In the simplest terms, there are four positions an investor can take in options:

- Buy call options (long)
- Sell/write call options (short)
- Buy put options (long)
- Sell/write put options (short)

First, we’ll consider call options. An investor that buys call options benefits from this position when the price of the underlying asset is higher than the strike price of the option at expiry. This allows the investor to buy the underlying asset at a price that is lower than the market price. Since the market price of the underlying asset could theoretically be infinitely high, the profit potential of this strategy is also unlimited.

Conversely, if at expiry the price of the underlying asset is lower than the strike price, the option expires with no intrinsic value and the investor’s loss is limited to the option premium paid when entering into the contract. The seller/writer of the call option has the opposite pay-off potential and receives a fixed option premium when they sell the contract. However, they may also have a theoretically unlimited loss.

- Long call option: an investor buys a call option on a share at a premium of €1, a strike price of €50, and the multiplier is 100. If at expiry the share price is below €50, the option will expire with no intrinsic value and the investor’s loss will be equal to the €100 premium paid to enter into the position. However, if the share price is higher than the strike price, then the option position starts earning a profit when the premium paid when entering into the position is offset, i.e. when it passes the break-even point, which is at €50 + €1 = €51.
- Short call option: on the other side of the trade is the investor who sold the call option. If at expiry the share price is below €50, the writer will earn a profit equal to the €100 premium received from the long buyer. However, if the price increases above the strike price, then the writer of the call option will incur a loss when the share price crosses €51.

Schematically, the pay-off of a long and short call position looks like this:

]]>In the simplest terms, there are four positions an investor can take in options:

- Buy call options (long)
- Sell/write call options (short)
- Buy put options (long)
- Sell/write put options (short)

Here, we’ll consider put options. An investor that buys put options benefits from this position when the price of the underlying asset is lower than the strike price of the option at expiry. The profit potential is generally capped, as most assets cannot have a value of less than 0 (though this is not always true). Conversely, if at expiry the price of the underlying asset is higher than the strike price, the option expires with no intrinsic value and the investor’s loss is equal to the option premium paid. The pay-off potential of the short put option position is the opposite of the buyer of the put option.

- Long put option: an investor buys a put option on a share at a premium of €1.50, a strike price of €40 and the multiplier is 100. If at expiry the share price is above €40, then the option will expire with no intrinsic value and the investor’s loss will be equal to the €150 premium paid. However, if the price is below €40, then the option position earns a profit when the price moves beyond the break-even point at €40 – €1.50 = €38.50.
- Short put option: on the other side of the trade is the investor that has written the put option. If at expiry the share price is above €40, then the writer will earn a profit equal to the €150 premium received from the option buyer. However, if the price drops below the strike price, the writer of the call option will incur a loss when the share price crosses €38.50.

Schematically, the pay-off of a long and short put position looks like this:

]]>Besides buying or selling single options, there are many other possible strategies that involve positions in multiple options simultaneously, as well as combining options with positions in the underlying assets. While there are infinite combinations possible, we start with two common combinations below.

A protective put is a strategy that can be used to insure a stock portfolio against losses. The investor combines a long position in the underlying asset with a long put option. The long put option position caps any potential loss caused by a drop in the share price, as the investor will be able to exercise the put option at the strike price and lock in the sell price, only losing the premium paid.

A covered call is constructed by combining a long position in the underlying asset with writing a call option against the same asset. By selling the call option, the investor receives an option premium. This guaranteed income offers a small downside protection; if a decline in the underlying price is lower than or equal to the amount of option premium received, the total position does not return a loss. In return, the investor caps the profit potential by agreeing to sell the shares at the strike price. As such, this strategy works well if the investor expects little change in the price of the underlying asset or has determined an exit level for their investment at which they are happy to sell.

]]>Besides buying or selling single options, there are many other possible strategies that involve positions in multiple options simultaneously, as well as combining options with positions in the underlying assets. While there are infinite combinations possible, we outline one common combination below.

