# Delta neutral

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**Delta neutral** is a trading strategy which involves having an equal number of long and short positions in derivatives such as options, with the goal of having a portfolio with no overall delta risk. This means that the investor is neither exposed to the upside nor the downside of the underlying security's price change. The delta risk is hedged by taking an offsetting long and short position in the same or related derivatives.

The primary benefit of delta-neutral trading is that it allows traders to focus on other factors such as volatility, time decay or interest rates, without having to worry about the direction of the underlying security’s price. This can allow traders to take advantage of price movements without being exposed to directional risk.

Delta neutral can be achieved in several ways, including the following:

- Buying a delta-neutral combination of options, such as a long call and a short put with the same strike price and expiration date.
- Buying and selling options in different expiration months with the same strike price and delta (risk-reversal strategy).
- Buying and selling options of the same expiration month but with different strike prices to create a “box spread” (ratio spread).
- Selling stock and buying an offsetting number of calls and puts.

Delta neutral strategies can be used by traders to take advantage of other factors such as volatility, time decay, and interest rates without the risk of directional exposure. In addition, they can be used to lock in profits or to hedge a portfolio of stocks and other securities.

## Example of Delta neutral

As an example of a delta neutral strategy, consider a trader who is long 100 shares of stock and wishes to hedge against potential downside risk. The trader can buy two offsetting options, a long call and a short put, both with the same strike price and expiration date. This will create a delta neutral position, meaning the trader is not exposed to the directional risk of the underlying security’s price movements. The trader can then focus on other factors such as time decay or volatility to take advantage of price movements without being exposed to directional risk.

To conclude, delta neutral is a trading strategy which involves having an equal number of long and short positions in derivatives such as options, with the goal of having a portfolio with no overall delta risk. Delta neutral can be achieved in several ways, such as buying and selling options of the same or different expiration month with the same strike price, or selling stock and buying an offsetting number of calls and puts. Delta neutral strategies can be used by traders to take advantage of other factors such as volatility, time decay, and interest rates without the risk of directional exposure.

## Formula of Delta neutral

The formula for delta neutral is as follows\[Delta\ Neutral=\frac{1}{2}(\Delta_{long}+\Delta_{short})\]

Where Δ_{long} is the delta for the long position and Δ_{short} is the delta for the short position. Delta neutral is calculated by taking the sum of the deltas for the long and short positions and dividing it by two. If the resulting number is zero, then the position is considered delta neutral.

## When to use Delta neutral

Delta Neutral strategies should be used when you want to take advantage of other factors such as volatility, time decay, and interest rates without the risk of directional exposure. Additionally, they can be used to lock in profits or to hedge a portfolio of stocks and other securities. It is important to note that delta neutral strategies can be used in both bullish and bearish markets.

## Types of Delta neutral

There are a few different types of delta neutral strategies that traders can employ:

**Long synthetic straddle**: This involves buying a call and a put with the same strike price and expiration date, and selling the underlying asset. This is a bullish strategy that profits from a large move in either direction.**Short synthetic straddle**: This involves selling a call and a put with the same strike price and expiration date, and buying the underlying asset. This is a bearish strategy that profits from a lack of movement in the underlying asset.**Long strangle**: This involves buying an out-of-the-money call and a put with the same expiration date, and no position in the underlying asset. This is a bullish strategy that profits from a large move in either direction.**Short strangle**: This involves selling an out-of-the-money call and a put with the same expiration date, and no position in the underlying asset. This is a bearish strategy that profits from a lack of movement in the underlying asset.

## Steps of Delta neutral

In order to implement a delta neutral strategy, the following steps should be taken:

- Analyze the underlying security and determine what type of delta neutral strategy is best suited for the trade.
- Calculate the delta of each option involved in the strategy and determine the number of long and short positions needed to achieve a delta-neutral portfolio.
- Calculate the total cost of the options used in the strategy and determine if the portfolio is within the trader’s budget.
- Monitor the delta of the portfolio and adjust the position size as needed in order to maintain a delta-neutral portfolio.

## Advantages of Delta neutral

**Allows traders to focus**on other factors such as volatility, time decay or interest rates: By establishing a delta neutral position, traders can focus on other factors such as volatility, time decay or interest rates instead of worrying about the direction of the underlying security’s price.**Locks in profits**: Traders can establish a delta neutral position to lock in profits on a position without having to close the position.**Hedges a portfolio of stocks and other securities**: Delta neutral strategies can be used to hedge a portfolio of stocks and other securities by taking an offsetting position in related derivatives.

## Limitations of Delta neutral

Delta neutral strategies can also have some limitations.

- Delta neutral strategies can be complex, and require knowledge and experience to execute successfully.
- The strategies often require more capital than a regular “long” or “short” position, as the investor needs to buy and sell offsetting positions.
- Delta neutral strategies can be affected by changes in the underlying security's volatility or other market conditions.

In addition to delta-neutral strategies, investors may also be interested in gamma-neutral, vega-neutral, and theta-neutral strategies.

- Gamma-neutral strategies involve having an equal number of long and short positions in derivatives with the same gamma risk. This means that the investor's delta exposure will remain unchanged regardless of the direction of the underlying security's price movement.
- Vega-neutral strategies involve having an equal number of long and short positions in derivatives with the same vega risk. This means that the investor's delta exposure will remain unchanged regardless of the volatility of the underlying security.
- Theta-neutral strategies involve having an equal number of long and short positions in derivatives with the same theta risk. This means that the investor's delta exposure will remain unchanged regardless of the time value of the underlying security.

Delta neutral strategies can be used in combination with other approaches related to delta, gamma, vega, and theta to create a portfolio with no overall directional exposure and no overall exposure to the other risk factors. This can allow investors to focus on other factors such as volatility, time decay, and interest rates without having to worry about the direction of the underlying security's price.

## Suggested literature

- Schmitt, C., & Kaehler, J. (1996).
*Delta-neutral volatility trading with intra-day prices: an application to options on the dax (No*. 96-25). ZEW Discussion Papers. - Karp, D. B., & Prilepkina, E. G. (2017).
*Some New Facts Concerning the Delta Neutral Case of Fox’s H Function*. Computational Methods and Function Theory, 17, 343-367. - Karp, D., & Prilepkina, E. (2015).
*Some new facts concerning the delta neutral H function of Fox*. arXiv preprint arXiv:1511.06612.