**Introduction to Option Greeks Basics:** What are the makings of a great cricket match? Is it just that brilliant hundred by a batsman, or one 5 wicket haul by a bowler or is it that sparkling catch or run-out by the fielder. Or is a combination of all of these along with some crucial moments in the game.

Let us take the example of the inaugural World T20 final 2007. The biggest match of the tournament. The Arch rivals, “India Vs Pakistan”. No bigger setup in the world of cricket. But what made this match memorable was the quality of cricket played. India did eventually win the world cup final by 5 runs.

But what made this match unforgettable? Was it the innings by Gautam Gambhir (75 off 54 deliveries), was it the dash by Rohit Sharma (30 off 16 deliveries) that propelled India to a competitive score, was it the genius of Robin Uthappa to get a direct hit run-out of rampaging Imran Nazir, was it the onslaught by Misbah-ul-Haq or was it the masterstroke by none other, but M S Dhoni, to give last over to Joginder Sharma and seal the deal. I guess it was a mix of everything that made it an event to remember.

## What are Greek Options?

Similarly, the Option Greeks are the ingredients of the recipe which eventually helps in pricing the options. Option Greeks are various factors which help option trader in trading options. With the help of these Greeks, one is able to price the options premium, understand volatility, manage risk, etc. These Greeks also have a major impact on each other.

There are majorly four different types of option Greeks – Delta, Gamma, Theta, Vega, and Rho. We will be discussing all of them in this post.

Quick Note: If you’re new to options trading, you can read our series of articles on options here.

**Delta of an Option**

In simple terms, Delta measures the change in the value of premium with respect to change in the value of underlying. For a call option, the value of Delta varies between 0 and 1 and for a Put option, the value of Delta varies between -1 and 0.

**The above Option chain is for Nifty at 09:57 am. Nifty spot is trading at 9320.**

**The above Option chain is for Nifty at 10:07 am. Nifty spot is trading at 9316.**

Now, form the above two tables, it is clear that with a small change in the value of Nifty, the premium for the option changes. The premium for 9100 CE in the first option chain is 291.65 and in the second option chain is 289.40.

Now, say if I were bullish on the market, so how would I find the premium for all the strike price if I were to expect the Nifty spot to be trading at 9400 by End of Day. So, this is where **Delta** comes into the picture.

**For a call option**, assume the delta for a strike price is 0.40. So for every 1 point change in the value of underlying, the value of premium will change by .40 points. Say, if I had bought 9350 CE at a premium of 142.70. The Nifty spot price is 9316 and the Delta for this option is .40. And if by the End of the day, the spot price of Nifty jumps to 9350.

So the change in the Premium will be = (9350-9316)*0.40 = 14.4 points. So the new Premium will be = 157.1. Similarly, if the spot price were to come down to 9250, then the change in the Premium will be = (9250-9316)*0.40 = 26.4 points. So the new premium in this case will be = 142.7-26.4 = 116.3.

**Delta value dependency on the Moneyness of an Option**

The value of the Delta is derived using the Black & Scholes model. Delta is one of the output form this model. The Moneyness of the contract helps in deciding the value of Delta:

Moneyness | Delta Value (Call Option) | Delta Value (Put Option) |
---|---|---|

In the Money | 0.6 to 1 | -0.6 to -1 |

At the Money | 0.45 to 0.55 | -0.45 to -0.55 |

Out of Money | 0 to 0.45 | 0 to -0.45 |

**Delta of a Put Option: **The delta of a Put option is always negative. The value ranges between -1 to 0. Let us understand it with the help of a situation. Say the spot price of Nifty 9450. And the strike price in consideration is 9500 PE (Put option). The Delta for this option is (-) 0.6 and the premium is 110.

Now, in Scenario 1, if the spot price of Nifty goes up by 80 points, then

New Spot price = 9530

Change in Premium = 80*(-.6) = -48 points

So the New Premium = 110-48 = 62. In case of Put options if the spot price of underlying asset goes up, then the premium is reduced (the premium and spot price of Put option are negatively co-related)

In Scenario 2, if the Spot price goes down by 90 points, then

New Spot price = 9360

Change in Premium = 90*(-.6) = 54 points

The New premium = 110+54 = 164 points

**Risk profiling for choosing Delta**

The risk taking ability of a trader has an impact in choosing the right strike price. It is always advisable to avoid trading in Deep out of Money Options as the chances of those options expiring In the money is like their Delta (5% to 10%). For a Risk Taker trader, a slight out of Money or At the Money contracts are the best strategy. A Risk Averse trader should always avoid trading Out of Money contracts. They should always trade At the Money or In the Money contracts as the chances of trade expiring in their favour is significantly higher than Out of Money contracts.

## Gamma of an Option

As we have seen, the Delta of an option measures the change in the value of premium with respect to change in the value of underlying. The value of delta also changes with the change in the value of underlying. But how does one measure the change in the value of delta? We introduce you to ‘GAMMA’.

