> For the complete documentation index, see [llms.txt](https://lucia-protocol.gitbook.io/lucia-protocol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://lucia-protocol.gitbook.io/lucia-protocol/redemption-mechanism.md).

# Redemption Mechanism

The Lucia Protocol employs a sophisticated Redemption Mechanism to ensure the stability and redeemability of its native stablecoin, LUCI. This mechanism serves as a critical component in maintaining asset value, offering arbitrage opportunities, and enhancing overall system robustness. 

**LUCI: A Fully Redeemable Stablecoin**

LUCI operates as a fully redeemable stablecoin that provides holders with the option to convert their tokens into various collateral types at face value, based on prevailing exchange rates. This feature creates a price floor for LUCI and aligns its value closely with established stable assets like USDT, USDC, and DAI.

<figure><img src="/files/geoXWe3Lt9jWplUpoL12" alt=""><figcaption></figcaption></figure>

**Redemption Process: Debt and Collateral Balancing**

In the event of a redemption, LUCI tokens are employed to neutralize debts in Sheds that have surpassed the predefined collateral risk ratio. An equivalent amount of collateral is shifted from these Sheds to the redeeming party. This transaction essentially nullifies any net losses for borrowers, thereby promoting a balanced and equitable environment for all participants.

<figure><img src="/files/LMzwp9xZkWA8Ab0jQy36" alt=""><figcaption></figcaption></figure>

**Systemic Impact: Enhanced Robustness and Stability**

The redemption mechanism amplifies the system's overarching collateralization levels, thus enhancing its robustness and price stability. Given that Sheds with suboptimal collateralization ratios (CRs) are settled first, this fosters increased user confidence in the long-term prospects of the Lucia Protocol.

<figure><img src="/files/AK57ExqTGLNOIChsKYMo" alt=""><figcaption></figcaption></figure>

**Automatic Shed Closure: Reclaiming Collateral Surplus**

Once a full redemption and debt nullification process is complete, the Sheds are programmatically closed, allowing borrowers to recover any leftover collateral. This ensures that borrowers resume complete control of their assets post-liability settlement.

<figure><img src="/files/pYaWMi3ppls49YOkC5rP" alt=""><figcaption></figcaption></figure>

**Redemption Fee and Base Rate Calculation**

The Lucia Protocol employs a dynamic fee structure for redemptions, initially set at a base rate of 0%. For each redemption event, this base rate is recalibrated using the formula:

<figure><img src="/files/JAcf2SXPSWOLp1w0xT2M" alt=""><figcaption></figcaption></figure>

Here, *m* represents the amount of LUCI redeemed, \\(n\\) indicates the current LUCI supply, and *a* is a constant parameter set at 0.5. This base rate is subject to decay, accounted for using the following formula:

<figure><img src="/files/rnsEACTyO6q7St4m0uAD" alt=""><figcaption></figcaption></figure>

Where *S* signifies an hourly decay factor (0.944 in our case), and *A\_t* denotes the time elapsed in hours since the last redemption or loan issuance.

The redemption fee is calculated as:

<figure><img src="/files/Y16bJib368UQLt3Qu2ex" alt=""><figcaption></figcaption></figure>

This fee is subtracted from the redeemed LUCI, effectively reducing the collateral returned to the redeemer.

The Lucia Protocol's Redemption Mechanism is meticulously engineered to support both token stability and user fairness. By offering direct arbitrage opportunities, ensuring equitable treatment for borrowers, and optimizing the fee structure, the Lucia Protocol fosters a resilient and equitable financial ecosystem.


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