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Crab Strategy

## Overview

The Crab strategy is designed to earn a yield by receiving the funding payments, while the ETH price stays within a range. This strategy is short gamma, and works the same way as a short position using GAMMA, however the Crab product allows the user to setup the position by selecting the size of the (ETH)² Perpetual instead of the gamma.
The Crab strategy does not automatically delta hedge the position as the ETH prices moves (unlike Opyn). This means that the position will suffer losses if the ETH price continues to move in one direction and does not return to the range where the trade was made.

## How to Use the Strategy

### Go Long

You should be long the Crab strategy (short gamma) when you think that the underlying is not going to change in price a lot, or you think it will tend towards the current price in the future. You are hoping that the funding rates you will be paid will outweigh the losses from price movement of the underlying outweigh the gains.

### Go Short

You should be short the Crab strategy (long gamma) when you think that the underlying is going to change in price a lot, but you're not sure in which direction. In other words, when you are long gamma, you are hoping for volatility that will allow you to benefit from the movement in price before your funding payments outweigh the gains. Alternatively, longing the Gamma strategy can be used to create a long gamma position.

## Technical Details

\begin{align*} ETH-Perpetual \\ &Underlying Asset = ETH &\\ &Index_{price} ={S}, (S = ETH_{price} \ from \ Chainlink) &\\ \\ &\Delta \ Delta =\frac {\delta {V}}{\delta S} \approx \frac {\delta S}{\delta S} = 1 = Constant &\\ &\Gamma \ Gamma =\frac {\delta {V}}{{\delta}^2 S} \approx \frac {\delta S}{{\delta}^2 S} = 0 &\\ &where, \ V = Index_{price} &\\ \\ ETH^2-Perpetual \\ &Underlying Asset = ETH &\\ &Index_{price} ={S^2} * \frac{1}{10,000}, (S = ETH_{price} \ from \ Chainlink) &\\ \\ &\Delta \ Delta =\frac {\delta {V}}{\delta S} \approx \frac {\delta {S^2}}{\delta S} * \frac{1}{10,000} = 2S * \frac{1}{10,000} &\\ &\Gamma \ Gamma =\frac {\delta {V}}{{\delta}^2 S} \approx \frac {\delta {S^2}}{{\delta}^2 S} * \frac{1}{10,000} = 2 * \frac{1}{10,000} = Constant &\\ &where, \ V = Index_{price} \end{align*}