The financial sector use mathematical models to calculate the potential value of an option depending on crucial criteria such as the price and volatility of the underlying securities, the time remaining before expiration, and interest rates, among others. Hence, the link between an option's price and each of these criteria can be mathematically stated, and five of these correlations have been given Greek letter designations.
Option Greeks, the Definition
Option Greeks are financial measurements of an option's price elasticity to its underlying deciding characteristics, such as volatility or the price of the underlying asset. The Greeks are applied in the study of an options portfolio. Many investors believe the measurements crucial for making rational selections in options trading.
In fact, when trading options, whether to hedge stock holdings, or developing stock and option investing strategies, it is essential to understand how the price of an option is likely to vary when these factors change. The option type and strike price are fixed for each contract, but all other factors are subject to vary, with the price and volatility of the underlying asset having a significant impact on the option's pricing.
The following metrics, named after Greek letters, illustrate these relationships:
Quantifies the sensitivity of an option's price movements to changes in the price of the underlying asset. In other words, if the underlying asset's price increases by $10, the option's price will change by the “delta” amount.
An option Greek that evaluates the price sensitivity of an option relative to the underlying asset's volatility. If the underlying asset's volatility increases by 10%, the option price will fluctuate by the “vega” amount.
Gauges the amount by which the “delta” of an option will fluctuate as the price of the underlying security changes. If the underlying asset's price increases by $1, the option's delta will vary by the amount of gamma.
Measures of the option price's sensitivity to the option's remaining time to maturity. For each passing day, the option’s price varies by the “theta” amount.
Indicates the option price's sensitivity to changes in interest rates. If a benchmark interest rate rises by 10% percentage points, the option price will vary by “rho”.
These, collectively known as the Greeks, can quantify both opportunity and risk, and they are commonly used to evaluate both aspects of a single option position, a combined stock-option strategy, or an entire portfolio. Greeks are often provided by firms that price options, so investors do not need to compute them.
Finding the Greeks
First of all, one should recognize that the statistics provided for each Greek are just hypothetical. This indicates that the values are predicted using mathematical models. The majority of the information investors need to trade options, such as the bid, ask, and last prices, volume, and open interest, is, again, real data provided by most data service and/or brokerages.
Delta represents the anticipated change in option price resulting from a change in the underlying security. The delta quantifies an option's sensitivity to fluctuations in the price of the underlying asset. It illustrates how much an option's value may grow if the underlying stock price rises.
Call options have positive deltas and put options have negative deltas. As the stock price moves, the delta changes as the option is in or out of the money – When a stock option is extremely in-the-money (with delta close to 100), it trades similarly to the underlying stock and moves almost in-line with it. Out-of-the-money options, on the other hand, have minimal monetary movement.
Given its importance, options traders are interested in the relationship between delta and the stock price. For that, gamma estimates the rate of change of the delta per one-point increase in an underlying security, which helps predict changes in the delta of an option or position.
The Greeks may be used in a variety of ways to construct or improve option strategies. They may:
- Aid in the selection of certain alternatives for a given strategy
- Be used to develop new strategies
- Offer guidance on strategy management
- Assist in determining opportune timing to close or roll options
- Aid in risk quantification and management
In addition to the aforementioned Greeks, options traders may use lesser-known components to acquire a complete picture of a position's whole risk profile, despite their less widespread application. Lambda, epsilon, charm, vomma, or color are examples of these lesser Greeks.
These Greeks influence variables such as the change in delta in response to a change in volatility, etc. Despite being less well-known, these complicated and even esoteric risk factors are being incorporated in options trading techniques because computer software can swiftly compute and account for them.
Implied Volatility, a Closely Related Instrument
Although implied volatility is not a Greek, it is nearly related. Implied volatility is a projection of the predicted future volatility of the underlying stock, but it is purely speculative. The implied volatility represented in the price of an option is an inference based on a variety of factors, including impending earnings releases, merger and acquisition speculations, and imminent product launches.
The Bottom Line
In a nutshell, option Greeks make it possible for investors to assess the level of risk and potential return associated with specific option contracts, intricate option strategies, or whole investment portfolios. They provide a valuable mathematical toolset for assessing risks and opportunities, picking strategies, and improving approaches. The Greeks have the ability to give valuable information on many choices that are not easily obvious based only on pricing.