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# Overall Theory

The current operating theory for this methodology is that market makers (MM) are the largest sellers of options contracts. Their goal is to stay delta neutral, such that they make money no matter which direction the price moves. In order to stay delta neutral, they need to buy or sell shares to meet their obligaions to the options contracts bought or sold short.

I recognize this is overly simplistic but sufficient for the purpose of explaining this tool.

Knowing that these market makers need to hedge their positions, this tool assumes that the entire open interest can be treated as an option portfolio for a single stock and the hedging calculations derived from that open interest.

## Some Observations

• For some tickers, the delta neutral price acts as a point of support / resistance. There is likely a correlation between the amount of open interest relative to the float. This becomes useful for determining buy/sell levels.
• Gamma Maximum looks to be a useful level to take profits. Market makers do not want the price to cross gamma maximum as that will dramatically shift their hedging obligaions.

# FAQ

## Delta Neutral

Delta Neutral is the price of the stock where the combined sum of all option delta values is 0.

## Gamma Neutral

Gamma Neutral is the price of the stock where the combined sum of all option gamma values is 0.

## Gamma Maximum

Gamma Maximum is the price of the stock where the combined sum of all option gamma is maximized.

## Methodology

### Implied Volatility

The Black Scholes formula is used to back out the implied volatility for each individual options contract. There are about 1.3M options contracts available across all tickers.

The underlying option price used when calculating the implied volatility is the midpoint between the bid and the ask price at the close. Keep in mind that some contracts are so thinly traded they have 0 volume. So there is no true price discovery against which the implied volatility can be calculated.

The raw implied volatility tends to have gaps in the vol surface due to issues between the price and the implied volatility. So the IV for these gap contracts are interpolated to try and fill in the gap.

### Delta Neutral

With the price assumed, and the implied volatility calculated, the total Delta is calculated. Depending on the closing Delta, the tool will iteratively simulate a different underlying price to determine at which point the total Delta is 0.

### Gamma Neutral

With the price assumed, and the implied volatility calculated, the total Gamma is calculated. Depending on the closing Gamma, the tool will iteratively simulate a different underlying price to determine at which point the total Gamma is 0.

### Gamma Maximum

This is more or less the inverse of Gamma Neutral. The algorithm is modified to find all the local maxima and from the various local maxima calcualted, return the one which produces the highest overall Gamma.

## Notes

• All the option data comes from OPRA. So this tool covers all ~5200 tickers with active options markets.
• All the options calculations are based on the Black Scholes formula. This is important to note as the Black Scholes formula calculates the price for European options, instead of American options.
• The risk free rate is hardcoded to be 0.25%
• Annualized dividend yield is set to 0 for all tickers.