# Introducing the Greeks, For Options Contracts

Read about the “Greeks” — Delta, Gamma, Theta, and Vega — and other factors that influence options prices in the developing crypto options market.

Updated July 4, 2021 • 4 min read

#### Summary

The “Greeks” are metrics used to measure, assess, and quantify the level of risk for options contracts. Analysts and traders use four “major” Greeks (Delta, Gamma, Theta, and Vega) to study factors that influence options prices, or “premiums.” In addition, traders may use “minor” Greeks (rho, lambda, and epsilon, derived from the major Greeks) to predict options price movements. Primarily, the Greeks evaluate options within the context of factors that influence their prices: volatility, direction, time, and interest rates.

## Options Basics

A stock options contract is a tentative agreement between two parties to engage in a securities transaction on or before a specified future date at a preset price (i.e., the strike price). You can trade many types of assets as an options contract, including stocks, bonds, exchange-traded funds (ETFs), and more. Options are derivative investments (derivatives) because they derive their value from the underlying assets that are being traded. There are numerous types of options contracts; two of the most common are calls and puts.

Calls: A call options contract gives the buyer the right to buy shares of an underlying security at the strike price for a specific amount of time, until the contract expires (the expiration date). The seller of a call option is obligated to sell those shares to the buyer of the call who exercises their option to buy on or before the expiration date.

Puts: A put options contract gives the buyer the right to sell shares of an underlying asset at the strike price for a specified time. The seller of a put option is obligated to buy those shares from the buyer of the put who exercises their option to sell on or before the expiration date.

Options are typically utilized for hedging purposes; however, they also may be used for speculative investing. The upfront cost of an options contract is called the premium. There are four factors that drive the price of an options contract: the current stock price, intrinsic value, time to contract expiration, and volatility.

## The Major Greeks

Delta: An option’s delta is the change in its premium as a result of price changes in its underlying security. It is a “directional” Greek and is expressed as a percentage of the underlying security’s price. For example, if a call option has a price of $1 and a delta of 0.25, then the option’s price will move by 25% of the corresponding change in the underlying security’s price. So, if the security’s price increases to $1.50, then the option’s price will be $1.12, or 25% of $0.50.

Call options have positive deltas, between 0 and 1, while put options have negative deltas, between 0 and -1. Options prices do not change significantly for low delta values of an option, even when there is a major change in the underlying security’s price. On the other hand, options contracts with high delta values are sensitive to even slight price movements in the underlying security’s price. Delta values of in-the-money options, or options that are approaching the strike price (the price at which an investor can exercise the right to buy or sell the underlying security in an options contract), increase as the time to expiration grows shorter. And delta values decrease when the strike price of an option is farther away.

Traders often use delta values as a probability indicator of whether an options contract will reach a strike price. For example, a delta of 0.3 represents a 30% chance that the option will be in-the-money or reach a desired strike price before it expires. Once they have the delta value, traders will often pair their options purchases with purchases of the underlying security, or with futures contracts — which is known as a delta hedging strategy.

Suppose you purchase a call option for 1 bitcoin with a strike price of $5,000 after a month. The option has a delta of 0.5, which means that there is a 50/50 chance that it will reach that price. If the price moves opposite of your desired direction, that is, if it decreases instead of increases, then you’d need to pay the premium plus 50% of the decrease percentage for the underlying security. To offset this potential loss, you could either purchase a bitcoin on the spot market or buy a bitcoin futures contract.

Gamma: An options contract’s gamma measures the speed at which delta changes, which lets you compare two options with the same delta values. Suppose options A and B have the same delta value of 0.3 and gamma values of 2 and 3, respectively. Then the contract with the higher gamma value, in this case B, will have a greater degree of risk because it is more susceptible to price changes in a short time. Gamma values are highest when they are near an option’s strike price, and they are lowest when the option is said to be out-of-the-money, or further from the strike price. All options have positive gamma values.

Theta: An options’ theta measures its time value and is expressed as a negative value. As the options’ expiration date draws near, there is a smaller chance of making a profit from it. Theta quantifies this risk with a figure that is supposed to represent a price drop for each day. For example, an option priced at $2 with a theta of -0.25 will lose $0.25 on a daily basis. Long-term options have a theta value of nearly zero because their time to expiration is relatively distant. Options that are close to their expiration dates, however, have high theta values because their time value is greater. All options have negative theta values.

Vega: An options’ vega measures its price sensitivity to implied volatility. Implied volatility refers to market participants’ anticipated future volatility. Vega changes for every one percent change in implied volatility and is higher when the options’ premium approaches its strike price. For example, suppose you purchase a call option for $1.50, with an implied volatility of 25% and a vega of 0.2. The day after your purchase, the implied volatility increases by 2%. Therefore, the calculation for the new premium will be: option premium = $1.50 + (2 x 0.2) = $1.90.

## Using the Greeks for Cryptocurrency Options Contracts

If you’re trading cryptocurrencies, you can use the Greeks — along with the same strategies, such as delta hedges — just as you would in trading other assets.

Price changes can be sudden and momentous, resulting in greater consensus among participants about future implied volatility. In the event of a price change, the Greeks metrics that depend on direction and volatility will be elevated. In sum, when trading crypto derivatives you should always consider your financial goals, risk tolerance, and understanding of the financial concepts and tools that you are using when executing transactions — and, consult a financial professional if you have any questions or concerns.

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