# The Greeks (Used in Options) ## WHAT ARE THE GREEKS?

The most relevant Greek symbols used in trading are: Delta, Gamma, Theta, Rho and Vega.

Less commonly discussed ones (covered in another post in more detail) are: Beta, Epsilon, Lambda, Ultima, Vera, Vomma, Vera, Zomma.

## WHAT ARE THEY USED FOR?

Each Greek symbol measures a different factor within the price of an option contract.

They present a mathematical understanding of the risk involved in the contract and, if used strategically, help us build portfolios where risk is minimized. Options contracts have a “fair value” and that is calculated using a Black-Scholes, Barone-Adesi-Whaley, or Cox-Ross-Rubinstein model, commonly called a options theoretical pricing model. Based on this model, we pull out the Greeks as variables that help shape the price of the contract over a period of time and changing characteristics. This model is built considering the Strike Price, Implied Volatility and Time to Expiration.

## MOST USED GREEKS:

Delta – is the variable which represents the rate of change that the Contract Price changes in respect to the Underlying Security. The Delta will be between 0-1 on a Call and between 0-(-1) on a Put.

The Delta will approach 1.0 as the option gets deeper IMO and as an IMO option gets closer to expiration. If it is OTM it will approach 0.0 as the option approaches expiration.

The opposite is true with Puts. The Delta will approach -1.0 as the option gets further IMO and as an already IMO contract nears expiration.

It can also be used an indicator if the Option Contract will expire In The Money (ITM). To hold a safe portfolio, take LOTS of SMALL options positions and balance the Deltas so that you have a net delta of 0. Sell ob both sides of the Option, calls and puts. If you only chose one side to sell, there only needs to be one movement that makes or kills those positions.

Gamma – is the derivative of Delta. It is the rate of change in Delta with respect to each \$1 move in the Underlying Security. A Delta value is only true for a single time and price of the underlying. So this is the value of how much it changes. If Delta=.20 and there is a \$1 move of the underlying security, the call is now \$ .20 more valuable. But since the contract is now deeper in the money, the Delta gets closer to 1.0. So now the value of the Delta moves from .20 to .25 at the new (+\$1) underlying security’s price. This means that Gamma value is .05 at the price before the \$1 increase.

## Time Decay

Theta – measures the rate of change of the price of the contract relative to time. This is commonly called Time Decay. For every day the contract gets closer to expiring, the value of your contract decreases in value. Time Value erosion is not linear however.

OTM contracts have a higher Theta early on and Theta decreases as the contract nears expiration.

ATM and IMO contracts have a Theta that starts small and gets larger as the contract nears expiration.

## Interest Rates

Rho – is the expected Contract price change per one percentage point change in interest rates. So you will be able to see how the price of your option should increase or decrease if the risk-free interest rate (U.S. Treasury Bills) increases or decreases. As I-rates increase, the value of a call option will increase and value of puts decrease.

Vega – measures the rate of change of the contract price relative to implied volatility (IV) changes in the underlying security.