What is Gamma?
In simple, Gamma is 2nd Greek Letter shows the rate at which the option's delta changes as the underlying changes.
It means Delta shows change in option premium as the change in
underlying while Gamma shows expected change in Delta with respect to
underlying change.
so, we can derive Delta is 1st order derivative, while Gamma is
2nd order derivative of premium.
Two Question coming in mind i.e.
- I know the delta changes, but why should I care about it?
- If the change in delta really matters, how do I estimate the likely change in delta?
Let discuss more on above Question by
taking few Example:
o Nifty Spot = 11100
o Strike = 11350
o Option type = CE
o Moneyness of Option
= Slightly OTM
o Premium = Rs.55/-
o Delta = 0.25
o Gamma = 0.0010
o Change in Spot = 200
points
o New Spot price =
11100 + 200 = 11300
o New Premium =??
o New Delta =??
o New moneyness =??
Let’s figure this out –
o Change in Premium =
Delta * change in spot i.e 0.25 * 200 = 50
o New premium = 55 + 50
= 105
o Rate of change of
delta = 0.0025 units for every 1 point change in underlying
o Change in delta =
Gamma * Change in underlying i.e. 0.0010*200 = 0.20
o New Delta = Old Delta
+ Change in Delta i.e. 0.25 + 0.2 = 0.45
o New Moneyness = ATM
When Nifty moves from 11100 to 11300, the 11350 CE premium
changed from Rs.55 to Rs.105, and along with this the Delta changed from 0.25
to 0.45.
Notice with the change of 200 points, the option transitions
from slightly OTM to ATM option. Which means the option’s delta has to change
from 0.25 to somewhere close to 0.45. This is exactly what’s happening here.
Further let us assume Nifty moves up another 200 points from
11300; let us see what happens with the 11350 CE option –
o Old spot = 11300
o New spot value =
11300 + 200 = 11500
o Old Premium = 105
o Old Delta = 0.45
o Change in Premium =
0.45 * 200 = 90
o New Premium = 105 +
90 = 195
o New moneyness = ITM
(hence delta should be higher than 0.5)
o Change in delta
=0.001 * 200 = 0.20
o New Delta = 0.45 +
0.2 = 0.65
Let’s take this forward a little further, now assume Nifty falls
by 100 points, let us see what happens with the 11350 CE option –
o Old spot = 11500
o New spot value = 11500
– 100 = 11400
o Old Premium = 195
o Old Delta = 0.65
o Change in Premium =
0.65 *(100) = – 65
o Premium = 195 – 65 = 130
o New moneyness =
slightly ITM (hence delta should be higher than 0.5)
o Change in delta =
0.0010 * (100) = – 0.10
o New Delta = 0.65 –
0.10 = 0.55
Unlike the delta, the
Gamma is always a positive number for both Call and Put Option. Therefore
when a trader is long options (both Calls and Puts) the trader is considered
‘Long Gamma’ and when he is short options (both calls and puts) he is
considered ‘Short Gamma’.
For example consider this – The Gamma of an ATM Put option is
0.002, if the underlying moves 50 points, what do you think the new delta is?
Before you proceed I would suggest you spend few minutes to
think about the solution for the above.
Here is the solution – Since we are talking about an ATM Put
option, the Delta must be around – 0.5. Remember Put options have a –ve Delta.
Gamma as you notice is a positive number i.e +0.006. The underlying moves by 50
points without specifying the direction, so let us figure out what happens in
both cases.
Case 1 – Underlying moves up by 50 points
o Delta = – 0.5
o Gamma = 0.002
o Change in underlying
= 50 points
o Change in Delta =
Gamma * Change in underlying = 0.002 * 50 = 0.1
o New Delta = We know
the Put option loses delta when underlying increases, hence – 0.5 + 0.1 = – 0.40
o
Case 2 – Underlying goes down by 50 points
o Delta = – 0.5
o Gamma = 0.002
o Change in
underlying = – 50 points
o Change in Delta =
Gamma * Change in underlying = 0.002 * – 50 = – 0.01
o New Delta = We know
the Put option gains delta when underlying goes down, hence – 0.5 + (-0.1)
= – 0.60
Learning Question:
Now, here is question for you – the Delta of the Futures contract in always 1,
so what do you think the gamma of the Futures contract is? kindly comment your
answer below post
Managing Risk using Gamma:
Gamma is useful to limit risk of position. Particularly, Retail
trader has to keep risk limit well define in advance. Example: In Aug. 2019 Mr.
A want to take position in stock market, he has 10 lakh Rs. in his account.