Gamma measures the change in the value of Delta with respect to change in the value of underlying. Gamma calculates the Delta gained or lost for a one-point change in the value of underlying. One important thing to remember here is that Gamma for both Call and Put option is positive. Let’s understand:

Spot price of Nifty: 10000

Strike price: 10100 CE

Call Premium: 25

Delta of option: .30

Gamma of option: .0025.

Now if Nifty goes up by 100 points, then

New Premium = 25 + 100(.3) = 55

Change in Delta will be = Change in Spot price * Gamma = 100*.0025 = .25

New Delta will be = .30+.25 = .55 (Option is now an At the Money contract)

Similarly if Nifty goes down by 70 points, then

New premium = 25 – 70(0.3) = 4

Change in Delta will be = Change in Spot Price * Gamma = 70*.0025 = 0.175

New Delta Will be = .30-.175 = 0.125 (Option is now a Deep Out of Money contract)

**Gamma Movement**

The movement of the gamma changes and varies with the change in the Moneyness of a contract. Just like Delta, the movement in Gamma is the highest for At the Money contracts and it is least for Out of Money contracts. So, one should ideally avoid selling/writing At the Money contracts. Out of money contracts are the best ones to write as they have a very good chance of expiring worthless for option buyer and the seller can pocket the premium.

Also read: Introduction to Candlesticks – Single Candlestick Patterns

## Theta of an Option

Theta is an important factor in deciding option pricing. They uses time as an ingredient in deciding the premium for a particular strike price. Time decay eats into the option Premium as it nears expiry. Theta is the time decay factor i.e., the rate at which option premium loses value with the passage of time as we near expiry. If we could recall, Premium is simply the summation of Time Premium and Intrinsic value.

**Premium = Time premium + Intrinsic value.**

Say, The Nifty spot is trading at 9450 and the strike taken into consideration is 9500 CE (call option). So the option is currently out of Money. There are 15 days to expiry and the premium charged for this option is 110. Now, the Intrinsic Value (IV) of this option = 9450-9500 = -50 = 0 (Since IV cannot be negative)

Now, Premium = Time value + IV

=> 110 = Time value + 0, hence the time value for this Out of Money option is 110 i.e., the buyer is willing to pay a premium for an Out of Money option. So, the analogy “**TIME IS MONEY**” holds true in case of options pricing.

Let’s take another example:

- Say, Time to expiry = 15 days, Spot price of share of XYZ company = Rs. 95, Strike price = 100 CE, Premium = 5.5
- Now, if the spot price of XYZ = 96.5, time to expiry = 7 days, then for the same strike the Premium reduces to 3
- Again if the share price increases to 98.5, for same strike price and with just 2 days to expiry, the premium reduces to 1.75
- Therefore, from the above example it is clear that even though the spot price is moving towards the strike price, the premium is reduced as the time remaining to make a substantial move above strike price is reduced. The option has less chances of expiring In the Money.
**The Greek Theta is a friend to Option writers.**It is advisable for option writers to write/sell the option at the starting of contract as they will be able rise the premium erosion with passage of time.

So from the above example, it is clear that the value of **Premium is Depreciating** with the passage of time.

## Vega of an Option

Vega as a Greek is sensitive to the current volatility. It is one of the most important factors in determining the option pricing. Volatility is simple terms is the rate of change. Vega simply signifies the change in the value of an option for 1% change in the price of underlying asset. Higher the volatility of underlying asset, the more expensive it is to buy the option and vice versa for lower volatility.

Say the spot price of XYZ Company is Rs. 250 on 5th May and the 270 call option is trading at a premium of 8.

Let’s assume that the Vega of the option is 0.15. And the volatility of the XYZ Company is 20%.

If the volatility increases from 20 % to 21%, then the price of the option will be 8+0.15 = 8.15

And similarly, if the volatility goes down to 18%, then the price of the option will drop to 8 – 2(0.15) = 7.7

**Key Takeaways**

If options is a team, then it has various players are Option Greeks like Delta, Gamma, Theta, Vega, volatility, etc. Each and every Greek has its own pivotal role in finding the exact pricing of the option. They play a pivotal role in deciding the Moneyness of the option.

A simple and clear understanding of all the Greeks goes a long way in deciding the right strike price and right option strategy. Risk Management both for option writers can be handled with a better understanding of the Greeks. Option buyers should ideally avoid trading Out of Money options and Option sellers should ideally write/sell Out of Money Options.

Hitesh Singhi is an active derivative trader with over +10 years of experience of trading in Futures and Options in Indian Equity market and International energy products like Brent Crude, WTI Crude, RBOB, Gasoline etc. He has traded on BSE, NSE, ICE Exchange & NYMEX Exchange. By qualification, Hitesh has a graduate degree in Business Management and an MBA in Finance. Connect with Hitesh over Twitter here!