any disparity between an index and an underlying asset is quickly traded by arbitrageurs. At this moment also, the increase in volume is caused by traders rolling over positions to the next contract or, in the case of equity index futures, purchasing underlying components of those indexes to hedge against current index positions.

On the expiry date, a European equity arbitrage trading desk in London or Frankfurt will see positions expire in as many as eight major markets almost every half an hour. When the deliverable asset exists in plentiful supply, or may be freely created, then the price of a futures contract is determined via arbitrage arguments. This is typical for stock index futures , treasury bond futures , and futures on physical commodities when they are in supply e. However, when the deliverable commodity is not in plentiful supply or when it does not yet exist — for example on crops before the harvest or on Eurodollar Futures or Federal funds rate futures in which the supposed underlying instrument is to be created upon the delivery date — the futures price cannot be fixed by arbitrage.

In this scenario there is only one force setting the price, which is simple supply and demand for the asset in the future, as expressed by supply and demand for the futures contract. Arbitrage arguments " rational pricing " apply when the deliverable asset exists in plentiful supply, or may be freely created. Here, the forward price represents the expected future value of the underlying discounted at the risk free rate —as any deviation from the theoretical price will afford investors a riskless profit opportunity and should be arbitraged away.

We define the forward price to be the strike K such that the contract has 0 value at the present time. Assuming interest rates are constant the forward price of the futures is equal to the forward price of the forward contract with the same strike and maturity. It is also the same if the underlying asset is uncorrelated with interest rates. Otherwise the difference between the forward price on the futures futures price and forward price on the asset, is proportional to the covariance between the underlying asset price and interest rates.

For example, a futures on a zero coupon bond will have a futures price lower than the forward price. This is called the futures "convexity correction. This relationship may be modified for storage costs, dividends, dividend yields, and convenience yields.

In a perfect market the relationship between futures and spot prices depends only on the above variables; in practice there are various market imperfections transaction costs, differential borrowing and lending rates, restrictions on short selling that prevent complete arbitrage. Thus, the futures price in fact varies within arbitrage boundaries around the theoretical price. When the deliverable commodity is not in plentiful supply or when it does not yet exist rational pricing cannot be applied, as the arbitrage mechanism is not applicable.

Here the price of the futures is determined by today's supply and demand for the underlying asset in the future. In a deep and liquid market, supply and demand would be expected to balance out at a price which represents an unbiased expectation of the future price of the actual asset and so be given by the simple relationship.

By contrast, in a shallow and illiquid market, or in a market in which large quantities of the deliverable asset have been deliberately withheld from market participants an illegal action known as cornering the market , the market clearing price for the futures may still represent the balance between supply and demand but the relationship between this price and the expected future price of the asset can break down.

The expectation based relationship will also hold in a no-arbitrage setting when we take expectations with respect to the risk-neutral probability. With this pricing rule, a speculator is expected to break even when the futures market fairly prices the deliverable commodity. The situation where the price of a commodity for future delivery is higher than the spot price , or where a far future delivery price is higher than a nearer future delivery, is known as contango.

The reverse, where the price of a commodity for future delivery is lower than the spot price, or where a far future delivery price is lower than a nearer future delivery, is known as backwardation. There are many different kinds of futures contracts, reflecting the many different kinds of "tradable" assets about which the contract may be based such as commodities, securities such as single-stock futures , currencies or intangibles such as interest rates and indexes. For information on futures markets in specific underlying commodity markets , follow the links.

For a list of tradable commodities futures contracts, see List of traded commodities. See also the futures exchange article. Trading on commodities began in Japan in the 18th century with the trading of rice and silk, and similarly in Holland with tulip bulbs. Trading in the US began in the mid 19th century, when central grain markets were established and a marketplace was created for farmers to bring their commodities and sell them either for immediate delivery also called spot or cash market or for forward delivery.

These forward contracts were private contracts between buyers and sellers and became the forerunner to today's exchange-traded futures contracts. Although contract trading began with traditional commodities such as grains, meat and livestock, exchange trading has expanded to include metals, energy, currency and currency indexes, equities and equity indexes, government interest rates and private interest rates.