Now, per lot margin for nifty say 1.5 lakh plus mark to market. he plan to
trade in Future & Option but at a time he doesn't want to hold more than 4
Future Contracts, Thus defining his risk limits, this parameter helps a lot.
But does the same logic work while trading options? Let’s figure
out if it is the right way to think about risk while trading options.
Here is a situation –
o Number of lots
traded = 8 lots (Note – 8 lots of ATM contracts with delta of 0.5 each is
equivalent to 4 Futures contract)
o Option = 11100 CE
o Spot = 11105
o Delta = 0.5
o Gamma = 0.002
o Position = Short
The trader is short 8 lots of Nifty 11100 Call Option; this
means the trader is within his risk boundary. We can essentially add up the
deltas to get the overall delta of the position. Also each delta of 1
represents 1 lot of the underlying. So we will keep this in perspective and we
can figure out the overall position’s delta.
o Delta = 0.5
o Number of lots = 8
o Position Delta = 8
* 0.5 = 4
So from the overall delta perspective the trader is within his
risk boundary of trading not more than 4 Futures lots. Also, do note since the
trader is short options, he is essentially short gamma.
The position’s delta of 4 indicates that the trader’s position
will move 4 points for every 1 point movement in the underlying.
Now, assume Nifty moves 200 points against him and the trader
continues to hold his position, hoping for a recovery. The trader is obviously
under the impression that he is holding 8 lots of options which is within his
risk appetite…
Let’s do some forensics to figure out behind the scenes
changes –
o Delta = 0.5
o Gamma = 0.002
o Change in
underlying = 200 points
o Change in Delta =
Gamma * change in underlying = 0.002 * 200 = 0.40
o New Delta = 0.5 +
0.40 = 0.90
o New Position Delta
= 0.90*10 = 9
Do you see the problem here? Although the trader has defined his
risk limit of 4 lots, thanks to a high Gamma value, he has overshot his risk
limit and now holds positions equivalent to 9 lots, way beyond his perceived
risk limit. An inexperienced trader can be caught unaware of this and still be
under the impression that he is well under his risk radar. But in reality his
risk exposure is getting higher.
Now since the delta is 9, his overall position is expected to
move 9 points for every 1 point change in the underlying. For a moment assume
the trader is long on the call option instead of being short – obviously he
would enjoy the situation here as the market is moving in his favor. Besides
the favorable movement in the market, his positions is getting ‘Longer’ since
the ‘long gamma’ tends to add up the deltas, and therefore the delta tends to
get bigger, which means the rate of change on premium with respect to change in
underlying is faster.
Read 2-3 times to understand well. Don't be confused. Read again
and again in small slot.
Since the trader is short in position he has to measure the size
of position as in option they started with ATM strike but with the movement of
market and passage of time it goes huge in size. For short GAMMA, Delta becomes
bigger and every stage of market increase, the delta and gamma move against
trader due to short Position. So, Shorting options carries the risk of being
Short Gamma.
I would strongly suggest
you avoid shorting option contracts which has a large(Big) Gamma.
Example: SBIN having large Gamma value, Generally Lower Beta
stock tend to have Larger Gamma.
Greek Notes:
One of the keys to successful options trading is to understand
how the individual option Greeks behave under various circumstances. Now
besides understanding the individual Greek behavior, one also needs to
understand how these individual option Greeks react with each other.
So far we have considered only the premium change with respect
to the changes in the spot price. We have not yet discussed time and
volatility. Think about the markets and the real time changes that happen.
Everything changes – time, volatility, and the underlying price. So an option
trader should be in a position to understand these changes and its overall impact
on the option premium.
Here, So far we Discuss Delta, Gamma and Theta & Vega yet to
discussed. So, 4 main Greek is using to decide the position of option. Involve
Few critical Aspect here.....
which is the best strike to trade?
What is your expectation of the
premium of that particular strike – would it increase or decrease? Hence would
you be a buyer or a seller in that option?
If you plan to buy an option – is
there a realistic chance for the premium to increase?
If you plan to short an option –
Chance of reduction in option price and risk involved in naked option.
The answers to all these questions will evolve once you fully
understand individual Greeks and their cross interactions.
Given this, here is how this module will develop going further –
Learning From this.....
Gamma measures the rate of change of deltaGamma is always a positive number for both Calls and PutsAvoid large Gamma option for short.When you buy CE or PE options, you are long GammaWhen you short CE or PE option you are short GammaDelta changes rapidly for ATM optionDelta changes slowly for OTM and ITM options
Derivativelearn
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