When seeking to understand the factors that influence an option contract’s premium value (price), the intrinsic value (moneyness) is relatively easy to understand (the amount of the premium that would be earned if the contract expired today). But, the option’s extrinsic value (time value) can be more nuanced and challenging. Practitioners often look to “the greeks” to help understand the forces having the most significant impact on an option’s time value. They are collectively referred to as the greeks because of their reference to components of the Greek alphabet:
Rho
Rho may be the most simple and least impactful factor that influences an option’s extrinsic value. It represents the rate of change between an option contact’s value and a 1% change in the risk-free interest rate (e.g., the rate on short-term US Treasury bills). For example, an option with a premium of $1.00 and a rho of 0.05 would increase to $1.05.
Delta
Delta is a measure of the expected movement in an option’s price based on the movement of the underlying stock. It is expressed in a range of 0 to 1 for call options and 0 to -1 for put options. For example, if a call option has a delta of 0.5 and its underlying stock increases in value by $1, then the option premium should increase by $0.50. An option with greater intrinsic value (moneyness) is expected to have a higher delta and will move more like the underlying stock, particularly for options that are very in-the-money and near expiration.
Gamma
Gamma may be the most complex of the greeks, as it is the only “second derivative”, meaning it is a function of delta. It represents the rate of change between the option’s delta and the underlying stock as the option moves closer-to or further-away-from the contract’s exercise price. In other words, as a contract moves further toward being profitable at expiration, it’s delta will increase at a faster rate. This non-linear rate of change is measured by gamma. Gamma indicates the amount the delta would change given a $1 change in the price of the underlying stock. For example, assume an investor owns a call option with a delta of 0.50 and a gamma of 0.10. If the underlying stock were to increase by $1, then the call option would increase by $0.50 because of the existing delta, but the delta itself would also increase by 0.10 to 0.60, so the option will have greater delta sensitivity to the next $1 move higher in the underlying stock’s price.
Vega
Vega can be thought of as the sensitivity of an option contract’s price to changes in the implied volatility of the underlying stock. For example, an option with a vega of 0.10 indicates that itsvalue is expected to change by $0.10 for every 1% change in implied volatility. Increased volatility indicates that the underlying stock should have a wider range of expected outcomes, which makes the option more valuable.
Theta
Theta represents the sensitivity of an option contract’s price to the passage of time. Theta is always negative because the value of options continuously declines as the time to expiration decreases, all else equal. For example, an option contract with a value of $1.00 and a theta of -0.05 would lose $0.05 with each passing day. Interestingly, time does not decay an option’s value in a linear fashion. For example, the impact of theta on an option expiring in 11 months vs. 12 months is fairly similar because, despite having an entire month difference in contract life,each option still has a very significant amount of time for the underlying stock to change in value. However, an option expiring tomorrow would be expected to have a much larger theta than an option expiring in one month because the first option’s range of outcomes is effectively limited to how much the underlying stock can change in one day. For options that are near-the-money (the underlying stock is trading close to the contract’s exercise price), theta tends to have a more modest erosion of premium value the further the option is from expiration, but the impact of theta increases at a more rapid rate as the option approaches expiration.
