Delta for a Call Option
The delta of a call option is a number between 0 and 1, in this case, 30 or 0.3. This informs us how the price of an option changes in relation to price movements of the underlying asset.
We can ascertain that the delta measures the rate of change of premium with every move in the underlying. With a 0.3 delta, it can be assumed that for each single point shift in the underlying, there will be a corresponding movement of 0.3 units in the premium or 30 points for each 100-point variation in the underlying.
Example 1:
Nifty @ 10:55 AM is at 11,500
Option Strike = 11,400 Call Option
Premium = 220
Delta of the option = +0.40
Nifty @ 3:15 PM is expected to reach 11,550
What can we expect the option premium value to be at 3:15 PM?
Given the Delta of the option being 0.40, we can calculate that any move of 1 point in the underlying will result in an equivalent 0.40-point change in the premium. We anticipate a 50-point increase in the underlying price (11,550 – 11,500), which leads to an expected increase in premium:
= 50 * 0.40
= 20
Therefore, the new option premium is expected to trade around 240 (220 + 20), which accounts for the old premium plus the expected change.
Example 2:
Nifty @ 10:55 AM is at 11,500
Option Strike = 11,400 Call Option
Premium = 220
Delta of the option = 0.40
Nifty @ 3:15 PM is expected to reach 11,400
What is the likely premium value at 3:15 PM?
We anticipate that Nifty will drop by 100 points, from 11,400 to 11,500, resulting in a decrease in the premium.
= -100 * 0.40
= -40
Therefore, the premium is expected to trade around
= 220 – 40
= 180 (new premium value)
By analysing the delta of the call options, you can quickly determine which one to buy. The delta provides an idea of how much the premium value is expected to gain with a 100-point move in Nifty.
Call Option 1 has a delta of 0.10
Call Option 2 has a delta of 0.30
To decide which option to buy, let’s calculate the change in premium for each:
Change in underlying = 100 points
Call Option 1 Delta = 0.10
Change in premium for Call Option 1 = 100 * 0.10= 10
Call Option 2 Delta = 0.30
Change in premium for Call Option 2 = 100 * 0.30= 30
Based on these calculations, Call Option 2 is expected to have a larger change in premium, making it a more favourable choice.
It’s clear from this example that the delta can help traders pick the best option strike to trade. However, there’s more to it than that – we’ll discuss additional factors soon.
At this juncture, an essential query arises – What is the rationale behind the restriction of delta for a call option between 0 and 1? What is stopping it from going above or below those limits?
To gain insight into this, I will present two situations where the delta value is set above 1 and below 0.
Scenario 1: Delta greater than 1 for a call option
Nifty @ 10:55 AM is at 12,000
Option Strike = 11,800 Call Option
Premium = 200
Delta of the option = 1.8 (intentionally set above 1)
Nifty @ 3:15 PM is expected to reach 12,300
What is the likely premium value at 3:15 PM?
Change in Nifty = 300 points
Therefore, the change in premium (considering the delta is 1.8)
= 1.8 * 300
= 540
This implies that a 300-point shift in the underlying results in a 540-point increase in the premium. It’s important to note that the option’s value cannot surpass that of its underlying asset since it is a derivative contract.
A delta of 1 is ideal, indicating that the option is closely tracking its underlying asset. Any delta value greater than 1 is considered nonsensical and is typically capped at either 1 or 100.
Let’s apply the same reasoning to understand why the delta of a call option is never less than 0.
Scenario 2: Delta lesser than 0 for a call option
Nifty @ 10:55 AM is at 12,500
Option Strike = 12,800 Call Option
Premium = 50
Delta of the option = -0.3 (deliberately set below 0, resulting in a negative delta)
Nifty @ 3:15 PM is expected to reach 12,200
What is the likely premium value at 3:15 PM?
Change in Nifty = -300 points (12,500 – 12,200)
Therefore, the change in premium (considering the delta is -0.3)
= -0.3 * -300
= 90
Just for this example, let us assume that this is correct. Therefore, the new premium would be
= 90 + 50
= 140
This scenario clearly demonstrates why the delta of a call option cannot be lower than 0. Remember that the premium of both call and put options can never be negative. Thus, if the delta of a call option drops below 0, the premium would go below 0, which is an impossible scenario.
–How is the value of delta decided, and by whom?
The Black & Scholes option pricing formula takes in a variety of inputs and outputs some key values, such as the delta. As previously stated, later on in this module we will explore the B&S formula more closely to gain further understanding of options. Remember, that the delta, along with the other Greeks, are derived from the market and calculated using the B&S formula.
To determine the delta of an option, you can rely on a B&S option pricing calculator.
– Delta for a Put Option
Remember that the Delta of a Put Option ranges from -1 to 0. The negative sign reflects the fact that when the underlying increases in value, the premium decreases.
The option 8268 is slightly ITM (In The Money) as shown on the table above, with a delta of approximately -0.55.
The aim is to assess the new premium cost in light of the delta value of -0.55. Please bear in mind the computations done below.
Scenario 1: Nifty is anticipated to 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
In this case, I am subtracting the delta value because I am aware that the value of a put option decreases as the underlying value increases.
Scenario 2: It is anticipated that Nifty will move to 8230
Expected change = 8268 – 8230
= 38
Delta = – 0.55
= -0.55*38
= -20.9
Current Premium = 128
New Premium = 128 + 20.9
= 148.9
Here, I’ve accounted for delta since knowing that the value of a Put option will increase as the underlying value decreases.
I trust that the two examples provided in this article have given you a clear understanding of how to utilise the delta of a put option to determine its updated premium value. I will not delve into the reasons behind the limitation of the put option’s delta between -1 and 0 in this discussion.
I suggest the readers employ the same thought process we used to comprehend the bounds of a call option’s delta (0 and 1) for understanding why a put option’s delta is (-1 and 0).
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