Greeks & Options

Delta of an option is the rate of change of the option price to a $1 change in the underlying price. Delta of a call option ranges from zero and 1 and the Delta of a put option ranges from zero to -1. I.e. put option delta is always negative while the call option delta is always positive.

if the call delta is 0.5, then a $1 increase in the price of the stock will increase the price of the option by $0.5

The delta is the sensitivity of the options price to the price of the underlying which is analogous to the bond price's sensitivity to the bond duration and the stocks sensitivity to the market as manifested by the stock beta.

Theta of an option represents the sensitivity of the option price to the change in time. Theta values are always negative for long options positions.

For example if theta is -0.5 then for every day the option will lose $0.5 in price.

Gamma is the sensitivity of the options delta to the underlying price. E.g. if Gamma is 0.5, then if the underlying asset price increases by $1 then delta will increase by 0.5$

Gamma = (change in delta)/(change in the underlying asset price)

Gamma is the highest value when the option is trading at the money. 

Vega - measures the change in the options price that would result from a 1% change in the implied volatility of the underlying security.

Price of the Underlying	At the money	Deep out of the money	Range	Short options	Other notes
Delta	Call options have delta of 0.5 Put options have delta of -0.5	Call & put options tend to have delta of zero especially closer to expiration	(0-1) for call options and (-1-0) for put options	Opposite sign to long positions	Deep in the money calls have delta close to 1 Deep in the money put options have delta close to -1
Gamma	highest	Zero	Always positive or zero	Negative	Gamma is also high closer to option expiration. Gamma is highest when the option is at the money
Theta	Highest for short term options	lower	Negative for long calls and long puts	Positive for short calls and puts	Long term options have low theta High volatility stocks have high theta

• deep in the money calls have delta of 1 and deep in the money puts have delta of -1
• if a long put and long call have identical features, then the sum of the absolute values of deltas will equal 1
• a call option on EUR/USD is identical to a put option on USD/EUR