# The “Greeks”

The options greeks are a set of measurements that quantify an option position’s exposure to risk. Options and other trading instruments have a variety of risk exposures that can vary dramatically over time or as markets move. Each of the option greeks represents a different variable of option pricing. To assess the probability of the trade making money, it is essential to determine the exposure of the position in relation to time, volatility and movement of the underlying security. Changes in the price of the underlying instrument trigger changes in the option delta, which will trigger changes in the rest of the greeks.

Each risk measurement is named after a different letter in the Greek alphabet, including delta, gamma, theta, and vega (vega is not actually a Greek letter, but is used in this context). In the beginning, it is important to be aware of all of the greeks, although understanding the delta is the most crucial to your success. Comprehending the definition of each of the greeks will give you the tools to decipher option pricing. Each of the terms defined below has a specific use in day-to-day options trading.

- Delta: The change in the price of an option relative to the change of the underlying security. Delta helps you to understand how an option’s premium will rise or fall in comparison to the price of the underlying security.
- Gamma: Change in the delta of an option with respect to the change in price of its underlying security. Gamma helps you to gauge the change in an option’s delta when the underlying security moves.
- Theta: Change in the price of an option with respect to a change in its time until expiry. Theta measures the amount an option will lose with the passage of one day.
- Vega: Change in the price of an option with respect to its change in volatility. Vega measures the amount an option will gain or lose with a one-percentage point change in volatility.

When broken down, all of these terms refer to simple concepts that can assist you thoroughly understand the risks and potential rewards of option positions. Having a comprehensive understanding of these concepts will help reduce risk exposure, reduce stress levels, and increase overall profitability as a trader. Learning how to integrate these basic concepts into your own trading programs can have a powerful effect on your success as an options trader. Although we could write an entire manual on the option greeks, in this primer we restrict the discussion to simply introducing the basic concepts.

### Delta

Delta is defined as the change in the price of an option relative to the change of the underlying security. Another way to think about it is that the delta is the amount by which the price of an option changes for every dollar move in the underlying instrument. This is a very important number to consider when constructing combination positions.

Call option deltas are positive (0 to 1) while put options have negative deltas (0 to -1). If a call option has a delta of 0.5, then that implies that the option will increase by $0.50 for a $1.00 move up in the stock price. Conversely, if a put option has a delta of -0.5 that implies that the option will increase by $0.50 for a $1.00 move down in the stock price.

Generally speaking, ATM options will have deltas of plus or minus 0.50, and deeper ITM options might have a delta of 0.80 or higher. Out-of-the-money options have deltas as small as 0.20 or less. These values will change as the option becomes further ITM or OTM. Just as option prices are not linear, neither are the changes in the option greeks.

When an option is very deep ITM, it will begin to trade like the stocks, moving practically dollar-for-dollar with the underlying stock. In contrast, far OTM options will not move much at all, even if the stock price starts rising or falling. As a general rule, you should usually steer clear of buying options that are far OTM. Your chances of making money buying short-term OTM options are generally pretty small because the option’s premium rapidly deteriorates. You also need a large move in the right direction from the underlying stock price in order to become profitable.

The delta of an option can also be thought of as an option’s chance of being in-the-money by expiry. For example, if a call has a delta of 0.35, it can be said there is theoretically a 35% chance of the call finishing in-the-money at expiry.

### The Delta Calculations

Successful option traders are usually proficient at understanding and calculating deltas. While there are several tools on the market that can automatically calculate an option’s delta, you can also calculate them manually by using the following formula:

(Price Change of an Option) / (Price Change of the Stock) = Delta

Let’s try an example where XYZ is trading at $13 per share and you buy an ATM 13 call option. If the call option increases $0.20 in price while XYZ increases $0.40 per share, the delta would then be: 0.2/0.4 = 0.50. In trading, this is a 50 delta, which means that this particular option will move at 50% of the speed of the stock price.

For those of you who have computer models that do delta calculations, there are other variables involved, but for on-the-run delta calculations, this formula can be used as a good basis. Bottom line, a change in the stock price will cause a change in the option delta, which will cause a change in the overall position delta.

### Gamma

Gamma can be defined as the rate of change in the delta for each one-point move in the underlying instrument. In other words, gamma is the degree by which the delta changes with respect to changes in the underlying instrument’s price. The gamma is a valuable tool because it can help you forecast changes in the delta of an option or an overall position.

For example, a call option with a gamma of 0.03 indicates the option will gain 0.03 positive deltas for each point increase in the stock price. A put option with a gamma of 0.03 indicates the option will gain 0.03 negative deltas for each point decrease in the stock price. Gamma is especially useful when larger positions are in place. It provides a more dynamic risk profile of the option position. Gamma is highest for ATM options because the deltas of ATM options are more sensitive to price moves in the underlying stock.

### Theta

Theta is a measure of the time decay of an option. Generally speaking, time decay increases as an option approaches expiry. Theta is one of the most important concepts for a beginner option trader to understand. It basically explains the effect of time on the premium of the options that have been purchased or sold. The less time that an option has until expiry, the faster that option is going to lose its extrinsic value.

Theta is a way of measuring the rate at which value is lost. The further out in time you go, the smaller the time decay will be for an option. Therefore, if you want to own an option, it is advantageous to purchase longer-term contracts. If you are using a strategy that profits from time decay, then you will want to be short (sell) the shorter-term options to take advantage of the loss in value due to time decay which can happen quickly.

### Vega

Vega is defined as the change in the price of an option with respect to its change in volatility. As the volatility of a stock increases, so does the premium for its options. Volatility is one of the most important determinants of an option’s price. The easiest way to understand volatility is to view a price chart over a period of time and look at the price change; the greater the price change, the higher the volatility. Vega measures the amount an option will gain or lose with a one percentage point change in volatility.

### Importance of the Greeks

The greeks can help you to explore the various risk exposures of every trade you consider placing. Options have a variety of risk exposures and these risks can vary dramatically with time and market movement. To recognise the probabilities of the trade making money, it is essential to be able to determine a variety of risk exposure measurements. Changes in the price of the underlying instrument trigger changes in the delta, which will trigger changes in the rest of the greeks.

Take time to study the effects that changes in price, time and volatility have on the Greeks and how they interrelate.

It is not important to understand all the mathematics behind the greeks. What is important is that you are familiar with how to interpret the numbers and how these numbers measure how an option or option strategy will behave given certain changes in market conditions.

Since prices are constantly changing, the greeks provide traders with the means to determine just how sensitive a specific trade is to price fluctuations. A solid understanding of the greeks can help you take your options trading to another level.