What are the Greeks?

Options greeks are derivatives of the options prices themselves. In short, they all measure some rate of change, much like taking a derivative in calculus would. 

Be that rate of change of the underlying share price, or rate of change of the option price, or acceleration of the rate of change of time.

There are three levels to greeks, with all being some form of a partial derivative. These three levels in terms of effects are known as first order, second order, and third order, respectively.

What are the first order Greeks?

Delta: Change in option price in relative to underlying stock change in price

Theta: Change in option price over time

Rho: Change in option price relative to interest (risk-free rate)

Vega: Change in option price relative to option Implied Volatility

What is Delta?

Delta is the change in option price relative to a change in the price of the underlying.

Delta ranges from 0 to 1 for long stocks, long calls, and short puts, while it ranges from 0 to -1 for short stocks, long puts, and short calls. 

What is Theta?

Theta can be seen as the decline of the price of an options contract due to passage of time. Theta will eat away at the value of a contract, and increases heavily heading into the expiration.

Theta is a disadvantage for long call and put buyers, but an advantage to short call and put sellers. 

What is Rho?

Rho is known as the effect of an options price relative to a 1% change in the risk-free rate / interest rates.

What is Vega?

Vega is known as the change in an options contract value relative to a 1% change in implied volatility. 

Implied volatility (“IV”) should be thought of as the market’s annualized prediction for the price range of an asset. When IV is lower, the predicted price range is more narrow.

What are the second order Greeks?

Gamma: The rate at which delta changes relative to a $1 move in the underlying price

Vanna: The change in delta relative to a change in volatility

Charm: The rate at which delta changes over time

Vera: The change in rho relative to a change in volatility

Veta: The change in vega relative to passage of time

Vomma: Rate of change of vega relative to change in volatility

What is Gamma?

Gamma is the instantaneous rate of change of delta.

Gamma is the only second order Greek that has a direct response with price movement of the underlying. Oftentimes, you will see gamma lumped together with the other first order Greeks, and this is done so because of gamma’s importance.

Gamma is the same for both call options and put options, with long calls/puts having positive gamma, and short calls/puts having negative gamma.

What is Vanna?

Vanna is the change of delta with respect to a change in volatility, or a change in delta with a change in volatility. When IV rises, the spread of delta gets wider, and vanna measures that. It is the same for both calls and puts, and changes accordingly.

What is Charm?

Charm (also known as “delta decay”) is the decay of delta with the passage of time. ATM delta will always be 50, regardless of how near-term the expiration of the contract is.

What is Vera?

Vera is the change in rho relative to a change in volatility. 

What is Veta?

Veta is the change in vega relative to passage of time.

What is Vomma?

Vomma is the rate of change of vega relative to change in volatility