Getting Started

Getting Started

Introduction to Paribus Protocol

You're currently viewing the Paribus documentation.

The Paribus Protocol is based on the Compound Protocol, the codebase is open-source, and currently maintained by the Paribus team.

The interface hosted at https://app.paribus.io is at the moment closed source and maintained by the Paribus team.

Guides

Networks

The Paribus Protocol is currently deployed on the following networks:

Ethereum

Ethereum Mainnet

Contract Name	Contract Address
PBX	0xD528cf2E081f72908e086F8800977df826B5a483

Arbitrum

Arbitrum Mainnet

Contract Name	Contract Address
PBX	0xbAD58ed9b5f26A002ea250D7A60dC6729a4a2403
pARB	0xFc2737a742A741d13fE6326011a78cd881dE3Eb9
pETH	0xAffd437801434643B734D0B2853654876F66f7D7
pUSDT	0xFB1dcFc67cC496Eb0cC592050AF7Fdf3bF3b5C13
pWBTC	0x1c762E00f1D9317a4214d22b2576995C427F61c9

Arbitrum Sepolia

Contract Name	Contract Address
PBX	0x71d6B4ACB0AF56e7B2378E9F2fd1b7A419490eDF

Cardano

Cardano Mainnet

Contract Name	Policy Id
PBX	cc8d1b026353022abbfcc2e1e71159f9e308d9c6e905ac1db24c7fb6

Protocol Math

The Paribus Protocol contracts use a system of exponential math, ExponentialNoError.sol, in order to represent fractional quantities with sufficient precision.

Most numbers are represented as a mantissa, an unsigned integer scaled by 1 * 10 ^ 18, in order to perform basic math at a high level of precision.

pToken and Underlying Decimals

Prices and exchange rates are scaled by the decimals unique to each asset; pTokens are ERC-20 tokens with 8 decimals, while their underlying tokens vary, and have a public member named decimals.

pToken	pToken Decimals	Underlying	Underlying Decimals
pARB	8	ARB	18
pETH	8	ETH	18
pUSDC	8	USDC	6
pUSDT	8	USDT	6
pWBTC	8	WBTC	8

Interpreting Exchange Rates

The pToken Exchange Rate is scaled by the difference in decimals between the pToken and the underlying asset.

onepTokenInUnderlying = exchangeRateCurrent / (1 * 10 ^ (18 + underlyingDecimals - pTokenDecimals))

Here is an example of finding the value of 1 cBAT in BAT with Web3.js JavaScript.

const pTokenDecimals = 8; // all pTokens have 8 decimal places
const underlying = new web3.eth.Contract(erc20Abi, batAddress);
const pToken = new web3.eth.Contract(pTokenAbi, cBatAddress);
const underlyingDecimals = await underlying.methods.decimals().call();
const exchangeRateCurrent = await pToken.methods.exchangeRateCurrent().call();
const mantissa = 18 + parseInt(underlyingDecimals) - pTokenDecimals;
const onepTokenInUnderlying = exchangeRateCurrent / Math.pow(10, mantissa);
console.log('1 cBAT can be redeemed for', onepTokenInUnderlying, 'BAT');

There is no underlying contract for ETH, so to do this with pETH, set underlyingDecimals to 18.

To find the number of underlying tokens that can be redeemed for pTokens, multiply the number of pTokens by the above value onepTokenInUnderlying.

underlyingTokens = pTokenAmount * onepTokenInUnderlying

Calculating Accrued Interest

Interest rates for each market update on any block in which the ratio of borrowed assets to supplied assets in the market has changed. The amount of interest rate changes are dependent on the interest rate model smart contract implemented for the market, and the amount of change in the ratio of borrowed assets to supplied assets in the market.

Interest accrues to all suppliers and borrowers in a market when any Ethereum address interacts with the market’s pToken contract, calling one of these functions: mint, redeem, borrow, or repay. Successful execution of one of these functions triggers the accrueInterest method, which causes interest to be added to the underlying balance of every supplier and borrower in the market. Interest accrues for the current block, as well as each prior block in which the accrueInterest method was not triggered (no user interacted with the pToken contract). Interest compounds only during blocks in which the pToken contract has one of the aforementioned methods invoked.

Here is an example of supply interest accrual:

Alice supplies 1 ETH to the Paribus Protocol. At the time of supply, the supplyRatePerBlock is 37893605 Wei, or 0.000000000037893605 ETH per block. No one interacts with the PEther contract for 3 Ethereum blocks. On the subsequent 4th block, Bob borrows some ETH. Alice’s underlying balance is now 1.000000000151574420 ETH (which is 37893605 Wei times 4 blocks, plus the original 1 ETH). Alice’s underlying ETH balance in subsequent blocks will have interest accrued based on the new value of 1.000000000151574420 ETH instead of the initial 1 ETH. Note that the supplyRatePerBlock value may change at any time.

Calculating the APY Using Rate Per Block

The Annual Percentage Yield (APY) for supplying or borrowing in each market can be calculated using the value of supplyRatePerBlock (for supply APY) or borrowRatePerBlock (for borrow APY) in this formula:

Rate = pToken.supplyRatePerBlock(); // Integer
Rate = 37893566
ETH Mantissa = 1 * 10 ^ 18 (ETH has 18 decimal places)
Blocks Per Day = 7200 (12 seconds per block)
Days Per Year = 365

APY = ((((Rate / ETH Mantissa * Blocks Per Day + 1) ^ Days Per Year)) - 1) * 100

Here is an example of calculating the supply and borrow APY with Web3.js JavaScript:

const ethMantissa = 1e18;
const blocksPerDay = 7200; // 12 seconds per block
const daysPerYear = 365;

const pToken = new web3.eth.Contract(pEthAbi, pEthAddress);
const supplyRatePerBlock = await pToken.methods.supplyRatePerBlock().call();
const borrowRatePerBlock = await pToken.methods.borrowRatePerBlock().call();
const supplyApy =
  (Math.pow(
    (supplyRatePerBlock / ethMantissa) * blocksPerDay + 1,
    daysPerYear
  ) -
    1) *
  100;
const borrowApy =
  (Math.pow(
    (borrowRatePerBlock / ethMantissa) * blocksPerDay + 1,
    daysPerYear
  ) -
    1) *
  100;
console.log(`Supply APY for ETH ${supplyApy} %`);
console.log(`Borrow APY for ETH ${borrowApy} %`);