# Greeks

Greeks refer to indicators that allow traders to evaluate option transactions in terms of risks. They are called the Greeks as Greek letters are embedded in the text of a title.

Each indicator demonstrates an imperfect assumption or connection of the option with another underlying indicator. Options traders rely on the Greek letters—delta, vega, theta, gamma—in order to control risks with options and manage option portfolios.

## Greeks Explained

Greeks include a lot of indicators, such as delta, theta, gamma and others. Each indicator is expressed as a numerical value, more often—as a percentage. It shows traders the variability of the financial derivatives and risks depending on changes in circumstances. The most important Greeks are Delta, Vega, Theta, Rho, and Gamma. They are calculated directly from market data (using the chosen mathematical model of options, for example, the Black-Scholes model).

The value can be variable over time. That’s why options traders tend to pay attention to the values every day to make sure that they don’t need to rebalance their portfolio.

Traders usually take into consideration the following Greeks.

**Delta**. This variable is the coefficient of transition of the change in the price of the underlying asset into an option premium. It means that the underlying asset will influence the price of the option. The delta of +0.50 on a call option with a strike of $20 and an option price of $2 shows that if the stock price goes up by $1 from $20 to $21, the option value will increase by 0.5 and will be $2.5.

Delta is also defined as the hedge ratio. For instance, if you buy an American call option with a 0.50 delta, you have to sell 50 shares of stock to be fully hedged.

Delta also indicates the probability that the option will expire in-the-money.

**Theta**. This variable indicates how the value of the option will change as the option is becoming closer to the expiration date. For example, if an option with a theta of 0.05 will lose $0.05 of its value daily and the option today is at value of $2.50, then tomorrow the price of it will be $2.45.

The closer the option gets to the expiration date, the more the value of theta grows and the more the time value of an options contract decreases.

Long calls and long puts tend to have negative theta, whie short calls and short puts are associated with positive theta. If the value of the share doesn’t change over time, it means that it has a zero theta.

**Gamma**. The value of gamma is affected by the price of the underlying asset. In other words, this variable demonstrates how the price of the option will change when the price of the underlying asset increases or decreases.

For example, if the value of gamma in the transaction is 0.10 and the delta is - 0.5 and the price of underlying asset increases by $1, the value of delta will increase to 0.6. If the price of the underlying asset decreases by $1, on the contrary, it will fall to 0.4.

**Vega**. It shows how the option price will change if the volatility of the underlying asset changes and demonstrates the rate of this change. For instance, if the value of vega is 0.10, then a decrease in volatility by 1% will lead to the decrease in value by 10 cents.

The change of option price is the key factor that influences its value. If the volatility increases, option prices go up as well. Consequently, if the volatility decreases, there is** **a decrease in an option's value. Vega is at minimum for options that are approaching the expiration date.

**Rho**. Rho measures how sensitive the option price is to the change in the interest rate by one percent. Rho is usually mentioned at the end of the list of Greeks as interest rates have a relatively weak impact on the price of options and therefore are practically ignored by traders. However, if there are high-yielding currencies, such as ruble, Brazilian real, and Turkish lira, interest rates can significantly affect a trader's income.

For example, if a call option has a rho of 0.06 and a price of $1.26 and if interest rates are raised by 1%, the value of the call option would rise to $1.32. It is untrue to put options.

## Minor Greeks

Other variables that are seldom used in comparison with Delta, Vega, Theta, are called minor Greeks. They are not that common in terms of options-trading. These are lambda, epsilon, vomma, vera, zomma, and ultima. They influence the change in the value of delta with the decrease or increase in volatility and other factors.

The minor Greeks are important while applying strategies for options trading because computer programs are able to search out these risk factors.