Option Greeks are the parameters used to measure an option's sensitivity with respect to changes in the price of the underlying asset, market volatility or time to expiration. They give traders a theoretical way to judge their exposure to these parameters, on which options are priced.

There are five primary Greeks:

1. Delta (δ)

2. Gamma (γ)

3. Vega (v)

4. Theta (θ)

5. Rho (ρ)

Here's what each represents:

1. Delta (δ) – It is the degree to which an option price will move given a change in the underlying asset price, all other factors being constant. It is measured on a scale of 1 to -1. For example, an option with a delta of 0.50 will move 50 paise for every one-rupee movement in the underlying asset. This means stock options with a higher delta will increase/decrease in value more with the same move on the underlying asset versus options with a lower delta value. A far out of the money option will have a delta very close to zero. An at-the-money option will have a delta close to 0.50. A deep in-the-money option will have a delta close to 1 or -1.

This is a chart for Nifty Option where Nifty Spot is trading at 15810 and expiry is 30 days away:

Nifty Spot 15810


Calls
Strike
 Price
Puts
ThetaGammaVegaDeltaDeltaVegaGammaTheta
ITM
-2.00990.00038.37310.89315000-0.11288.69410.0003-2.1415
OTM
-3.54160.000717.23910.654515600-0.364117.0650.0006-3.6019
-3.65580.000718.0050.5915700-0.4317.84720.0007-3.6873
ATM-3.69270.000718.13920.520415800-0.500318.12730.0007-3.6912ATM
OTM
-3.55230.000717.69890.447415900-0.573817.81590.0007-3.507
ITM
-3.32130.000616.78350.373316000-0.647216.87810.0007-3.2526
-1.38150.00037.35760.089716500-0.90777.51640.0003-1.4151


From the table, you can see puts have a negative Delta value since a put option will always have an inverse relationship with the spot price of Nifty. Hence, for call options, the Delta fluctuates between 0 to 1 and for put options, it fluctuates between -1 to 0.

2. Gamma (γ) – Gamma of an option indicates how the Delta of an option will change relative to a 1 point move in the underlying asset. In other words, the Gamma shows the option Delta's sensitivity to market price changes. Gamma is important because it shows us how fast our position's Delta changes in relation to the market price of the underlying asset, however, it is not normally needed for calculation for most option trading strategies. Gamma is higher for options that are at-the-money (ATM) and lower for options that are in-and out-of-the-money.                                                    


In the below example, Gamma values for ATM strike 15800 are high compared to strikes 15000 and 16500                            

Nifty Spot 15810


Calls
Strike
 Price
Puts
ThetaGammaVegaDeltaDeltaVegaGammaTheta
ITM
-2.00990.00038.37310.89315000-0.11288.69410.0003-2.1415
OTM
-3.54160.000717.23910.654515600-0.364117.0650.0006-3.6019
-3.65580.000718.0050.5915700-0.4317.84720.0007-3.6873
ATM-3.69270.000718.13920.520415800-0.500318.12730.0007-3.6912ATM
OTM
-3.55230.000717.69890.447415900-0.573817.81590.0007-3.507
ITM
-3.32130.000616.78350.373316000-0.647216.87810.0007-3.2526
-1.38150.00037.35760.089716500-0.90777.51640.0003-1.4151


Gamma is important for traders who deploy Delta neutral strategies as high Gamma will impact Delta and cause imbalance.

3. Vega (v) - The Vega of an option indicates how much the price of the option will change with respect to the underlying asset's volatility. For example, an option with a Vega of 0.20 indicates the option's value is expected to change by 20 paise if the implied volatility changes by 1%. Vega is at its maximum for at-the-money options and decreases as we move away from the spot price.                                                                


In the below example, you can see Vega is maximum for at-the-money option strike price 15800        

Nifty Spot 15810


Calls
Strike
 Price
Puts
ThetaGammaVegaDeltaDeltaVegaGammaTheta
ITM
-2.00990.00038.37310.89315000-0.11288.69410.0003-2.1415
OTM
-3.54160.000717.23910.654515600-0.364117.0650.0006-3.6019
-3.65580.000718.0050.5915700-0.4317.84720.0007-3.6873
ATM-3.69270.000718.13920.520415800-0.500318.12730.0007-3.6912ATM
OTM
-3.55230.000717.69890.447415900-0.573817.81590.0007-3.507
ITM
-3.32130.000616.78350.373316000-0.647216.87810.0007-3.2526
-1.38150.00037.35760.089716500-0.90777.51640.0003-1.4151


Vega accounts for the risk that the option seller is taking based on the current and estimated volatility of the underlying asset. Increased volatility indicates that the underlying asset is more likely to experience extreme price fluctuations.


4. Theta (θ) - Theta of an option indicates the rate of change between the option price with respect to time. It is also known as an option's time decay. Theta indicates the amount an option's price would decrease as the time to expiration approaches, all else equal. For example, a trader has bought a call option with a theta of -0.70. The option's price would decrease by 70 paisa every day that passes, other factors being constant. Theta is high for options at-the-money and decreases when options are in- and out-of-the money. Also, the rate of decay increases as the time to expiration approaches for that option
                                                  

In the below example, the Nifty Spot value is around 15810 on 29th June for the options contract with the 29th July expiration date.        

Nifty Spot 15810


Calls
Strike
 Price
Puts
ThetaGammaVegaDeltaDeltaVegaGammaTheta
ITM
-2.00990.00038.37310.89315000-0.11288.69410.0003-2.1415
OTM
-3.54160.000717.23910.654515600-0.364117.0650.0006-3.6019
-3.65580.000718.0050.5915700-0.4317.84720.0007-3.6873
ATM-3.69270.000718.13920.520415800-0.500318.12730.0007-3.6912ATM
OTM
-3.55230.000717.69890.447415900-0.573817.81590.0007-3.507
ITM
-3.32130.000616.78350.373316000-0.647216.87810.0007-3.2526
-1.38150.00037.35760.089716500-0.90777.51640.0003-1.4151

                                                 

A negative theta indicates the option will lose value due to time decay.        


Theta is a friend for option sellers but not for buyers— as the value decreases from the buyer's side as time goes by but increases for the seller. The value of theta will be zero at the time of expiry.        

5. Rho (ρ) - Rho measures the sensitivity of an option or options portfolio to a change in interest rate. For example, a call option has a rho of 0.10 and a price of Rs.1.50. If interest rates rise by 1%, the value of the call option would increase to Rs.1.60, all else being constant. The opposite is true for put options. Rho is highest for at-the-money options and decreases further away. It may however be noted that option prices do not change much with changes in the risk-free rate.

Important points to consider about Option Greeks                            

  • Greeks do not work in a vacuum. They are constantly changing, and a change in one can affect all the other Greek   
  • Greeks help you analyze your exposure to various options centric risks related to the underlying asset movement, time and volatility.                            
  • Greeks can help you plan your trades to take advantage of or minimize, the effects of these risks                             
  • Greeks can help you manage your trades by showing how the trade exposure has changed with respect to these risks