Learn Option Greeks

What are Option Greeks?

Option Greeks are a set of risk measures that help investors understand how the price of an option might change in response to various factors, such as changes in the underlying asset's price, time decay, volatility, and interest rates. These measures are essential for options traders to assess and manage risk effectively.

Delta

Delta measures the rate of change of the option price with respect to changes in the price of the underlying asset. It indicates how much the option price will move for a $1 change in the underlying asset's price. Mathematically, Delta can be calculated using the following formula:

Δ = ΔOption Price / ΔUnderlying Asset Price

Gamma

Gamma measures the rate of change of Delta with respect to changes in the price of the underlying asset. In other words, it represents the acceleration of Delta. Gamma is crucial for understanding how Delta itself changes as the underlying asset's price fluctuates. The formula for Gamma is:

Γ = Δ²Option Price / ΔUnderlying Asset Price²

Theta

Theta measures the rate of change of the option price with respect to time decay. It reflects how much the option price will decrease as time passes, assuming all other factors remain constant. Theta is particularly important for option buyers, as it quantifies the impact of time decay on the option's value. The formula for Theta is:

Θ = -ΔOption Price / ΔTime

Vega

Vega measures the rate of change of the option price with respect to changes in volatility. It indicates how much the option price will change for a 1% change in volatility. Vega helps traders assess the sensitivity of an option's price to changes in implied volatility. The formula for Vega is:

Vega = ΔOption Price / ΔVolatility

Rho

Rho measures the rate of change of the option price with respect to changes in interest rates. It reflects how much the option price will change for a 1% change in interest rates. Rho is particularly relevant for options impacted by interest rate fluctuations, such as long-term options. The formula for Rho is:

Rho = ΔOption Price / ΔInterest Rate

Example

Let's consider a call option on Company XYZ with the following details:

Strike Price: $100
Current Stock Price: $105
Time to Expiry: 30 days
Implied Volatility: 20%
Risk-free Interest Rate: 5%

Using the Black-Scholes model, we can calculate the following option Greeks:

Delta: 0.636
Gamma: 0.089
Theta: -0.042
Vega: 0.155
Rho: 0.118

Now, let's say the stock price increases by $1. The new option price can be calculated using the Delta:

New Option Price = Old Option Price + (Delta * Change in Stock Price) = $6.36 + (0.636 * $1) = $7.996

Similarly, we can assess the impact of changes in time, volatility, and interest rates on the option price using Theta, Vega, and Rho, respectively.