Understanding the Greeks

Delta Δ

Delta of an option is defined as the rate of change of the option price with respect to the price of the underlying asset. For example, assuming the delta of a call option on asset ABC is 0.5, this means that when ABC’s price changes by a small amount, the option price changes by about 50% of that amount (i.e. if ABC’s price is $100 and 1 call option price is $10, if ABC’s price goes up by $1, the option price will tend to go up by 0.5 * $1 = $0.50). The delta of the option does not remain constant. Call options will have a positive delta (between 0 and 1) while put options will have a negative delta (between 0 and -1). In general, in-the-money options will move more than out-of-the-money options, and short-term options will react more than longer-term options to the same price change in the underlying asset.

Gamma γ

Gamma of an option on an underlying asset is the rate of change of the option’s delta with respect to the price of the underlying asset. Options with high gamma are very responsive to changes in the price of the underlying asset. The price of near-term at-the-money options will exhibit the most explosive response to price changes in the underlying asset. If gamma is small and delta changes slowly, adjustments to keep a portfolio delta neutral need to be made only relatively infrequently. However, if gamma is highly negative or highly positive, delta is very sensitive to the price of the underlying asset.

Theta θ

Theta of an option is the rate of change of the value of the option with respect to the passage of time with all else remaining the same, also known as the time decay of an option. At-the-money options will experience more significant dollar losses over time than in- or out-of-the-money options with the same underlying asset and expiration date. That’s because at-the-money options have the most time value built into the premium. And the bigger the chunk of time value built into the price, the more there is to lose.

Vega ν

Vega is the rate of change of the value of the option with respect to the volatility of the underlying asset. If vega is highly positive or negative, the option’s value is very sensitive to small changes in volatility. If vega is close to zero, volatility changes have relatively little impact on the value of the option.

Rho ρ

Rho is the rate of change of the value of the option with respect to the interest rate. It measures the sensitivity of the value of the option to a change in the interest rate when all else remains the same.