papers/lux-perpetuals-derivatives/sections/06-gmx2-integration.tex

\section{GMX2 Integration}


\subsection{Liquidity Pool Model}

We adopt GMX2's GLP token model with enhancements:

\begin{lstlisting}[caption={Enhanced GLP Manager}]
contract EnhancedGLPManager {
    struct PoolComposition {
        address[] tokens;
        uint256[] weights;
        uint256[] utilizations;
        uint256 totalValue;
    }

    function addLiquidity(
        address token,
        uint256 amount
    ) external returns (uint256 glpAmount) {
        uint256 aum = getAUM();
        uint256 tokenValue = getTokenValue(token, amount);

        // Apply dynamic fees based on pool balance
        uint256 fee = calculateDynamicFee(token, amount, true);
        uint256 netValue = tokenValue.sub(fee);

        glpAmount = aum == 0
            ? netValue
            : netValue.mul(glpSupply).div(aum);

        _mint(msg.sender, glpAmount);
        vault.directPoolDeposit(token, amount);

        emit AddLiquidity(msg.sender, token, amount, glpAmount);
    }
}
\end{lstlisting}

\subsection{GLP Token Mechanics}

GLP represents liquidity provider shares with dynamic pricing:

\begin{equation}
\text{GLP}_{\text{price}} = \frac{\text{AUM} - \text{PnL}_{\text{traders}}}{\text{GLP}_{\text{supply}}}
\end{equation}

\subsection{Fee Distribution}

Fees flow to multiple recipients:

\begin{table}[h]
\centering
\begin{tabular}{|l|c|c|}
\hline
\textbf{Fee Type} & \textbf{Rate} & \textbf{Distribution} \\
\hline
Opening Fee & 0.1\% & 70\% LP, 30\% Treasury \\
Closing Fee & 0.1\% & 70\% LP, 30\% Treasury \\
Funding Fee & Variable & 100\% Counterparty \\
Liquidation Fee & 0.5\% & 50\% Liquidator, 50\% Insurance \\
Borrowing Fee & 0.01\%/hour & 100\% LP \\
\hline
\end{tabular}
\caption{Fee structure and distribution}
\end{table}

\subsection{Cross-Margin vs Isolated Margin}

Cross-margin shares collateral across positions:

\begin{equation}
M_{\text{account}} = C_{\text{total}} - \sum_{i} L_i - \sum_{i} F_i
\end{equation}

Isolated margin segregates risk:

\begin{equation}
M_{\text{position}} = C_{\text{position}} - L_{\text{position}} - F_{\text{position}}
\end{equation}