# What Is Delta In Options? Explained With 7 Easy Examples and Analysis

In this post we will be learning about what is delta in options? and how knowing delta of an option helps you as an option trader. There is a very important term which should be to known to an option trader termed as Option Greeks.

The Option Greeks represent the unanimity of the stock market.

It help us to know how the option will behave to changes in certain variables attached with the pricing of an option contract. Greeks is a term used in the options trading to represent the different dimensions of risk involved if you take any position in option trading.

Before we go in depth in to option Greeks and delta i would request you to have Basic understanding of options ,Option moneyness and How to read option chain table?

Having said that let us now understand deeply what is Delta of an Option and how it will be enhancing your option trading?

There are majorly four Greeks one should be aware i.e. Delta, Gamma, Vega, Theta.

1. Delta – Delta is the amount an option price (premium) is expected to move based on a 1 rupee change (up or down) in the underlying stock or index.
2. Gamma – It helps in measuring Rate of change of delta.
3. Vega – This calculate rate of change of premium depending up on change in volatility.
4. Theta – It helps in knowing the effect on premium in respect to days or time left for expiry

We will be learning all these option Greeks in forthcoming blogs. As of now let us concentrate on first and most important delta in options.

## What Is Delta In Options?

In general you might have heard of this word Delta if you have studied math’s, physics or geography. The Greek uppercase letter delta is the standard mathematical symbol to represent change in some quantity. Where as in general physics, delta-v is simply a change in velocity.

However in options “Delta is the amount an option price (premium) is expected to move based on a 1 rupee change in the underlying stock”.

In other words Delta of an option helps in Measuring how an options value changes with respect to the change in the underlying.

Most of the beginners in option trading assume that when a stock moves Rs.1, the price of options premium based on that stock will move more than Rs.1.

Always remember the option is a derivative contract, it derives its value from its respective underlying, it can never move faster than the underlying. In reality it does not work like this at all.

This is when we need to be aware of Delta of an option. By knowing this you will be able to find ” how many points will the option premium change for every 1 point change in the underlying.

### What is Delta of an Option Understanding through Example?

As an illustration for you i clicked a snapshot of Nifty 50 trading at 11,145 (Green box) in spot. The strike price selected is 11000 C.E. Now the premium value is showing Rs.196.25. Now Observe the change in premium just after 40 minutes at 15:11 p.m IST. Underlying value of Nifty50 in spot market trading at 11080 (green box). As a matter of fact notice change in premium value it declined to Rs. 155 from Rs.196.25. What do you think why there is change in nifty premium value? Notice, underlying is down about 11145-11080 = 65 points, whereas the decline for the premium for same strike price (11000 CE) is 196-155= Rs.41.

Observation that you can withdraw from above is when the value of the spot changes, the value of option premium also changes.

But this thing we already know, call option premium increases with the increase in the spot value and vice versa, but do we know by how much? What will be the value of the 11000CE premium if Nifty reaches 11200 in spot market?

In fact this is precisely where the ‘Delta of an Option’ becomes very important. As we learned above the delta, evaluate how an options value changes with respect to the change in the underlying.

#### What Exactly is delta ?

• The delta is a number which fluctuates Between 0 and 1 for a call option, sometime it also referred as 0 to 100 scale. Suppose the delta value of 0.30 on 0 to 1 scale is identical to 30 on the 0 to 100 scale.
• For a put option its ranges Between -1 and 0 or -100 to 0. Similar to Call option the delta value of Put option can be calculated as -0.50 on the -1 to 0 scale is equal to -50 on the -100 to 0 scale . ## How Delta for a Call Option(C.E)Works?

Now we know the delta is a number that fluctuates between 0 and 1. Let us try to understand through an example how exactly it works in case of a call option.

To begin with Assume for now a call option (C.E) has a delta of 0.6 or 60. We will learn from where you will get delta values and how later.

As we know Delta of an option helps in measuring how an options value changes with respect to the change in the underlying, So a delta of 0.60 indicates that for every 1 point change in the underlying (Spot), the premium is likely to change by 0.60 units.

In other words for every 100 point change in the underlying the premium is expected to change by 60 points.

