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70 lines
2.6 KiB
TeX
70 lines
2.6 KiB
TeX
\section{RWA-Backed Price-Stable Currencies}
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\subsection{Design}
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A Real World Asset (RWA) token represents a claim on a physical
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asset (gold, silver, uranium, real estate). When users stake RWA tokens
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into a governance pool, they mint a price-stable currency pegged to
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the underlying asset's market value. The bonding curve automatically
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adjusts an interest rate to maintain the peg.
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\subsection{Interest Rate Algorithm}\label{sec:interest}
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Let:
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\begin{itemize}[nosep]
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\item $b_{\text{LUX}}$ = value of one unit of the RWA token on
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QuantumSwap (in USD)
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\item $b_{\text{market}}$ = value of the same underlying asset on
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major external exchanges (in USD)
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\item $\text{premium} = (b_{\text{LUX}} - b_{\text{market}}) /
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b_{\text{market}}$
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\end{itemize}
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The annualized interest rate $r$ is determined by:
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\begin{equation}\label{eq:interest-rate}
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r = \begin{cases}
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0\% & \text{if } \text{premium} = 0\% \\
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2\% & \text{if } 0\% < \text{premium} \leq 2\% \\
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\text{premium} & \text{if } 2\% < \text{premium} \leq 15\% \\
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15\% & \text{if } \text{premium} > 15\%
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\end{cases}
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\end{equation}
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\subsection{Stability Analysis}
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The rate schedule in~\eqref{eq:interest-rate} has three regimes:
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\begin{enumerate}[nosep]
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\item \textbf{Dead zone} ($\text{premium} = 0$): No incentive to
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issue or redeem. The peg is exact.
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\item \textbf{Threshold} ($0 < \text{premium} \leq 2\%$): A fixed
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2\% rate provides a clear signal to issuers. The step function
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avoids oscillation around zero.
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\item \textbf{Linear tracking} ($2\% < \text{premium} \leq 15\%$):
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Rate tracks premium 1:1, providing proportional incentive.
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\item \textbf{Cap} ($\text{premium} > 15\%$): Protects holders from
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unbounded interest obligations.
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\end{enumerate}
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\begin{remark}
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The 2\% threshold was chosen empirically: users respond more
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reliably to a discrete step than to continuous micro-incentives. The
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15\% cap prevents death spirals where rising rates cause holder panic
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and further depegging.
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\end{remark}
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\subsection{Comparison to Prior Art}
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BitShares' pegged currencies (bitUSD, bitCNY) were collateralized
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solely by BTS, a volatile crypto-asset. This created reflexive
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collapse risk: BTS price drops $\rightarrow$ collateral falls
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$\rightarrow$ peg breaks $\rightarrow$ BTS price drops further.
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QuantumSwap's design requires 1:1 physical asset collateral (gold,
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uranium, etc.), breaking the reflexivity. The interest rate mechanism
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then handles \emph{demand}-side deviations from peg, while the
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physical collateral handles \emph{supply}-side solvency.
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%% ============================================================
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