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

27-11-2018

     

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 Under-pricing

 

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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