Yield Accrual Mechanism

Overview

PBTC accrues yield through a floating exchange rate for BTC, similar to non-rebase token models implemented by Rocketpool's rETH, Coinbase's cbETH, and Mantle's mETH. This floating exchange rate accounts for minting/redeeming activities, rewards, and fees.

The total supply of PBTC always equals the total amount of BTC principal deposited or staked into the protocol. Unlike rebase tokens, PBTC does not automatically increase the balance but updates its exchange rate based on the total controlled BTC divided by the total PBTC supply.

Photon Labs ensures a "true" exchange rate, reflecting each user's share of the PBTC value. Users can realize their accrued yield through redemption or unloading.

Underlying Collateral

PBTC is a yield-bearing asset with a soft peg to BTC, backed by deposited BTC. Users have four primary operations:

1. Minting PBTC: Deposit BTC into Photon Labs' contracts to receive PBTC.

2. Redeeming PBTC: Redeem PBTC from Photon Labs' contracts to receive an amount of BTC corresponding to the principal plus any accrued yield.

3. Acquiring PBTC: Swap other assets for PBTC via third-party liquidity pools (LPs).

4. Unloading PBTC: Swap PBTC for other assets via third-party LPs.

Exchange Rate

Primary variables in the exchange rate equation are:

1. Conversion rate = Total controlled BTC / Total PBTC Supply

2. Total controlled BTC = BTC principal deposited - BTC principal redeemed + Net rewards

3. Total PBTC Supply = PBTC issued - PBTC redeemed

4. Net Rewards = (Bitcoin staking rewards + PnL from positions + Other rewards) x (1 - Net Fee Rate)

Minting PBTC

PBTC = (PBTCSupply/TotalControlledBTC) * BTCAmount

Redeeming PBTC

BTC = (TotalControlledBTC/PBTCSupply) * PBTCAmount

Worked Examples

Example 1: Minting PBTC

Given Parameters	Value
BTC Principal Deposited	100 BTC
Net Rewards	5 BTC
Total PBTC Supply (Issued)	100 PBTC
BTC Amount to Mint	2 BTC

1. Total Controlled BTC

100 BTC - 0 BTC + 5 BTC = 105 BTC

1. Exchange Rate

105 BTC / 100 PBTC = 1.05

1. Using the Minting Formula

PBTC = (100 PBTC / 105 BTC) * 2 BTC ≈ 1.905 PBTC

1. Total PBTC Minted

≈ 1.905 PBTC

Example 2: Redeeming PBTC

Given Parameters	Value
Total Controlled BTC	105 BTC
Total PBTC Supply	100 PBTC
PBTC Amount to Redeem	3 PBTC

1. Using the Redeeming Formula

BTC = (105 BTC / 10 PBTC) * 3 PBTC = 3.15 BTC

1. Total BTC Withdrawn

3.15 BTC