Professional Trading through Option Theory

Lesson -> Delta - 'The option Greek' Section -1

9.1 -Outlook

Yesterday, I watched the latest Bollywood flick 'Piku. Quite nice I must say. It was a very enjoyable movie. I found myself wondering what made me like Piku. Was it the story, Amitabh Bachchan’s amazing acting, Deepika Padukone’s charm, or Shoojit Sicar's stunning direction. It was probably a combination of all these elements that made the movie so enjoyable.

I was also struck by the striking similarities between an option trade and a bollywood film. An options trade must be successful on the market, just like a bollywood film. These forces are collectively known as 'The Option Greeks. These forces can influence the premium of an option contract on a minute-by-minute basis. These forces can not only affect the premiums directly, but they also have an indirect influence on each other.

This is why you should think of these two actors from Bollywood - Aamir Khan & Salman Khan. They are two independent actors (similar to the option Greeks of Bollywood) that movie buffs will recognize. The outcome of the movie can be influenced by them individually (think of it as an option premium). If you have both of these men in one movie, there is a good chance they will pull each other down and push each other to be better. Can you see the juggling? Although it may not be the best analogy, I hope you get a better understanding of what I am trying to convey.

Options Premiums, options Greeks, and the natural demand-supply environment of the markets all have an impact on each other. Each of these factors can act as an independent agent but they all interact with each other. The final outcome of this combination can be seen in the option's cost. Options traders must be able to evaluate the premium variation. He must understand how these factors interact before he can setup an option trade.

Without much further ado let me introduce you to the Greeks -

  1. Delta- This measure the rate at which options premiums are changing based on the direction of the underlying
  2. Gamma- The rate of change in the delta itself
  3. Vega - Rate of premium change based on volatility change
  4. Theta- Measures premium impact based on expiry time

These Greeks will be discussed in the following chapters. This chapter focuses on understanding the Delta.

9.2 - Understand the Delta of an Option

These two snapshots are from Nifty's 8250 CE option. The first snapshot was taken on 09:18 AM, when Nifty spot was at 89292.

A while later...

Notice the premium change - Nifty was at 829 at 09:18 PM the call option was trading for 144 at that time, but at 10:00 AM Nifty traded at 8315 and the same call option traded at 150 at 10:00 AM

Here's a snapshot from 10:55 AM. Nifty fell to 8288, and the option premium dropped to 133.


One thing is clear from the above observations: as the spot value changes, so does option premium. As we all know, the premium for call options increases with an increase in spot value.

This is a good example of how to keep things in perspective. Imagine that you predicted that Nifty would reach 8355 today at 3:00 pm. The above snapshots show that the premium will change, but how much? Is the premium of 8250 CE likely to increase if Nifty hits 8355?

So exactly here comes the 'Delta of an option'. The Delta is a measure of how an option's value changes in relation to the change made by the underlying. The Delta of an option, in simpler terms, is the ratio of an option's value to the change in the underlying. It answers the following questions: "By how much will the option premium change for every one point change of the underlying?"

The Option Greek's "Delta" captures the impact of market direction on the Option premium.

The delta number is a number that varies.

  1. Some traders prefer the 0-10 scale for call options. The delta value of 0.55 for the 0-1 scale is equivalent to 55 for the 0-100 scale.
  2. For a put option, the delta value is between -1 and 0. (-100 to 0,). The delta value of -0.4 is equal to -40 on a scale from -100 up to 0
  3. Soon, we will understand why the delta of the put option has a negative value.

This is the stage where I would like to give you an overview of the chapter's structure. Please keep this in mind, as it will help you connect the dots better.

  1. We will discuss how to use the Delta value in Call Options
  2. Here's a quick overview of how the Delta values were arrived at
  3. Learn how to use the Delta value in Put Options
  4. Delta Characteristics – Delta vs. Spot and Delta Acceleration (continued at the next chapter).
  5. Optional positions in terms Delta (continued at next chapter).

Let's get on the road!

9.3 -What is Delta Call Option?

The delta can be described as a number between 0 to 1. Let's say a call option has an delta of 0.3, or 30, what does that mean?

As we all know, the delta is the rate at which the premium changes for each unit of underlying change. A delta of 0.3 means that for every 1 unit change in the underlining, the premium will likely change by 0.3 units. Similarly, for every 100 points in the underlying, it is likely that the premium will change by 30 percent.


You can understand this from given example-

Nifty at 10:55AM is at 8288

Option Strike = 8250 Call Options

Premium = 133

Delta of the option = + 0.55

Expect Nifty to Reach 8310 at 3:15PM

What is the expected premium value of an option at 3:15 pm?

This is easy to calculate. The Delta of the option is 0.55. This means that for every 1 point increase in the underlying premium, the premium will change by 0.55.

The underlying is expected to change by 22 percentage points (8310-8288). Therefore, the premium should increase by

= 22*0.55

= 12.1

The new option premium should trade at 145.1 (133+12.1).

What is the sum of premiums old and expected premium changes?

Let's take another example: what happens if there is a drop of Nifty? What happens to the premium? Let's figure it out.

Nifty at 10:55AM is at 8288

Option Strike = 8250 Call Options

Premium = 133

Delta of the option = 0.55

Expect Nifty to hit 8200 at 3:15PM

What is the expected premium value at 3:15 p.m.?