Contracts on financial instruments were introduced in the s by the Chicago Mercantile Exchange CME and these instruments became hugely successful and quickly overtook commodities futures in terms of trading volume and global accessibility to the markets. This innovation led to the introduction of many new futures exchanges worldwide, such as the London International Financial Futures Exchange in now Euronext.

Today, there are more than 90 futures and futures options exchanges worldwide trading to include:. Most futures contracts codes are five characters. The first two characters identify the contract type, the third character identifies the month and the last two characters identify the year.

Futures traders are traditionally placed in one of two groups: In other words, the investor is seeking exposure to the asset in a long futures or the opposite effect via a short futures contract. Bei unbedingten Termingeschäften findet jedoch in der Regel kein sogenannter Realtausch , sondern ein Barausgleich statt.

Das bedeutet, dass der Basiswert nicht ge- bzw. Der börsliche Handel erfolgt über die weltweiten Terminbörsen, zu denen Broker direkten Zugang gewähren. Sie unterliegen keiner Regulierung und behördlicher Aufsicht wie Börsengeschäfte. Prinzipiell handelt es sich bei Termingeschäften um Geschäfte mit aufgeschobener Lieferzeit. Gegenstand können nicht nur Wertpapiere wie Indizes oder Aktien, sondern auch Waren sein, z.

Nahrungsmittel wie Getreide oder Reis. Auch klassische Optionen stehen zur Verfügung. Die Differenz zwischen diesen beiden Terminkontrakten ist der Gewinn oder Verlust. Ein Future-Kontrakt enthält dabei die folgenden Merkmale:. Unterschieden wird bezüglich des Basiswertes zwischen Futures auf Wertpapiere wie z. Indizes financial futures oder Rohstoffe commodity futures , wie z. Stattdessen wird von beiden Kontrahenten Käufer und Verkäufer eine Zahlung geleistet, die praktisch als Vorschuss zu sehen ist und eine Sicherheitsleistung darstellt, die Initial Margin.

Die Margin beträgt einen prozentualen Bruchteil des Kontraktes, z. Futures werden mit hohen Hebeln gehandelt. Das tatsächlich gehandelte Volumen ist damit um ein Vielfaches höher als im Handel 1: Hier handelt es sich nicht um ein Termingeschäft mit bestimmter Laufzeit , sondern um eine Zahlungsvereinbarung über einen Wert aus der Differenz des Basiswert-Kurses zum Zeitpunkt des Kaufs und des Verkaufs.

Die Zahlungsvereinbarung bezieht sich also nicht auf einen festgelegten Zeitpunkt in der Zukunft wie bei Futures oder Optionen. Gegenstand der Vereinbarung mit dem Broker ist somit lediglich, dass eine Zahlung der Differenz zwischen dem aktuellen Basiswert-Kurs und dem künftigen Kurs erfolgt. Entwickelt sich der Kurs allerdings für den Trader in der entgegengesetzten Richtung , führt dies für ihn zu einem Verlust.

CFDs können auf zahlreiche Basiswerte wie z. Daraus ergibt sich der Hebeleffekt. This strategy acts as an insurance when investing on the underlying stock, hedging the investor's potential loses, but also shrinking an otherwise larger profit, if just purchasing the stock without the put.

The maximum profit of a protective put is theoretically unlimited as the strategy involves being long on the underlying stock. The maximum loss is limited to the purchase price of the underlying stock less the strike price of the put option and the premium paid.

A protective put is also known as a married put. Another important class of options, particularly in the U. Other types of options exist in many financial contracts, for example real estate options are often used to assemble large parcels of land, and prepayment options are usually included in mortgage loans.

However, many of the valuation and risk management principles apply across all financial options. There are two more types of options; covered and naked. Options valuation is a topic of ongoing research in academic and practical finance. In basic terms, the value of an option is commonly decomposed into two parts:. Although options valuation has been studied at least since the nineteenth century, the contemporary approach is based on the Black—Scholes model which was first published in The value of an option can be estimated using a variety of quantitative techniques based on the concept of risk neutral pricing and using stochastic calculus.

The most basic model is the Black—Scholes model. More sophisticated models are used to model the volatility smile. These models are implemented using a variety of numerical techniques. More advanced models can require additional factors, such as an estimate of how volatility changes over time and for various underlying price levels, or the dynamics of stochastic interest rates.