A protective collar strategy is a combination of a protective put and a covered call strategy. The long put option protects the investor from a downward move in the underlying asset’s price, while writing a call option generates a premium that offsets (some) of the cost of buying the long put (though it also limits the upside potential). This combination can be used to lock in unrealized gains in the underlying asset without having to sell the shares right away. If the underlying asset’s price declines, the position is insured against losses via the long put option. Conversely, if the price of the underlying asset increases beyond the strike price of the call options, it will be exercised, with the investor selling the shares and realizing any gains.

]]>Besides buying or selling single options, there are many other possible strategies that involve positions in multiple options simultaneously, as well as combining options with positions in the underlying assets. While there are infinite combinations possible, we outline one common combination below.

A long straddle involves buying a call and put option on the same underlying asset with the same strike price and expiration date. This strategy can be used by an investor that believes the price of the underlying asset will move significantly, but is unsure about the direction of the move. The maximum loss of the strategy is limited to the sum of the premiums paid for the call and the put options. The further away from the strike price that the price of the underlying asset moves, the higher the pay-off of the straddle.

]]>Besides buying or selling single options, there are many other possible strategies that involve positions in multiple options simultaneously, as well as combining options with positions in the underlying assets. While there are infinite combinations possible, we outline one common combination below.

A call spread (put spread) is a combination that involves buying and selling call (put) options with different strike prices, called a vertical spread, or different expiration dates, called a horizontal or calendar spread. Compared to buying single call or put options, these strategies have more limited profit potential, but they are also cheaper to enter into because of the option premium received from writing options. Based on the direction the investor thinks the price of the underlying asset will move, spreads can be constructed as bullish to benefit from price increases in the underlying assets or as bearish to benefit from price decreases or no move.

**Examples**

A bull spread with calls involves a combination of a long and short call option with the same expiry, where the strike price of the short call is higher than that of the long call. A bull spread with puts involves a long and short put option, where the strike price of the short put is higher than that of the long put. This strategy works well when an investor is bullish on the market direction and also has an exit level where they are happy to sell.

A bear spread with calls involves a combination of a long and short call option, where the strike price of the long call option is higher than that of the short call option. A bear spread with puts involves a long and short put option, where the strike price of the long put is higher than that of the short put. This strategy works well when an investor is bearish on the market direction.

]]>There are two types of volatility:

- Historical volatility, also called realized volatility, is the backward-looking measure of volatility. It measures the level of price fluctuations in the past by looking at the historical price movement.
- Implied volatility is the forward-looking measure of volatility. In the case of options, the implied volatility is ‘implied’ from their price and reflects the market’s expectation of the volatility of the option’s underlying asset from now until the expiration of the option.

Implied volatility is one of the inputs used in option pricing models, e.g. the Black-Scholes model, along with the price of the underlying asset, the option’s strike price, its expiration date, the interest rate and dividends. Most of these inputs can be readily observed in the market, but the implied volatility can’t. Using the market price of the option, it is possible to reverse engineer an option pricing model to find out what level of implied volatility is priced in. The other exception is the dividend, which in normal conditions can be determined ahead of time with relative certainty. Unexpected deviations can, however, have a large impact on option prices.

Market makers use their assessment of implied volatility to determine the value of option contracts and the bid and offer prices they will show in the market. An option’s implied volatility is dynamic and fluctuates according to changes in the market’s expectation of future price movements in the price of the underlying asset. News events such as earnings announcements could lead to changes in those expectations and result in more or less demand for the option, driving its price up or down regardless of the price movement of the underlying asset.

All else being equal, when implied volatility increases, the value of the option will increase and vice versa. This is because a higher than expected volatility increases the likelihood of the price of the underlying asset further deviating from the strike price, a movement that is positive for the holder of the option. The amount by which the price of put and call options will change in response to a one-point change in implied volatility is expressed by vega, one of the Greek options.

If the shares of Airbus Group are trading at €100 and the implied volatility of an option contract on this share is 15%, then a one standard deviation move over the next 12 months will be plus or minus €100 * 15% = €15.

In theory, it is assumed that the share price follows a normal distribution. This implies that, after one year, the share could end up within one standard deviation of its original price 68% of the time, with a 32% chance the share price will be outside this range.

As such, the implied volatility of 15% means the market’s current expectation is that there is a 68% chance the share price will end up between €85-115 in a year from now.

