**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 delta Gamma is always a positive number for both Calls and Puts Avoid large Gamma option for short.When you buy CE or PE options, you are long Gamma When you short CE or PE option you are short Gamma Delta changes rapidly for ATM option Delta changes slowly for OTM and ITM options

**Nifty Live Example :**

NIfty Trading near 10895

Expiry date: 29 Aug

ATM CE Option 10900 having Delta of 0.50 and Gamma of 0.0009

Gamma Always High At ATM Strike

Check the expected Movement if nifty goes 100 point up here

Expected Nifty 11000

Delta of 10900 is 0.50

Gamma is 0.0009

Premium of 10900 CE is 168

Now, Expecting 100 point up @ 11000

what will be value of 10900?

Delta change : 100*0.50 = 50

Premium + 168+50 = 218

New Delta of 10900 = Gamma* 100 ( 0.009*100 = 0.09)

New Delta will be 0.50+ 0.09 = 0.59

Now, Next movement will be different due to Gamma added to Delta.

Great information, thanks sir

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