We expect Nifty to fall -88 (8288 - 8200) and therefore the premium will increase by -

= -88 * 0.55

- 48.4

The premium should trade at around

= 133 - 48.4

= 84.6 (new premium value).

The two above examples show that the delta is used to evaluate premium value based upon the direction of the underlying. This information is very useful when trading options. Let's say you anticipate a huge 100-point uptrend in Nifty. Based on that expectation, you decide to purchase an option. You have two call options, and you must decide which one to purchase.

Call Option 1 has a delta value of 0.05

Call Option 2 has an average delta of 0.2

The question now is: Which option do you want to buy?

Let's do some math and find out the answer.

Change in the underlying = 100 points

Call option 1 Delta = 0.05

Call option 1 premium change = 100

= 5

Call option 2 Delta = 0.2

Call option 2 premium change = 100 * 0.2

= 20

As you can see, a 100-point move in an underlying has different effects for different options. The trader would be better buying Call Option 2 in this instance. This should give you an idea - the delta can help you choose the best option strike to trade. There are many other dimensions to this equation, which we'll explore shortly.

Let me ask a very important question at this point: Why is the delta value of a call option limited to 0 or 1? Why can't the delta value for a call option go beyond 0 or 1?

Let's look at two scenarios that will help us understand the situation. In each case, I will deliberately keep the delta value between 1 and 0.

Scenario 1 - Delta greater than 1 to call option

Nifty @ 10:55AM at 8268

Option Strike = 8250 Call Options

Premium = 133

Delta of the option = 1.5 (purposely keeping above 1)

Expect Nifty to Reach 8310 at 3:15PM

What is the expected premium value at 3:15 p.m.?

42 points = Change in Nifty

The premium change (considering that the delta is 1.5), will therefore be 1.5

= 1.5*42

= 63

Is that something you noticed? This means that premium value is rising by 63 points for every 42-point change in the underlying. The option is now worth more than the underlying. The option is a derivative contract. It derives its value form its respective underlying. Therefore, it cannot move faster than the latter.

The delta of an option that is greater than 1 indicates that it is in line with its underlying. A delta value higher than 1 is not acceptable. The delta value for an option can be set to either 1 or 100.

Let's continue the logic and see why the delta for a call option has a lower bound than 0.

Scenario 2 - Delta less than 0 for the call option

Nifty @ 10:55AM at 8288

Option Strike = 8300 Call Option

Premium = 9

Delta of the option = 0.02 (have intentionally changed the value to lower than 0, thus negative delta).

Expect Nifty to hit 8200 at 3:15PM

What is the expected premium value at 3:15 p.m.?

Change in Nifty =88 points (8288-8200).

The premium change (taking into account the delta) is therefore -0.2

= -0.2*88


We will assume for a moment that this is true. Therefore, a new premium will be

= -17.6 + 9.


This case shows that if the delta of a call option is below 0, it is possible for the premium to drop below 0. However, this is not possible. Remember that the premium, regardless of whether you make a call or a put, can never go negative. The delta for a call option is therefore lower bound than zero.

9.4 - Who determines the value for the Delta?

One of many outputs of the Black & Scholes option pricing model is the value of the Delta. The B&S formula, as I mentioned in the module, takes in many inputs and produces a few key outcomes. This output also includes other Greeks and the option's Delta value. To help us better understand options, we'll also discuss all the Greeks. For now, however, it is important to remember that the B&S formula calculates the delta and other Greeks as market driven values.

Here's a table that will help you determine the delta value of a particular option.

You can also use a B&S pricing calculator to determine the exact delta for an option.

9.5- What is Delta for a put option?

Recall that the Delta of a Put Option can range from -1 to 0. This negative sign illustrates the fact that premiums decrease when the underlying value increases. Keep this in mind and consider the following:

Notice - 8268 can be used as an ITM option. The delta is therefore around -0.55 (as shown in the table).

It is important to determine the new premium value, taking into account the –0.55 delta value. Pay attention to the following calculations.

Case 1 - Nifty will move to 8310

Expected Change = 8310 -8268

= 42

Delta = - 0.55

= -0.55*42

= 23.1

Current Premium = 128

New Premium = 128 -23.1

= 104.9

Since I know that a Put option's value decreases when its underlying value is higher, I am subtracting delta.

Case 2 Nifty will move to 8230

Expected Change = 8268-8230


Delta = - 0.55

= -0.55*38

= 20.9

Current Premium = 128

New Premium = 128 + 20.9

= 148.9

Since I know that a Put option's value increases when its underlying value is lower, I am adding delta to this equation.

With the two illustrations above, I hope you now understand how to use the Put Option’s delta value to determine the premium value. I won't go into detail about why the Put Option delta is between -1 and 0.

To be more specific, I encourage readers to use the same logic that we used to explain why the delta of the call option is between 0 & 1, and why the delta of the Put option is between -1 & 0.

We will continue to explore Delta and learn some of its unique characteristics in the next chapter.


  1. Option Greeks are forces that affect the premium of an option
  2. Delta is an Option Greek which captures the effect on the direction of market
  3. Some traders prefer to use between 0 and 1 for call option delta, while others prefer 0 to 100.
  4. The put option delta can vary between -1 to 0 (-100 up to 0).
  5. A negative delta value for a put option indicates that the option premium or underlying value is moving in the opposite direction
  6. ATM options offer a delta of 0.5
  7. ITM options have a delta close to 1
  8. OTM options have a delta close to 0.