What are Options Greeks?
Options Greeks are a set of measures used to quantify the risk associated with options trading. They are used to help traders better understand the price sensitivity of an option to changes in various market variables, such as volatility and time decay. In this article, we’ll take an in-depth look at each of the Options Greeks, their formulas, and how they are used in options trading.
Delta
Delta measures the rate of change of the option price in relation to changes in the underlying asset price. In other words, it tells us how much the option price will change for every $1 change in the underlying asset price. The delta of a call option ranges from 0 to 1, while the delta of a put option ranges from -1 to 0. The formula for delta is:
Call Option Delta = N(d1)
Put Option Delta = -N(-d1)
Where N() is the cumulative probability function and d1 is the individual standard normal distribution:
d1 = (ln(S/X) + (r + (σ²/2)T)) / (σ x SQRT(T))
In the formula, S is the current stock price, X is the option’s strike price, r is the risk-free rate of interest, σ is the stock’s volatility, and T is the time remaining until option expiration.
Gamma
Gamma measures the rate of change of an option’s delta in relation to changes in the underlying asset price. In other words, it tells us how much the delta will change for every $1 change in the underlying asset price. The formula for gamma is:
Gamma = N'(d1) / (S x σ x SQRT(T))
In the formula, N'(d1) is the standard normal distribution, S is the current stock price, σ is the stock’s volatility, and T is the time remaining until option expiration.
Theta
Theta measures the rate of change of an option’s price in relation to changes in the time remaining until expiration. In other words, it tells us how much the option price will change for every day that passes. The formula for theta is:
Theta = -(S x N'(d1) x σ) / (2 x SQRT(T)) – r x X x e(-rT) x N(-d2)
In the formula, S is the current stock price, N'(d1) is the standard normal distribution, σ is the stock’s volatility, T is the time remaining until option expiration, X is the option’s strike price, r is the risk-free rate of interest, and d1 and d2 are standard normal distribution values.
Vega
Vega measures the rate of change of an option’s price in relation to changes in the underlying asset’s volatility. In other words, it tells us how much the option price will change for every 1% change in volatility. The formula for vega is:
Vega = S x SQRT(T) x N'(d)
In the formula, S is the current stock price, T is the time remaining until option expiration, and N'(d) is the standard normal distribution.
Rho
Rho measures the rate of change of an option’s price in relation to changes in the risk-free rate of interest. In other words, it tells us how much the option price will change for every 1% change in interest rates. The formula for rho is:
Rho = X x T x e(-rT) x N(d2)
In the formula, X is the option’s strike price, T is the time remaining until option expiration, r is the risk-free rate of interest, and d2 is the standard normal distribution value.
Conclusion
Options Greeks are a powerful tool for understanding the risks and potential rewards of options trading. By providing measures of an option’s sensitivity to various market variables, Options Greeks can help traders make more informed decisions about which options to buy or sell and when to enter or exit a trade. Understanding the formulas for each of the Options Greeks and how they are used in practice is an essential first step for any aspiring options trader.
By Astrobulls Research Pvt. Ltd