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A **call option**, often simply labeled a "call", is a contract, between the buyer and the seller of the call option, to exchange a security at a set price.^{ [1] } The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of a particular commodity or financial instrument (the underlying) from the seller of the option at a certain time (the expiration date) for a certain price (the strike price). The seller (or "writer") is obligated to sell the commodity or financial instrument to the buyer if the buyer so decides. The buyer pays a fee (called a premium) for this right. The term "call" comes from the fact that the owner has the right to "call the stock away" from the seller.

Option values vary with the value of the underlying instrument over time. The price of the call contract must act as a proxy response for the valuation of (1) the estimated time value — thought of as the likelihood of the call finishing in-the-money and (2) the intrinsic value of the option, defined as the difference between the strike price and the market value multiplied by 100. The call contract price generally will be higher when the contract has more time to expire (except in cases when a significant dividend is present) and when the underlying financial instrument shows more volatility. Determining this value is one of the central functions of financial mathematics. The most common method used is the Black–Scholes formula. Importantly, the Black-Scholes formula provides an estimate of the price of European-style options.^{ [2] }

Whatever the formula used, the buyer and seller must agree on the initial value (the premium or price of the call contract), otherwise the exchange (buy/sell) of the call will not take place.

Adjustment to Call Option: When a call has the strike price above the break even limit, i.e. when the buyer is making profit, there are many avenues to explore. Some of them are as follows:

- Sell the call and book profit.
- Continue to hold the position, if there is hope of making more money.
- Buy a protective "put" of the strike that suits, If there is interest in holding the position but at the same time, having some protection.
- Sell a call of higher strike price and convert the position into "call spread" and thus limiting loss if the market reverses.

Similarly, if the buyer is making loss on his position i.e. the call is out-of-the-money, the buyer can make several adjustments to limit his loss or even make some profit.

Trading options involves a constant monitoring of the option value, which is affected by the following factors:

- Changes in the
**base asset price**(the higher the price, the more expensive the call option is) - Changes in the
**volatility**of the base asset (the higher the volatility, the more expensive the call option is) **Time decay**– as time goes by, options become cheaper and cheaper.

Moreover, the dependence of the option value to price, volatility and time is **not linear** – which makes the analysis even more complex.

One very useful way to analyze and track the value of an option position is by drawing a **Profit / Loss chart** that shows how the option value changes with changes in the base asset price and other factors. For example, this Profit / Loss chart shows the profit / loss of a call option position (with $100 strike and maturity of 30 days) purchased at a price of $3,5 (blue graph – the day of the purchase of the option; orange graph – at expiry):

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". Derivatives can be used for a number of purposes, including insuring against price movements (hedging), increasing exposure to price movements for speculation or getting access to otherwise hard-to-trade assets or markets. Some of the more common derivatives include forwards, futures, options, swaps, and variations of these such as synthetic collateralized debt obligations and credit default swaps. Most derivatives are traded over-the-counter (off-exchange) or on an exchange such as the Chicago Mercantile Exchange, while most insurance contracts have developed into a separate industry. In the United States, after the financial crisis of 2007–2009, 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 and debt. The oldest example of a derivative in history, attested to by Aristotle, is thought to be a contract transaction of olives, entered into by ancient Greek philosopher Thales, who made a profit in the exchange. Bucket shops, outlawed in 1936, are a more recent historical example.

The **Black–Scholes** or **Black–Scholes–Merton model** is a mathematical model for the dynamics of a financial market containing derivative investment instruments. From the partial differential equation in the model, known as the Black–Scholes equation, one can deduce the **Black–Scholes formula**, which gives a theoretical estimate of the price of European-style options and shows that the option has a *unique* price regardless of the risk of the security and its expected return. The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the Chicago Board Options Exchange and other options markets around the world. It is widely used, although often with some adjustments, by options market participants.

In finance, a **put** or **put option** is a stock market instrument which gives the holder the right to sell an asset, at a specified price, by a specified date to a given party. The purchase of a put option is interpreted as a negative sentiment about the future value of the underlying stock. The term "put" comes from the fact that the owner has the right to "put up for sale" the stock or index.

In finance, a **warrant** is a security that entitles the holder to buy the underlying stock of the issuing company at a fixed price called **exercise price** until the expiry date.

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.

In finance, a **futures contract** is a standardized legal agreement to buy or sell something at a predetermined price at a specified time in the future, between parties not known to each other. The asset transacted is usually a commodity or financial instrument. The predetermined price the parties agree to buy and sell the asset for is known as the *forward price*. The specified time in the future—which is when delivery and payment occur—is known as the *delivery date*. Because it is a function of an underlying asset, a futures contract is a derivative product.

