Γ GAMMA

Overview

Using the Gamma trading function allows a user to define the gamma exposure they want, and Predy will create a position that has the specified constant gamma, and neutral (zero) delta.

This strategy will hedge the downside of the long (ETH)² position with a short ETH position. he trade will profit regardless of the direction of the move as long as the move is large enough that the move is large enough to overcome the cost of funding the long (ETH)² position.

Let's look at what happens as the price of the underlying moves in either direction (assuming a long gamma position).

Price goes up: The delta of the position becomes more positive as the positive delta of the long (ETH)² position outweighs the negative delta of the short ETH position. This means that as the price continues to move up, the overall position will increase in value, however, if the price moves back towards the opening price, the position will decrease in value.

Price goes down: The delta of the position becomes more negative as the negative delta of the short ETH position outweighs the positive delta of the long (ETH)² position. This means that as the price continues to move down, the overall position will increase in value, however, if the price moves back towards the opening price, the position will decrease in value.

How to Use the Strategy

Go Long

You should be 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.

Go Short

You should be 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. Alternatively, longing the Crab strategy can be used to create a short gamma position.

Technical Details

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