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Restructured from flat .tex/.pdf files into per-paper subdirectories. Added Antje Worring as co-author on all papers. Synced PDFs to pdfs/ for download site.
99 lines
3.4 KiB
TeX
99 lines
3.4 KiB
TeX
\section{Liquidation Engine}
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\subsection{Liquidation Threshold Calculation}
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A position becomes liquidatable when:
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\begin{equation}
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\text{Margin Ratio} = \frac{C - L_{\text{unrealized}} - F_{\text{accrued}}}{S} < M_{\text{maintenance}}
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\end{equation}
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where $L_{\text{unrealized}}$ is unrealized loss, $F_{\text{accrued}}$ is accrued funding, and $M_{\text{maintenance}}$ is maintenance margin ratio.
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\begin{algorithm}
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\caption{Multi-Tier Liquidation Process}
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\begin{algorithmic}[1]
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\STATE \textbf{function} liquidatePosition($\text{account}$, $\text{position}$)
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\STATE $\text{marginRatio} \gets \text{calculateMarginRatio}(\text{position})$
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\IF{$\text{marginRatio} \geq \text{maintenanceMargin}$}
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\RETURN $\text{NotLiquidatable}$
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\ENDIF
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\STATE $\text{liquidationSize} \gets \text{position.size}$
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\IF{$\text{position.size} > \text{partialLiquidationThreshold}$}
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\STATE $\text{liquidationSize} \gets \text{position.size} \cdot \text{partialLiquidationRatio}$
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\ENDIF
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\STATE $\text{liquidationPrice} \gets \text{calculateLiquidationPrice}(\text{position})$
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\STATE $\text{penalty} \gets \text{liquidationSize} \cdot \text{liquidationFee}$
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\STATE $\text{remainingCollateral} \gets \text{position.collateral} - \text{penalty}$
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\IF{$\text{remainingCollateral} < 0$}
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\STATE $\text{insuranceFund} \gets \text{insuranceFund} + \text{remainingCollateral}$
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\ENDIF
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\STATE $\text{closePosition}(\text{position}, \text{liquidationSize}, \text{liquidationPrice})$
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\STATE $\text{distributePenalty}(\text{penalty}, \text{liquidator}, \text{insuranceFund})$
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\RETURN $\text{LiquidationSuccess}$
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\end{algorithmic}
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\end{algorithm}
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\subsection{Automated Liquidation Bots}
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Our keeper network ensures timely liquidations:
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\begin{lstlisting}[caption={Liquidation Bot Implementation}]
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contract LiquidationBot {
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struct LiquidationCandidate {
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address account;
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bytes32 positionKey;
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uint256 marginRatio;
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uint256 expectedProfit;
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}
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function scanPositions() external view returns (LiquidationCandidate[] memory) {
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LiquidationCandidate[] memory candidates;
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uint256 count = 0;
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for (uint256 i = 0; i < vault.positionKeysLength(); i++) {
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bytes32 key = vault.positionKeys(i);
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Position memory pos = vault.getPosition(key);
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uint256 marginRatio = calculateMarginRatio(pos);
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if (marginRatio < vault.maintenanceMargin()) {
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candidates[count++] = LiquidationCandidate({
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account: pos.account,
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positionKey: key,
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marginRatio: marginRatio,
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expectedProfit: calculateLiquidationProfit(pos)
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});
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}
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}
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// Sort by profitability
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return sortByProfit(candidates);
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}
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}
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\end{lstlisting}
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\subsection{Insurance Fund Mechanism}
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The insurance fund absorbs losses from underwater positions:
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\begin{equation}
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\Delta I_t = \sum_{i \in L_t} \max(0, -C_i) + \alpha \cdot F_{\text{collected}}
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\end{equation}
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where $L_t$ is set of liquidated positions at time $t$, and $\alpha$ is insurance fund allocation ratio.
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\subsection{Partial vs Full Liquidation}
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Partial liquidation reduces cascade risk:
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\begin{equation}
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S_{\text{liquidate}} = \begin{cases}
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S & \text{if } S < T_{\text{partial}} \\
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\max(T_{\text{min}}, S \cdot r_{\text{partial}}) & \text{otherwise}
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\end{cases}
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\end{equation}
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where $T_{\text{partial}} = \$100,000$, $T_{\text{min}} = \$10,000$, and $r_{\text{partial}} = 0.25$.
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