Let’s calculate impact on premium of a call option now:

Suppose on a given day Nifty is trading at 11000 in morning at 10 A.M. You selected to trade a call option

Choose Option Strike = 10900 Call Option (C.E)

Premium value = 150

Delta of the option = + 0.60

You are expecting Nifty to move and reach in spot 11150 @ 3 PM

Can you calculate what will be the expected option premium value at 3 PM?

Lets calculate it:

We know the Delta of the option is 0.60, which means for every 1 point change in the underlying the premium is likely to change by 0.60 points.

We are expecting the underlying value of Nifty to change by 50 points (11150 – 11000), therefore the premium value is likely to increase by

= 50*0.60

= 30, Our older premium value was at 150 in morning

Whereas new option premium is expected to trade around 180 (150+30) old premium + expected change in premium.

Similarly in case if nifty drops by let’s say 80 points from the morning value of 11000. Currently trading @10920 What will happen to the premium? Just repeat the above calculation we did.

=-80*0.60

= -48 our older premium was @150 now the expected premium value will be 150-48=102 (new premium value )

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### What is the use of Delta In Options?

From the above two examples, we can conclude that the delta helps us to evaluate the premium value depending upon the change in the value of underlying.

But what to do by knowing this, see if you know the probable value of change in premium, you can select correct strike price while trading option. Delta helps you to select the right option strike to trade in market.

For example: You heard some news which will be impacting the stock market. Next day you thought of buying an call option, which strike price would you be selecting to garner maximum benefit.

Furthermore, assume you expect a huge 150 point up move on Nifty, and based on this presumption you decided to buy an option. However you are confused to choose strike price. This where knowing delta is important while trading options.

Example 1:

1st Call Option delta = 0.09

2nd Call Option delta = 0.3 which option will you choose to buy?

Expected Change in underlying = 150 points

Change in premium for call option 1 = 150 * 0.09 (Expected change in option premium = Option Delta * Points change in underlying)

= 13.50

Change in premium for call option 2 = 150 * 0.3

= 45

As you can see 150 point move in the underlying has different effects on different options. Distinctly buying option 2 would be better choice.

#### Why delta value for a call option always ranges between by 0 and 1:

The delta value for a call option always ranges between by 0 and 1 but why? Why can’t the call option’s delta go beyond 0 and 1?

It is because the moment you keep delta value above 1, option will be gaining more value than the underlying itself.

An option is itself a derivative which derives its value from the underlying assets hence it can’t be more than the actual spot value. It can be equal but never more.

To illustrate further let’s take an example :

When Delta is greater than 1 for a call option:

Suppose Nifty is trading 11200 in morning at@ 10 AM

We are choosing Option Strike price  = 11100 C.E

Premium value = 100

Considering Delta of the option as = 2 (instead of 1)

We are expecting Nifty to touch around 11270 at the end of market around 3 PM

Let’s calculate premium value at 3 PM :

Change in Nifty from morning to afternoon = 11270-11200 = 70

Change in premium = 2 *70

= 140

Did you able to find what happened exactly ? Check once again the nifty spot value changed 70 points where as the premium value changed 140.

This is not possible as option is itself a derivative which derives its value from the underlying assets hence it can’t be more than the actual spot value. It can be equal but never more.

That is why the delta of an option is fixed to a maximum value of 1 or 100. Now it’s an homework for you to check why the delta can’t be below zero for a call option. (Hint :  the premium irrespective of a call or put can never be (-)negative). ## What is Delta for a Put Option?

We learned at the beginning, Put Option fluctuated from -1 to 0. As we know put option buyer thinks the securities will fall and he buy put option to benefit from fall. The negative sign in front is to explain – when the underlying gains in value eventually value of premium goes down.

Before we begin to understand few things to remember:

• Value of Put option (premium) declines when the underlying value (spot price ) increases.
• Where as value of Put option (premium) gains when the underlying value (spot price) decreases.

