Fira Wrapped Tokens

Fira wrapped tokens are wrapped versions of the underlying asset or token which is being borrowed and lent in a fixed rate market. Fira wraps these tokens for accounting purposes specifically retaining to the yield distribution for Coupon Tokens (CTs) as well as the reserve accounting for rehypothecation. For purposes of explanation, we use FW-USDC.

Wrapping Rate

For every USDC deposited, the user is minted some FW-USDC. However, this relationship is not 1:1 as FW-USDC reserves are rehypothecated and earn yield from floating rate markets. Therefore, the wrapping rate from USDC to FW-USDC (and vice-versa) is as follows:

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

Where $\mu \geq 1$ and accrues as rehypothecated FW earns yield (or stops accruing when a bad debt loss is realized).

BT & CT Decomposition

Moreover, FW-USDC can then be decomposed into Bond and Coupon Tokens (BT & CT). BT are specifically used to facilitate fixed rate lending and borrowing while CT are used for yield trading among Dynamic Lenders (LPs).

For each FW-USDC decomposed, the user is minted $\mu$ BT & CT as follows:

$1 \hspace{0.1cm} \text{FW-USDC} = \mu \hspace{0.1cm} \text{BT-USDC} + \mu \hspace{0.1cm} \text{CT-USDC}$

As such, this relationship is symmetric, meaning BT & CT can also be used to recompose FW. This implies the following:

$1 \hspace{0.1cm} \text{USDC} = 1 \hspace{0.1cm} \text{BT-USDC} + 1 \hspace{0.1cm} \text{CT-USDC}$

This is specifically designed this way as the accrued yield from rehypothecation (which is mathematically represented as $\mu - 1$) is distributed to CT holders (see Yield Distribution). Furthermore, by separating the actual underlying reserve in USDC and the wrapped version, we can deposit USDC from the reserve to floating rate markets via rehypothecation without impacting FW-USDC supplies in the fixed rate market (creating zero impact on rate discovery).

Example

For example, if the wrapping rate is 1.25 ($\mu=1.25$) and a user with 100 USDC wants to mint FW-USDC, that user would mint 80 FW-USDC (100/1.25).

If the user then decomposes this to BT-USDC and CT USDC, he would mint 100 BT-USDC and 100 CT-USDC (80 x 1.25).