- Delta – Measures the rate of change of options premium based on the directional movement of the underlying
- . Gamma – Rate of change of delta
- Vega – Rate of change of premium based on change in volatility
- Theta – Measures the impact on premium based on time left for expiry
We will discuss these Greeks over the next few chapters. The focus of this chapter is to understand the Delta.
The delta is a number which varies –
Between 0 and 1 for a call option,
Between -1 and 0 for a put option.
Delta for a Call Option
We know the delta is a number that ranges between 0 and 1. Assume a call option has a delta of 0.5
Well, as we know the delta measures the rate of change of premium for every unit change in the underlying. So a delta of 0.5 indicates that for every 1 point change in the underlying, the premium is likely change by 0.5 units,
The following example should help you understand this better –
Nifty @ 11 AM is at 11000
Option Strike = 11000 Call Option
Premium = 140
Delta of the option = + 0.51
Nifty @ 3:15 PM is expected to reach 10900
What is the likely option premium value at 3:15 PM?
It is easy to calculate expected premium of option with the help of Delta, Here for every 1 point change in the underlying the premium is expected to change by .51 points.
We are expecting the underlying to change by 100 points (11000 –10900), hence the premium is supposed to Decrease by
= 100*0.51
= 51
Therefore the new option premium is expected to trade around 89 (140- 51)
Which is the sum of old premium + or - expected change in premium
Let us pick another case – what if go up in Nifty? What will happen to the premium? Let us figure that out –
Nifty @ 11 AM is at 11000
Option Strike = 11000 Call Option
Premium = 140
Delta of the option = 0.51
Nifty @ 3:15 PM is expected to reach 11110
What is the likely premium value at 3:15 PM?
We are expecting Nifty to Up by 110 points (11110 – 11000), hence the change in premium will be –
= 110 * .51
= 56.1
Therefore the premium is expected to trade around
= 140+ 56.1
= 196.1 (new premium value)
It will help us to identify expected premium if nifty moves up 100 points. Particularly it helps to understand on expiry week where sensitive movement may be possible. It is extremely useful concept for option trader. Even it is useful to select Strike of option ……….
Call option having Delta of .10
Call option having Delta of .30
Now the question is, which option will you buy?
Let us do some math to answer this –
Change in underlying = 100 points
Call option Delta For 0.10= 0.1*100 = 10
Call option Delta For 0.30 = 0.3*100
= 30
As you can see the same 100 point move in the underlying has different effects on different options. In this case clearly the trader would be better off buying Call Option having Delta 0.30.
Can delta value for a call option bound by 0 and 1?
Why can’t the call option’s delta go beyond 0 and 1?
Scenario 1: Delta greater than 1 for a call option
Nifty @ 11 AM at 11000
Option Strike = 11000 Call Option
Premium = 140
Delta of the option = 1.3 (purposely keeping it above 1)
Nifty @ 3:15 PM is expected to reach 11150
What is the likely premium value at 3:15 PM?
Change in Nifty = 150 points
Therefore the change in premium (considering the delta is 1.3)
= 1.3*150
= 195
Do you notice that? The answer suggests that for a 150 point change in the underlying, the value of premium is increasing by 195 points! In other words, the option is gaining more value than the underlying itself. Remember the option is a derivative contract, it derives its value from its respective underlying, hence it can never move faster than the underlying.
Let us extend the same logic to figure out why the delta of a call option is lower bound to 0.
Scenario 2: Delta lesser than 0 for a call option
Nifty @ 11 AM at 11000
Option Strike = 11500 Call Option
Premium = 15
Delta of the option = – 0.2 (have purposely changed the value to below 0, hence negative delta)
Nifty @ 3:15 PM is expected to reach 11100
What is the likely premium value at 3:15 PM?
Change in Nifty = 100 points (11100 -11000)
Therefore the change in premium (considering the delta is -0.2)
= -0.2*100
= -22
For a moment we will assume this is true, therefore new premium will be
= -22 + 15
= – 7.
As you can see in this case, when the delta of a call option goes below 0, there is a possibility for the premium to go below 0, which is impossible. At this point do recollect the premium irrespective of a call or put can never be negative. Hence for this reason, the delta of a call option is lower bound to zero.
Delta for a Put Option
Do recollect the Delta of a Put Option ranges from -1 to 0.
The following example should help you understand this better –
Nifty @ 11 AM is at 11000
Option Strike = 11000 Put Option
Premium = 140
Delta of the option = -0.51
Nifty @ 3:15 PM is expected to reach 10900
What is the likely option premium value at 3:15 PM?
It is easy to calculate expected premium of option with the help of Delta, Here for every 1 point change in the underlying the premium is expected to change by -0.51 points.
We are expecting the underlying to change by -100 points (10900-11000), hence the premium is supposed to Increase by
= -100*-0.51
= 51
Therefore the new option premium is expected to trade around 191 (140+51)
Which is the sum of old premium + or - expected change in premium
Let us pick another case – what if go up in Nifty? What will happen to the premium? Let us figure that out –
Nifty @ 11 AM is at 11000
Option Strike = 11000 Put Option
Premium = 140
Delta of the option = 0.51
Nifty @ 3:15 PM is expected to reach 11110
What is the likely premium value at 3:15 PM?
We are expecting Nifty to Up by 110 points (11110 – 11000), hence the change in premium will be –
= 110 *-0.51
= -56.1
Therefore the premium is expected to trade around
= 140-56.1
= 83.9 (new premium value)
It will help us to identify expected premium if nifty down than 100 points. Particularly it helps to understand on expiry week where sensitive movement may be possible. It is extremely useful concept for option trader. Even it is useful to select Strike of option ……….
Put option having Delta of -.10
Put option having Delta of -.30
Now the question is, which option will you buy?
Let us do some math to answer this –
Change in underlying = -100 points
Call option Delta For -0.10= -0.1*-100 = 10
Call option Delta For -0.30 = -0.3*-100
= 30
As you can see the same 100 point move in the underlying has different effects on different options. In this case clearly the trader would be better off buying Put Option having Delta -0.30.
I hope with the above two Illustrations you are now clear on how to use the Put Option’s delta value to evaluate the new premium value.
In fact I would encourage the readers to apply the same logic we used while understanding why the call option’s delta is bound between 0 and 1, to understand why Put option’s delta is bound between -1 and 0.
Learning of the Lesson:
- It influence change of option premium
- Delta is help to calculate change in underlying with respect to change in option value.
- Call option delta varies between 0 and 1
- Put option delta varies between -1 and 0
- The negative delta value for a Put Option indicates that the option premium and underlying value moves in the opposite direction
- 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.
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