Delta is a measure of the rate of change in an option's theoretical value for a one-unit change in the price of the underlying. Call deltas are positive; put deltas are negative, reflecting the fact that the put option price and the underlying price are inversely related.
Gamma is a measure of the rate of change in an option's delta for a one-unit change in the price of the underlying. Long options will always have Positive Gamma and Short options will always have Negative Gamma.
Theta is a measure of the rate of change in an option's theoretical value for a one-unit change in time to the option's expiration date. This price decrease accelerates as the expiration date approaches. American options Theta will always be positive while European options Theta can be Negative or Positive.
Vega is a measure of the rate of change in an option's theoretical value for a one-unit change in the volatility assumption (Implied Volatility or IV). If the Vega is high then option will rapidly gain or lose value. It is also known as Kappa.
Rho is a measure of the expected change in an option's theoretical value for a 1 percent change in interest rates. An increase in risk free interest rate increases the value of calls and decreases the value of puts and vice versa.
Volatility A measure of stock price fluctuation. Mathematically, volatility is the annualized standard deviation of a stock's daily price changes.
Premium is the price of an option and is equal to its intrinsic value plus time value.
Theoretical value The estimated value of an option derived from a mathematical model.
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