The ‘Greeks’ refer to the various dimensions of risk that an options position entails.
Greeks are used by options traders and portfolio managers to hedge risk and understand how their P&L will behave as prices move.
The most common Greeks include the Delta, Gamma, Theta, and Vega – which are first partial derivatives of the options pricing Model.
Delta
Delta (Δ) represents the rate of change between the option’s price and a $1 change in the underlying asset’s price.
In other words, the price sensitivity of the option relative to the underlying.
Delta of a call option has a range between zero and one, while the delta of a put option has a range between zero and negative one.
For example, assume an investor is long a call option with a delta of 0.50. Therefore, if the underlying stock increases by $1, the option’s price would theoretically increase by 50 cents.
Gamma
Gamma (Γ) represents the rate of change between an option’s delta and the underlying asset’s price. This is called second-order (second-derivative) price sensitivity.
Gamma indicates the amount the delta would change given a $1 move in the underlying security.
For example, assume an investor is long one call option on hypothetical stock XYZ. The call option has a delta of 0.50 and a gamma of 0.10.
Therefore, if stock XYZ increases or decreases by $1, the call option’s delta would increase or decrease by 0.10.
Theta
Theta (Θ) represents the rate of change between the option price and time, or time sensitivity – sometimes known as an option’s time decay.
Theta indicates the amount an option’s price would decrease as the time to expiration decreases, all else equal.
For example, assume an investor is long an option with a theta of -0.50. The option’s price would decrease by 50 cents every day that passes, all else being equal.
If three trading days pass, the option’s value would theoretically decrease by $1.50.
Theta increases when options are at-the-money, and decreases when options are in- and out-of-the money.
Long calls and long puts will usually have negative Theta; short calls and short puts will have positive Theta.
Volatility
Vega (v) represents the rate of change between an option’s value and the underlying asset’s implied volatility.
This is the option’s sensitivity to volatility.
Vega indicates the amount an option’s price changes given a 1% change in implied volatility.
For example, an option with a Vega of 0.10 indicates the option’s value is expected to change by 10 cents if the implied volatility changes by 1%.
Increased volatility implies that the underlying instrument is more likely to experience extreme values, a rise in volatility will correspondingly increase the value of an option.
Conversely, a decrease in volatility will negatively affect the value of the option.
Vega is at its maximum for at-the-money options that have longer times until expiration.
Rho
Rho (p) represents the rate of change between an option’s value and a 1% change in the interest rate.
This measures sensitivity to the interest rate.
For example, assume a call option has a rho of 0.05 and a price of $1.25. If interest rates rise by 1%, the value of the call option would increase to $1.30, all else being equal.
The opposite is true for put options.
Rho is greatest for at-the-money options with long times until expiration.
