# Option Greeks

## Gamma Delta Neutral Option Strategy

By now, we very well know that by hedging the net gamma and net delta of our position, we can safely keep our position direction neutral. Traders use this strategy to minimize their exposure to volatility. It is also a very good strategy to secure the profits generated by a trade so far.

We will use a ratio call write (A ratio call write is an option strategy similar to a covered call, where an investor owns shares in the underlying stock and then writes/sells more call options than the shares owned. The objective of a ratio call write is to capture the additional premiums received by selling the option. We will buy options at a lower strike price than that at which they are sold.

For example, if we buy the Nifty call option with a 17000 strike price, we will sell the call option at a 17500 strike price. We will adjust the ratio of buying and selling options to eliminate the net gamma of our position.

We know that in a ratio write options strategy, more options are sold than purchased. This means that some options are sold "**naked**” which can prove to be very risky. The risk here is that if the stock rallies enough, we will lose money because of the risk involved by selling naked options. By reducing the net gamma to a value close to zero, we eliminate the risk of delta changing significantly (assuming a very short time frame).

To effectively neutralize the gamma, we first have to find the ratio at which we will buy and sell. We can quickly find out the gamma neutral ratio by doing the following:

- Find the gamma of each option.

For example, if we have our Nifty 17000 call with a gamma of 0.0007 and our 17500 call with a gamma of 0.0005, we would buy 5 contracts of 14000 calls and sell 7 contracts of 17500 calls. Remember this is per share, and each option represents 50 shares.

- Buying calls with gamma of 0.0007 is a gamma of (50*5*0.0007) =0.175
- Selling calls with gamma of 0.0005 is a gamma of -(50*7*0.0005)=-0.175 (Negative because we are going short on options)

This adds up to a net gamma of 0. Because the gamma is usually expressed in up to three decimal places, your actual net gamma might vary by very points from zero. After the gamma is neutralized, we will have to make the net delta of our position to zero. If our 17000 calls have a delta of 0.56 and our 17500 calls have a delta of 0.23, we can calculate the following.

- 5 contracts of 17000 call bought gives us a delta of (0.56*5*50)= 140
- 7 contracts of 14500 call sold gives us a delta of (-0.23*7*75)= -80.5

This results in a net delta of positive 59.5. To make this net delta very close to zero, we can short 59 shares of the underlying stock. This is because each share of stock has a delta of 1. This adds -59 to the delta, making it -0.25, very close to zero. Because you cannot short parts of a share, -0.25 is as close as we can get the net delta to zero.

Now that our position is effectively price neutral, let us compute its profitability. The 17000 calls have a theta of -5.5 and the 17500 calls have a theta of -4.1. This means:

- 5 contracts of 17000 call bought gives us a theta of (-5.5*5*50)= - 1375
- 7 contracts of 17500 call sold gives us a theta of (4.1*7*50)= 1435 (positive because we are selling options)

This results in a net theta of 60. This can be interpreted as your position making ₹60 per day. You'll have to hold your position because option behavior is not adjusted daily.

A few risks are associated with this strategy. Very large price moves can throw this out of proportion. If we hold the position for a week, adjustment of ratio and delta hedge is not required. However, if held for a longer time, the stock price will have more time to move in one direction.

The position's value can change dramatically because of changes in IV, because volatility is not hedged here. Although the risk of daily price movement has been eliminated, we have another risk factor to worry about, i.e. increased exposure to changes in IV. Changes in volatility have a small role to play in your position over a short time period of a week.

The risk of ratio can be minimized by adjusting positions in the underlying stock and also by hedging certain characteristics of the options. By doing this, we can profit from the time value of the options sold.