If the implied volatility were to rise to 20%, there would be a 68% chance the share price would end up between €80-120 and 32% chance it would be outside this range. As the likelihood of the share price deviating further from the strike prices increases, the option contract typically increases in value. If the option’s vega is 0.5, the implied volatility increases from 15% to 20% would result in the option’s price rising by 5 * 0.5 = €2.50.

]]>An option is a derivative contract that derives its value from the underlying asset and gives the holder the right – but not obligation – to buy or sell the underlying asset at the pre-determined strike price at or before the contract expires. The relationship between the (forward) price of the underlying asset and the strike price determines the intrinsic value or ‘moneyness’ of the option. At a given point in time during the contract or when it expires, there are three possible scenarios:

- The option is in the money (ITM). A call option is ITM when the strike price is lower than the underlying asset’s current or forward price. In this case, the call option gives the holder the right to buy the underlying asset at a price lower than the current price, giving value to the option. A put option is ITM when the strike price is above the underlying asset’s current or forward price. An ITM put option gives the holder the right to sell the underlying asset at a price higher than the current price.

- The option is at the money (ATM). The underlying asset’s current or forward price and the strike price are the same.

- The option is out of the money (OTM). A call option is OTM when the underlying asset’s current or forward price is lower than the strike price. A put option is OTM when the underlying asset’s price is higher than the strike price. If an option is OTM at expiration, it expires with no intrinsic value. OTM options do have value prior to their expiry date, as explained below.

The price that the buyer of the option has to pay for the right granted by the option, i.e. the option premium, is the value market participants place on the option. This reflects the likelihood that the option will expire ITM. Also, the higher the likelihood, the higher the premium.

The option premium (P) consists of two components: the intrinsic value (I) and the time (extrinsic) value (X) or P = I + X. The intrinsic value is the option holder’s pay-off, if they were to exercise the option right now. The intrinsic value is calculated as the difference between the current or forward price of the underlying asset and the strike price of the option, as explained above. An ITM call option with a strike price of $20 on an underlying asset priced at $30 has an intrinsic value of $10. In contrast, ATM or OTM options have no intrinsic value.

The time value represents the additional amount investors are willing to pay for the likelihood that the option will increase in value between now and the expiration date. The longer the time to expiration, the more time there is for the option to increase in value. Also, the higher the volatility of the underlying asset, the more potential there is for large price fluctuations and the more likely it is that the option expires ITM. The time value is not as straightforward to calculate, as the intrinsic value and option traders use pricing models to determine the fair value and time value of the option contract. Time value can be deduced by looking at the option premium in the market and subtracting the intrinsic value, if any.

To summarize, the intrinsic and time value help investors understand the risk and rewards of options. The option premium of ITM options consists of both intrinsic and extrinsic value. In contrast, ATM or OTM options do not have any value if they are exercised immediately, so the premium on those options only consists of time value.

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Understanding the Greeks helps to better comprehend how factors such as the price of the underlying asset, time to expiry and volatility impact option prices. These factors apply to individual options, but can also be combined to measure the exposure of options portfolios, making the Greeks useful in assessing the overall riskiness of a portfolio that includes several options positions. This explainer defines the five main Option Greeks.

Delta represents the change in the price of an option resulting from a change in the price of the underlying asset[EM1] . Delta ranges from 0 to 1 for call options and from 0 to -1 for put options. At-the-money call (put) options have a delta close to 0.5 (-0.5), which will increase (decrease) towards 1 (-1) as the option gets deeper in the money, and closer to 0 as it gets further out of the money.

Delta also gives an indication of the likelihood of an option expiring in the money; an option with a delta of 0.7 has a roughly 70% chance of expiring in the money.

- A call option is currently priced at $4 and has a delta of +0.60 (delta is higher than 0.5, so the option is currently in the money). If the price of the underlying asset increases by $1, the option’s premium will change by 0.60 * $1 = $0.6 and the new option price will be $4.60, all else being equal.

Delta is not constant; it changes as the price of the underlying asset moves. Gamma measures the change in the delta of the option in response to a change in price of the underlying asset. Mathematically, it is the second derivative of the option price with respect to the price of the underlying asset. The higher the value of gamma, the more sensitive the option’s delta to price changes in the underlying asset. Gamma is highest for options that are at the money and with shorter time to expiry, and decreases as the option becomes deeper in or out of the money.

