Option Greeks are financial measures of the sensitivity of an option’s price to its underlying determining parameters, such as volatility or the price of the underlying asset. The Greeks are utilized in the analysis of an options portfolio and in sensitivity analysis of an option or portfolio of options.

Option Greek Delta

Delta (Δ) is a measure of the sensitivity of an option’s price changes relative to the changes in the underlying asset’s price. In other words, if the price of the underlying asset increases by $1, the price of the option will change by Δ amount. Mathematically, the delta is found by Δ=δV/δS where V is the option’s price and S is the underlying asset’s price. Delta is also known as a hedge ratio. If a trader knows the delta of the option, he can hedge his position by buying or shorting the number of underlying assets multiplied by delta.

Gamma

Gamma (Γ) is a measure of the delta’s change relative to the changes in the price of the underlying asset. If the price of the underlying asset increases by $1, the option’s delta will change by the gamma amount. The main application of gamma is the assessment of the option’s delta. Long options have a positive gamma. An option has a maximum gamma when it is at-the-money (option strike price equals the price of the underlying asset). However, gamma decreases when an option is deep-in-the-money or out-the-money Γ=δΔ/δS=(δ^2)(V)/(δ^2)(S)

Option Greek Vega

Vega (ν) is an option Greek that measures the sensitivity of an option price relative to the volatility of the underlying asset. If the volatility of the underlying asses increases by 1%, the option price will change by the vega amount. v=δV/δσ Where σ is the volatility of the underlying asset.

The vega is expressed as a money amount rather than as a decimal number. An increase in vega generally corresponds to an increase in the option value (both calls and puts).

Theta

Theta (θ) is a measure of the sensitivity of the option price relative to the option’s time to maturity. If the option’s time to maturity decreases by one day, the option’s price will change by the theta amount. The Theta option Greek is also referred to as time decay. θ=-δV/δτ where τ is the option’s time to maturity.

In most cases, theta is negative for options. However, it may be positive for some European options. Theta shows the most negative amount when the option is at-the-money

Rho

Rho (ρ) measures the sensitivity of the option price relative to interest rates. If a benchmark interest rate increases by 1%, the option price will change by the rho amount. The rho is considered the least significant among other option Greeks because option prices are generally less sensitive to interest rate changes than to changes in other parameters.

Generally, call options have a positive rho, while the rho for put options is negative.