papers/lux-credit-lending/sections/03-90-ltv-achievement.tex

\section{90\% LTV Achievement}


\subsection{Mathematical Foundation}

To safely achieve 90\% LTV with zero liquidations, Lux Credit employs a multi-layered safety model:

\textbf{Required Conditions:}
\begin{equation}
\text{Annual Yield} > \frac{\text{LTV}}{1 - \text{LTV}} \times \text{Price Volatility}
\end{equation}

For 90\% LTV with 11\% APY on LUX:
\begin{equation}
11\% > \frac{90\%}{10\%} \times \sigma_{price} \implies \sigma_{price} < 1.22\%
\end{equation}

This requires collateral volatility < 1.22\% annually, achievable through diversification and hedging.

\subsection{Risk-Adjusted LTV Table}

\begin{table}[h]
\centering
\begin{tabular}{@{}lrrr@{}}
\toprule
\textbf{Asset} & \textbf{Base LTV} & \textbf{Yield APY} & \textbf{Max LTV} \\ \midrule
LUX (staked) & 85\% & 11.0\% & 90\% \\
BTC (wrapped) & 75\% & 4.2\% & 80\% \\
ETH (staked) & 80\% & 5.5\% & 85\% \\
USDC & 90\% & 8.0\% & 95\% \\
Mixed Portfolio & 87\% & 9.3\% & 90\% \\ \bottomrule
\end{tabular}
\caption{Asset-specific LTV ratios and yields}
\end{table}

\subsection{Dynamic LTV Adjustment}

\begin{lstlisting}[language=Solidity, basicstyle=\small\ttfamily]
contract LuxCredit {
    struct RiskParams {
        uint256 baseLTV;          // Base loan-to-value
        uint256 volatilityPenalty; // Reduce LTV if volatile
        uint256 yieldBonus;       // Increase LTV with yield
        uint256 durationFactor;   // Time-weighted adjustment
    }
    
    function calculateMaxLTV(
        address asset,
        uint256 collateralAmount,
        uint256 loanDuration
    ) public view returns (uint256) {
        RiskParams memory params = riskParams[asset];
        
        // Start with base LTV
        uint256 ltv = params.baseLTV;
        
        // Adjust for 30-day volatility
        uint256 vol = getVolatility(asset, 30 days);
        if (vol > VOLATILITY_THRESHOLD) {
            ltv -= params.volatilityPenalty;
        }
        
        // Boost for high-yield assets
        uint256 apy = getExpectedYield(asset);
        if (apy > 10e18) { // 10% APY
            ltv += params.yieldBonus;
        }
        
        // Reduce for short-term loans (riskier)
        if (loanDuration < 90 days) {
            ltv -= 5e18; // -5%
        }
        
        // Cap at 90% maximum
        return min(ltv, 90e18);
    }
}
\end{lstlisting}