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UniV3 LP Hedge

## Overview

The UniV3 LP Hedge strategy allows a user to select a Uniswap V3 NFT (or specify the ID) and hedge the impermanent loss of that LP position. Predy will create a position that offsets the LP position using a combination of ETH and (ETH)² Perpetuals. This creates a long gamma position, refer to that section for further details of how the position will perform.

## How to Use the Strategy

The UniV3 LP Hedge should be used when you have an LP position that you want to hedge the impermanent loss for. This can be useful if you are generating trading/farm rewards that are greater than the cost of the funding from the UniV3 LP Hedge position, or when you are concerned about short term volatility in the pair.

## Technical Details

\begin{align*} V&= Value \ of \ Liquidity \ Position \\ &= Value_{wETH} + Value_{USDC} \\ &= 2L \sqrt{p} - L \sqrt{p_a} - p \frac {L}{\sqrt{p_b}} \end{align*} \\ \begin{align*} Where: \\ Pair &= wETH \ and \ USDC \\ Value_{wETH} &= Value_{USDC} \\ p & = ETH_{price} \ from \ Chainlink \\ p_a & = ETH_{min} \ in \ range \\ p_b & = ETH_{max} \ in \ range \end{align*} \\ \begin{align*} \\ Then, L \ is \ calculated: \\ Delta_V &= \frac {\delta {V}}{\delta p} \\ &= L( \frac{1}{\sqrt{p}} - \frac{1}{\sqrt{p_b}}) \\ Gamma_V &= \frac {\delta {V}}{{\delta}^2 p} \\ &= -0.5 L *p^{-3/2} \\ \end{align*}
\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*}