10. My big fat greek wedding: relationships between the greeks
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In this module, we kept harping on the Option Greeks, namely, delta, gamma, theta and vega. Like most things in life and finance, these option Greeks are related! Let’s learn what their relationship is like!
Let’s Dive Into an Example!
Have you ever watched a cricket match that was simply astounding? Do you remember what made it so special? Did a batsman strike a quick hundred or did a bowler land a hattrick? Was it a spectacular catch with which the fielder enchanted everyone? Or was it a combination of all of these moments along with other crucial moments in the game?
Let’s look back on the inaugural World T20 final 2007. Handsdown, the biggest match of the tournament was when arch rivals, India and Pakistan met on the field. For most people, these two teams playing against one another for a final is exciting enough, but what made this match even more memorable was the quality of cricket played. Gautam Gambhir played a fantastic innings with 75 off 54 deliveries, Rohit Sharma scored 30 off 16 deliveries and Joginder Sharma bowled a fabulous last over. It was a mix of all these successes that came together to make India victorious.
It’s a similar story with our dear Option Greeks!
What are Option Greeks?
Option Greeks are the ingredients of a recipe that eventually come together to make a wholesome dish. Using these Greeks, traders can price options premium, understand volatility and manage risk. These Greeks, namely, Delta, Gamma, Theta and Vega also have a major impact on each other.
1. Delta : Measure of option price sensitivity to changes in stock price.
Delta is the most popular Greek used by option traders as it measures the degree to which the price of the option will change according to market dynamics.
 It is calculated separately for call and put options.
 Calls have positive delta and puts have a negative delta.
2. Gamma: Measure of option price sensitivity to changes in Delta.
Gamma is a second level derivative and is widely used by option traders. It measures the degree to which the delta of an option will change according to market dynamics.
 It is calculated separately for call and put options of the same strike.
 It measures the momentum.
3. Theta: Measures the time decay of an option as we move towards expiry.
Theta is one of the most popular Greeks used by the option sellers, for whom profits are limited to premiums and losses are unlimited. It measures the degree to which the option price will decay with every passing day.
 It is also called a measure of time decay.
 It is always negative because the value of an option always goes down with each passing day.
 It only refers to the decay of time value and not of the intrinsic value of the option.
4. Vega: Measures the sensitivity of the option price to changes in volatility.
Vega measures the amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage point.
 Volatility impacts the call and puts options in a similar fashion.
 Increase in volatility will increase the value of call and put options while a fall in volatility will decrease the value of call and put options.
Wrapping Up
Take a look at the table below and observe the relationship between the option Greeks.
RIL CMP 
1110 
The current base price of the instrument, e.g., the closing price of Reliance Industries on 26th Nov 2018 

Exercise Price 
1100 
The price at which the underlying instrument will be exchanged. Also called Strike Price 

Today's Date 
27112018 

Expiry Date 

Historical Volatility 
25% 
The Historical Volatility of the asset's returns 

Risk Free Rate 
6.00% 
The current risk free interest rate i.e. your return on cash held in the bank 

Dividend Yield 
0.00% 
The Annualized Dividend Growth Rate of the Stock 

Call Option 
Put Option 

Theoretical Option Price 
39.8145 
24.4032 

Delta 
0.5913 
0.4087 
The amount that the theoretical price will change if the market moves up/down 1 point 

Gamma 
0.0049 
0.0049 
The amount that the Delta will change if the market moves up/down 1 point 

Theta 
0.6164 
0.4365 
The amount that the theoretical price will change when 1 day passes. 

Vega 
1.2361 
1.2361 
The amount that the theoretical price will change if the volatility of the asset moves up/down by 1 percentage point 

Rho 
0.5067 
0.3929 
The amount that the theoretical price will change if interest rates move up/down by 1 percentage point 

Call Option 
Put Option 

Market Price 
45.75 
28.90 
Overpricing and Underpricing 

Implied Volatility 
29.79% 
28.63% 
The volatility that is implied by the market prices of the option 
A Quick Recap
 There are four option Greeks: Delta, Gamma, Theta and Vega.
 Delta is the measure of option price sensitivity to changes in stock price.
 Gamma is the measure of option price sensitivity to changes in Delta.
 Theta measures the time decay of an option as we move towards expiry.
 Vega measures the sensitivity of the option price to changes in volatility.
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