Fixed-Rate Markets

Fixed-rate markets are the core innovation in Fira. Borrowers lock a rate at origination. Lenders earn predictable yield. Both sides know their terms before executing.

The mechanism is built on zero-coupon bond mechanics: Bond Tokens (BTs) trade at a discount before maturity and converge to par at term. The discount is the rate.

How Fixed-Rate Borrowing Works

1. Post collateral — The borrower deposits an approved collateral asset.

2. Mint BTs — The protocol creates Bond Tokens backed by that collateral. Each BT has a face value of 1 unit of the loan token.

3. Swap BT for loan token — The borrower swaps BTs for FiraWrapped tokens (FW) through the AMM, then unwraps FW into the underlying asset (e.g., USDC).

4. Repay at maturity — The borrower returns the same number of BTs borrowed, regardless of how much they received at origination.

The interest cost is not charged explicitly. It is embedded in the discount at which BTs trade. A borrower who receives 0.95 USDC per BT and repays 1.00 USDC per BT at maturity has paid a fixed rate proportional to that 5% spread over the holding period.

Fixed-Rate Guarantee

This mechanism delivers a fixed-rate loan when held to maturity. Both the repayment amount and the maturity date are set at origination.

Early repayment is always possible but does not guarantee the same effective rate — the BT/USDC exchange rate fluctuates before maturity, so closing early may result in a higher or lower realized cost.

How Fixed-Rate Lending Works

Lenders provide the other side of the AMM. By supplying FiraWrapped tokens (FW) to the liquidity pool, they enable borrowers to swap BTs for loan tokens.

When FW enters the pool, it is decomposed into its two components:

$$1 \hspace{0.1cm} \text{FW} = \mu_{s}(t) \hspace{0.1cm} \text{BT} + \mu_s(t) \hspace{0.1cm} \text{CT}$$

• BT remains in the pool to facilitate borrowing

• CT (Coupon Token) goes to the LP and represents the yield portion

Lenders who buy BTs at a discount and hold to maturity earn the difference — a fixed yield locked at purchase.

Rate Discovery

Rates are not set by governance. They emerge from supply and demand in the BT/FW AMM. We define a BT/FW exchange rate (exchange rate expressed as BT acquired per 1 FW) as follows:

$$\text{exchangeRate}(t) = \mu_s(t)\cdot\left( \frac{\ln\!\left( \tfrac{p(t)}{1 - p(t)} \right)}{\text{rateScalar}(t)} + \text{rateAnchor}(t) \right)$$

Where:

• $\mu_s (t)$ is the modified wrapping rate (see Token Mechanics).

• $p(t) =n_{\text{BT}}(t) /(n_{\text{BT}}(t) + n_{\text{FW}}(t))$, such that $n_{BT}(t) , \space n_{FW}(t)$ are the number of BT and FW in the pool.

• $rateScalar(t)=rootScalar / timeToExpiry(t)$, such that $rootScalar$ is a DAO set concentration parameter (and $timeToExpiry(t)$ is the time to expiry, in years, for the fixed-rate market at time $t$).

• $rateAnchor(t)$ is a DAO set concentration parameter that drifts with the realized implied fixed-rate of the AMM (see Whitepaper).

Using the AMM, borrowers can swap to FW from BT (or vice versa for lenders). Using FW, they can then unwrap to the underlying asset at the wrapping rate:

$$1 \hspace{0.1cm} \text{FW-USDC}= \mu (t)\hspace{0.1cm} \text{USDC}$$

Therefore the full conversion rate from BT to the underlying asset is:

$$conversionRate(t)=\mu(t)\cdot exchangeRate(t)^{-1}=\frac{\mu(t)}{\mu_s(t)}\left(\frac{\ln\!\left( \tfrac{p(t)}{1 - p(t)} \right)}{\text{rateScalar}(t)} + \text{rateAnchor}(t)\right)$$

Meaning the implied fixed borrowing/lending rate is:

$$impliedRate(t)=\left( conversionRate(t)^{-1} -1 \right) ^{\frac{1}{timeToExpiry(t)}}$$

Settlement at Maturity

To simplify loan repayment at maturity, users can mint BT-USDC using USDC (via FW-USDC). Conversely, holders of BT-USDC can redeem their tokens for USDC (also via FW-USDC) after maturity. This creates a robust primary market for loan settlement and avoids potential inefficiencies or liquidity shortages that might arise from relying solely on secondary market pricing through the AMM.

However, it should be noted that the wrapping rate is modified after maturity and is fixed based on the last wrapping rate before maturity. Therefore the loan technically accrues some minimal interest while users wait to repay after maturity. This comes from the difference between the actual wrapping rate (from USDC to FW-USDC) and the now fixed modified wrapping rate (from FW-USDC to BT-USDC and CT-USDC).

FiraWrapped Tokens (FW)

FW tokens wrap the underlying loan asset (e.g., FW-USDC wraps USDC). The wrapping rate is not constant — it reflects the total reserve value relative to FW supply:

$$\mu (t) = \frac{Reserve(t)}{Supply_{FW}(t)}$$

At protocol initialization, 1 FW = 1 USDC. Over time, as reserves earn yield through rehypothecation, the rate increases. This means FW gradually represents more underlying per token.

Borrowers receive FW and unwrap it to USDC. To repay, they rewrap USDC into FW before settlement.

Coupon Token (CT) Trading

CTs represent the yield component of decomposed FW. They are tradable in the fixed-rate market through flash loan mechanisms:

• Buy CT: Flash-borrow FW → decompose into BT + CT → swap BT back to FW to repay the loan → keep CT

• Sell CT: Flash-borrow BT → combine with CT to reconstruct FW → swap portion to BT to repay → keep remaining FW

These operations execute atomically. LPs can also sell their CT positions early to realize yield upfront while adding liquidity to the pool.

Maturity Settlement

At maturity, BTs redeem 1:1 for the underlying asset (via FW). Holders can:

• Redeem BT for USDC through FW

• Mint BT using USDC (via FW) to repay loans

This primary market settlement avoids dependence on secondary AMM liquidity at maturity.

Related

• Floating-Rate Markets — Variable-rate borrowing without maturity

• Token Mechanics — BT, CT, and FW token reference

• Rehypothecation — How idle reserves earn yield

• Whitepaper — Full mathematical treatment