In mathematical finance, the **Greeks** are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of these sensitivities are denoted by Greek letters. Collectively these have also been called the **risk sensitivities**, **risk measures** or **hedge parameters**.

In financial mathematics, the **implied volatility** (**IV**) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model, will return a theoretical value equal to the current market price of said option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an implied volatility. Implied volatility, a forward-looking and subjective measure, differs from historical volatility because the latter is calculated from known past returns of a security. To understand where implied volatility stands in terms of the underlying, **implied volatility rank** is used to understand its implied volatility from a one-year high and low IV.

In finance, **moneyness** is the relative position of the current price of an underlying asset with respect to the strike price of a derivative, most commonly a call option or a put option. Moneyness is firstly a three-fold classification: if the derivative would have positive intrinsic value if it were to expire today, it is said to be **in the money**; if it would be worth less if expiring at the current price it is said to be **out of the money**, and if the current price and strike price are equal, it is said to be **at the money**. There are two slightly different definitions, according to whether one uses the current price (spot) or future price (forward), specified as "at the money spot" or "at the money forward", etc.

A **hedge** is an investment position intended to offset potential losses or gains that may be incurred by a companion investment. A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, gambles, many types of over-the-counter and derivative products, and futures contracts.

In finance, the **time value** (**TV**) of an option is the premium a rational investor would pay over its *current* exercise value, based on the probability it will increase in value before expiry. For an American option this value is always greater than zero in a fair market, thus an option is *always* worth more than its current exercise value.. As an option can be thought of as 'price insurance', TV can be thought of as the *risk premium* the option seller charges the buyer—the higher the expected risk, the higher the premium. Conversely, TV can be thought of as the price an investor is willing to pay for potential upside.

**Rational pricing** is the assumption in financial economics that asset prices will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.

In finance, a **foreign exchange option** is a derivative financial instrument that gives the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified date. See Foreign exchange derivative.

In finance, a **long** position in a financial instrument means the holder of the position owns a positive amount of the instrument. The holder of the position has the expectation that the financial instrument will increase in value. This is known as a bullish position. It is contrasted with *going short*, also called a bearish position.

In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see Mathematical finance § Derivatives pricing: the Q world for discussion of the mathematics, Financial engineering for the implementation, as well as Financial modeling § Quantitative finance generally.

A **covered call** is a financial market transaction in which the seller of call options owns the corresponding amount of the underlying instrument, such as shares of a stock or other securities. If a trader buys the underlying instrument at the same time the trader sells the call, the strategy is often called a "buy-write" strategy. In equilibrium, the strategy has the same payoffs as writing a put option.

The **iron condor** is an option trading strategy utilizing two vertical spreads – a put spread and a call spread with the same expiration and four different strikes. A long iron condor is essentially selling both sides of the underlying instrument by simultaneously shorting the same number of calls and puts, then covering each position with the purchase of further out of the money call(s) and put(s) respectively. The converse produces a short iron condor.

**Option strategies** are the simultaneous, and often mixed, buying or selling of one or more options that differ in one or more of the options' variables. Call options, simply known as calls, give the buyer a right to buy a particular stock at that option's strike price. Conversely, put options, simply known as puts, give the buyer the right to sell a particular stock at the option's strike price. This is often done to gain exposure to a specific type of opportunity or risk while eliminating other risks as part of a trading strategy. A very straightforward strategy might simply be the buying or selling of a single option; however, option strategies often refer to a combination of simultaneous buying and or selling of options.

The **backspread** is the converse strategy to the ratio spread and is also known as reverse ratio spread. Using calls, a bullish strategy known as the call backspread can be constructed and with puts, a strategy known as the put backspread can be constructed.

In finance, an **option** is a contract which gives the buyer the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price prior to or on a specified date, depending on the form of the option. The strike price may be set by reference to the spot price of the underlying security or commodity on the day an option is taken out, or it may be fixed at a discount or at a premium. The seller has the corresponding obligation to fulfill the transaction – to sell or buy – if the buyer (owner) "exercises" the option. An option that conveys to the owner the right to buy at a specific price is referred to as a call; an option that conveys the right of the owner to sell at a specific price is referred to as a put. Both are commonly traded, but the call option is more frequently discussed.

- ↑ O'Sullivan, Arthur; Sheffrin, Steven M. (2003).
*Economics: Principles in Action*. Upper Saddle River, New Jersey 07458: Pearson Prentice Hall. p. 288. ISBN 0-13-063085-3.CS1 maint: location (link) - ↑ Fernandes, Nuno (2014).
*Finance for Executives: A Practical Guide for Managers*. NPV Publishing. p. 313. ISBN 978-9899885400.

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