What Are the Greeks?
"Greeks" is a term used in the options market to describe the different dimensions of risk involved in taking an options position. These variables are called Greeks because they are typically associated with Greek symbols. Each risk variable is a result of an imperfect assumption or relationship of the option with another underlying variable. Traders use different Greek values, such as delta, theta, and others, to assess options risk and manage option portfolios.
The Basics of The Greeks
Greeks encompass many variables. These include delta, theta, gamma, vega, and rho, among others. Each one of these variables/Greeks has a number associated with it, and that number tells traders something about how the option moves or the risk associated with that option. The primary Greeks (Delta, Vega, Theta, Gamma, and Rho) are calculated each as a first partial derivative of the options pricing model (for instance, the Black-Scholes model).
The number or value associated with a Greek changes over time. Therefore, sophisticated options traders may calculate these values daily to assess any changes which may affect their positions or outlook, or to check if their portfolio needs to be rebalanced. Below are several of the main Greeks traders look at.
- 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 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. For more on the delta, see our article: Going Beyond Simple Delta: Understanding Position Delta.
Theta represents the rate of change between the option price and time, or time sensitivity. Theta indicates the amount an option's price would decrease as the time to expiration decreases. 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.
Gamma represents the rate of change between an option's delta and the underlying asset's price. This is called second-order 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.
Vega 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%.
Rho 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.
Some other Greeks, with aren't discussed as often, are lambda, epsilon, vomma, vera, speed, zomma, color, ultima. These Greeks are second- or third-derivatives of the pricing model and affect things such as the change in delta with a change in gamma and so on.