- Imagine the call in the previous example has a gamma of 0.03. If the price of the underlying asset increases by $1, the delta will change by 0.03 * 1 = 0.03, and so increase from the initial 0.60 to 0.63.

Theta represents the time decay of an option contract and specifies the ‘time value’ or ‘extrinsic value’ the call or put option loses every day as it approaches expiration. The daily loss in time value is not linear over the life of the option, but accelerates as expiration approaches. So theta is higher – more negative – for options closer to expiration. It is also higher for at-the-money options, as these have more time value built in the premium than in- or out-of-the-money options with the same underlying asset and expiration date.

- The same call option has a theta of 0.02. If it is priced at $4 today then, all else being equal, the option’s value will be $3.98 after one day.

Vega measures the rate of change in the price of the option due to a change in the implied volatility, which is the expected volatility of the underlying asset from now until the option expires. The higher the implied volatility, the higher probability of large price movements in the underlying asset, which means the option is more likely to move further away from the strike price. This is positive for the value of options, which is why option prices increase when the volatility of the underlying asset rises.

- The same call option has a vega of 0.3 and the implied volatility is currently 10%. If the implied volatility increases to 11.5%, the option price will increase by 1.5 * 0.3 = $0.45 to $4.45.

Rho measures the change in the price of an option relative to a change in the interest rate. If an investor holds a call option, they delay payment for the underlying asset until the option expires. Until then, this capital can be put aside and generate interest. As such, an increase in interest rates increases the value of call options. For put options, the opposite happens, i.e. an increase in interest rates decreases the value of put options.

- The same call option has a rho of 0.15. If interest rates increase by 0.5%, the value of the call option will increase by 0.15 * 0.5 = $0.075 to $4.075. In contrast, if the investor has a put option with the same rho, the price of the option will decrease by $0.075

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A future is a type of derivative contract that represents an agreement to buy or sell an asset at a specified future date, for a price determined today. It is a standardized contract traded on a derivatives exchange. Futures are an important hedging/insurance tool that can be used to protect against adverse price movements, or to fix the price of otherwise volatile assets to assist in corporate long-term budgeting. They may also be used to express an opinion about the direction of the market. Futures were initially created as a hedging product for commodity producers, but today exist on a wide range of underlying assets besides commodities such as currencies, interest rates, indices and stocks.

The standardized features of a future contract include the contract size, expiration date and delivery arrangement. The contract size is the standardized quantity of the underlying asset that the future controls. For example, an oil future represents a contract on 1000 barrels of oil. Futures trade in specific expiration cycles that can be weekly, monthly, quarterly, etc. The expiration date is the date on which the contract lapses. The delivery arrangement details whether the future will be settled physically or in cash. A commodity producer looking to lock in a price for their product would likely prefer a physically settled commodity future, whereas an investor looking to express a view on the commodity’s price movement with no intention of holding the asset would prefer a cash settlement.

Futures, like other derivatives, are used to hedge, which is to eliminate or reduce the risk of adverse price movements. A wheat farmer can use a physically settled future to lock in the sale of the harvest at a known price, and so eliminate uncertainty on the proceeds of the future sale.

Futures can also be used to take a position and express an opinion on the future direction of the market, giving investors access to products that would otherwise not be accessible. For example, it is more efficient for an investor to buy a Eurostoxx 50 future than to buy every underlying stock in the index. At the same time, as opposed to holding a couple of single securities, futures give an investor exposure to a wider market as well as the ability to express a macro view. The leverage effect in future contracts can give an investor a large exposure for a small initial amount of capital, which magnifies both profits and losses. Due to the leveraged nature and the relatively large size of most contracts, futures are more commonly traded by institutional investors than retail investors.

- Imagine an investor that buys a Eurostoxx 50 future in March that expires in December, has a multiplier of 10 and is priced at 3100. Suppose that in December the future expires at a level of 3150; this means the investor’s profit amounts to €50 x 10 = €500. If the future expires at a level of 3050 instead, the investor loses €500.

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