To understand it better let’s consider an example :

In case of Nifty rising above spot value :11300

Nifty value in spot market – 11300
Strike price chosen – 11200
Premium value – 140
Assuming Delta @  -0.40
Expected change in Nifty Value  11380

Expected change = 11380 – 11300 = 80

Delta = – 0.40

= -0.40*80

= -32

Current Premium value = 140

New Premium value= 140-32

= 108

In case we are expecting nifty to fall from its spot value : 11300

Nifty expected move = 11220

Expected change = 11300 – 11220

= 80

Delta considered = – 0.40

= -0.40*80

= -32

Current Premium value = 140

New Premium =  140+ 32 (The reason we are adding as we know when nifty spot values goes down, the premium value of put option increases)

= 172

Now you might be thinking why I added the delta value to the premium instead of subtracting. Please go back above I told you to remember 2 points.

Value of Put option (premium) declines when the underlying value (spot price ) increases. So if spot moves up, the call option delta increases and the put option delta decreases.

When it comes to put options, there is negative association between price of the underlying and option price. Above all Put option premium inversely proportional to spot price.

Where as value of Put option (premium) gains when the underlying value (spot price) decreases. For this reason I’m adding the value of delta since the value of a Put option (premium) gains when the underlying value decreases.

As a matter of fact the premium of Put option increases with the decrease in the spot price.

#### Few important thing to remember:

• Call option lose value when the underlying drops in value. As a result Delta is +ve for call option.
• Call option gains value when the underlying gains in value. As a result Delta is +ve for call option.
• Put option gains value when the underlying drops in value. Delta is -ve for put option.
• Put option loses value when the underlying gains in value. Delta is -ve for put option .
• Expected change in option premium = Option Delta * Points change in underlying
• ATM options have a delta of 0.5
• ITM option have a delta of close to 1
• OTM options have a delta of close to 0
• For put option just use -sign in front
• Put option delta ranges between -1 and 0
• Call option delta ranges between 0 and 1

Also just a reminder to known moneyness of an option :

For Call options :  ITM – ATM – OTM. So all strike below ATM are ITM and all above are OTM.

For Put options  : OTM – ATM – ITM. So all option strikes above ATM are ITM.

### Where to find value of the Delta?

Black-Scholes is a pricing model used to decide the fair price for a call or a put option. This is based on various different variables such as Dividends, volatility, type of option, underlying stock price, time, strike price, and risk-free rate.

Delta and other Greeks are market driven values and are calculated by the B&S formula. You can find out the exact delta of an option by using a B&S option pricing calculator. It is easily available on google.

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Majority for online top brokers such as Upstox, Zerodha, Fyers and 5Paisa have this calculator in built in their trading platform.

Meanwhile you can also check this table below to know the approx. delta value of a option:

Type of Option
Precise Delta value for Call Option
Precise Delta value for Put Option
Deep ITM
Between + 0.8 to + 1
Between – 0.8 to – 1
Slightly ITM
Between + 0.6 to + 1
Between – 0.6 to – 1
ATM
Between + 0.45 to + 0.55
Between – 0.45 to – 0.55
Slightly OTM
Between + 0.45 to + 0.3
Between – 0.45 to -0.3
Deep OTM
Between + 0.3 to + 0
Between – 0.3 to – 0

‌In case you want to calculate it using formula in the first place you should be aware of following things:
1. Dividends – Check if company is providing any dividend in between the expiry of your contract.
2. Volatility – You can find this information easily from NSE website under option chain.
3. Type of option – Select which type of options your are trading ,Call option (C.E) or Put option (P.E)
4. Underlying Stock Price – The current price or spot price in market
5. Time – Expiry or no. of days left for contract
6. Strike Price – Need to select the strike price you are thinking to trade.
7. Risk -Free Rate – Interest or risk free rate is what currently prevailing in our economy. You need to check the current RBI 91 day Treasury bill rate for this purpose. You can get the rate from the RBI website. Click on market trends you will find the information. ## Conclusion:

Option trading involves various factors working at the same time. This is one of the factor impacting the premium for options. I Hope you have thoroughly understood what is delta in options and its functioning area, and you may use it in option trading next time instead of just mere speculation while selecting the strike price.

Another thing you need to keep in mind, delta will behave normal at the start of the contract as the time lapses there are other variables which makes a effect on the options contract.

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