The following are some of the principal valuation techniques used in practice to evaluate option contracts. Following early work by Louis Bachelier and later work by Robert C. Merton , Fischer Black and Myron Scholes made a major breakthrough by deriving a differential equation that must be satisfied by the price of any derivative dependent on a non-dividend-paying stock.

By employing the technique of constructing a risk neutral portfolio that replicates the returns of holding an option, Black and Scholes produced a closed-form solution for a European option's theoretical price. While the ideas behind the Black—Scholes model were ground-breaking and eventually led to Scholes and Merton receiving the Swedish Central Bank 's associated Prize for Achievement in Economics a.

Nevertheless, the Black—Scholes model is still one of the most important methods and foundations for the existing financial market in which the result is within the reasonable range. Since the market crash of , it has been observed that market implied volatility for options of lower strike prices are typically higher than for higher strike prices, suggesting that volatility is stochastic, varying both for time and for the price level of the underlying security.

Stochastic volatility models have been developed including one developed by S. Once a valuation model has been chosen, there are a number of different techniques used to take the mathematical models to implement the models. In some cases, one can take the mathematical model and using analytical methods develop closed form solutions such as Black—Scholes and the Black model.

The resulting solutions are readily computable, as are their "Greeks". Although the Roll-Geske-Whaley model applies to an American call with one dividend, for other cases of American options , closed form solutions are not available; approximations here include Barone-Adesi and Whaley , Bjerksund and Stensland and others. Closely following the derivation of Black and Scholes, John Cox , Stephen Ross and Mark Rubinstein developed the original version of the binomial options pricing model.

The model starts with a binomial tree of discrete future possible underlying stock prices. By constructing a riskless portfolio of an option and stock as in the Black—Scholes model a simple formula can be used to find the option price at each node in the tree. This value can approximate the theoretical value produced by Black Scholes, to the desired degree of precision.

However, the binomial model is considered more accurate than Black—Scholes because it is more flexible; e. Binomial models are widely used by professional option traders.

The Trinomial tree is a similar model, allowing for an up, down or stable path; although considered more accurate, particularly when fewer time-steps are modelled, it is less commonly used as its implementation is more complex.

For a more general discussion, as well as for application to commodities, interest rates and hybrid instruments, see Lattice model finance. For many classes of options, traditional valuation techniques are intractable because of the complexity of the instrument. In these cases, a Monte Carlo approach may often be useful.

Rather than attempt to solve the differential equations of motion that describe the option's value in relation to the underlying security's price, a Monte Carlo model uses simulation to generate random price paths of the underlying asset, each of which results in a payoff for the option.

The average of these payoffs can be discounted to yield an expectation value for the option. The equations used to model the option are often expressed as partial differential equations see for example Black—Scholes equation. Once expressed in this form, a finite difference model can be derived, and the valuation obtained.

A number of implementations of finite difference methods exist for option valuation, including: A trinomial tree option pricing model can be shown to be a simplified application of the explicit finite difference method.

Other numerical implementations which have been used to value options include finite element methods. Additionally, various short rate models have been developed for the valuation of interest rate derivatives , bond options and swaptions. These, similarly, allow for closed-form, lattice-based, and simulation-based modelling, with corresponding advantages and considerations.

As with all securities, trading options entails the risk of the option's value changing over time. However, unlike traditional securities, the return from holding an option varies non-linearly with the value of the underlying and other factors. Therefore, the risks associated with holding options are more complicated to understand and predict. This technique can be used effectively to understand and manage the risks associated with standard options. We can calculate the estimated value of the call option by applying the hedge parameters to the new model inputs as:.

A special situation called pin risk can arise when the underlying closes at or very close to the option's strike value on the last day the option is traded prior to expiration. The option writer seller may not know with certainty whether or not the option will actually be exercised or be allowed to expire. Therefore, the option writer may end up with a large, unwanted residual position in the underlying when the markets open on the next trading day after expiration, regardless of his or her best efforts to avoid such a residual.

A further, often ignored, risk in derivatives such as options is counterparty risk. In an option contract this risk is that the seller won't sell or buy the underlying asset as agreed.