Equations

Staking
deposit=withdrawaldeposit = withdrawaldeposit=withdrawal
Swaps between FIDL and sFIDL during staking and unstaking are always honored 1:1. The amount of FIDL deposited into the staking contract will always result in the same amount of sFIDL. And the amount of sFIDL withdrawn from the staking contract will always result in the same amount of FIDL.
rebase=1−(fidlDeposits/sFIDLOutstanding)rebase = 1 - ( fidlDeposits / sFIDLOutstanding)rebase=1−(fidlDeposits/sFIDLOutstanding)
The treasury deposits FIDL into the distributor. The distributor then deposits FIDL into the staking contract, creating an imbalance between FIDL and sFIDL. sFIDL is rebased to correct this imbalance between FIDL deposited and sFIDL outstanding. The rebase brings sFIDL outstanding back up to parity so that 1 sFIDL equals 1 staked FIDL.
Bonding
bondPrice=1+Premiumbond Price = 1 + PremiumbondPrice=1+Premium
FIDL has an intrinsic value of 1 BUSD, which is roughly equivalent to $1. In order to make a profit from bonding, Trapeza Protocol charges a premium for each bond.
Premium=debtRatio∗BCVPremium = debt Ratio * BCVPremium=debtRatio∗BCV
The premium is derived from the debt ratio of the system and a scaling variable called BCV. BCV allows us to control the rate at which bond prices increase.
The premium determines profit due to the protocol and in turn, stakers. This is because new FIDL is minted from the profit and subsequently distributed among all stakers.
debtRatio=bondsOutstanding/fidlSupplydebt Ratio = bondsOutstanding/fidlSupplydebtRatio=bondsOutstanding/fidlSupply
The debt ratio is the total of all FIDL promised to bonders divided by the total supply of FIDL. This allows us to measure the debt of the system.
bondPayoutreserveBond=marketValueasset / bondPricebondPayout_{reserveBond} = marketValue_{asset}\ /\ bondPricebondPayoutreserveBond​=marketValueasset​ / bondPrice
Bond payout determines the number of FIDL sold to a bonder. For reserve bonds, the market value of the assets supplied by the bonder is used to determine the bond payout. For example, if a user supplies 1000 BUSD and the bond price is 250 BUSD, the user will be entitled 4 FIDL.
bondPayoutlpBond=marketValuelpToken / bondPricebondPayout_{lpBond} = marketValue_{lpToken}\ /\ bondPricebondPayoutlpBond​=marketValuelpToken​ / bondPrice
For liquidity bonds, the market value of the LP tokens supplied by the bonder is used to determine the bond payout. For example, if a user supplies 0.001 FIDL-BUSD LP token which is valued at 1000 BUSD at the time of bonding, and the bond price is 250 BUSD, the user will be entitled 4 FIDL.
FIDL Supply
FIDLsupplyGrowth=FIDLstakers+FIDLbonders+FIDLDAO+FIDLtfidlExerciseFIDL_{supplyGrowth} = FIDL_{stakers} + FIDL_{bonders} + FIDL_{DAO} + FIDL_{tfidlExercise}FIDLsupplyGrowth​=FIDLstakers​+FIDLbonders​+FIDLDAO​+FIDLtfidlExercise​
FIDL supply does not have a hard cap. Its supply increases when:
FIDL is minted and distributed to the stakers.
FIDL  is minted for the bonder. This happens whenever someone purchases a bond.
FIDL is minted for the DAO. This happens whenever someone purchases a bond. The DAO gets the same number of FIDL as the bonder.
FIDL is minted for the team. This happens whenever the aforementioned party exercises their tFIDL.
FIDLstakers=FIDLtotalSupply∗rewardRateFIDL_{stakers} = FIDL_{totalSupply} * rewardRateFIDLstakers​=FIDLtotalSupply​∗rewardRate
At the end of each epoch, the treasury mints FIDL at a set reward rate. These FIDL will be distributed to all the stakers in the protocol.
FIDLbonders=bondPayoutFIDL_{bonders} = bondPayoutFIDLbonders​=bondPayout
Whenever someone purchases a bond, a set number of FIDL is minted. These FIDL will not be released to the bonder all at once - they are vested to the bonder linearly over time. The bond payout uses a different formula for different types of bonds. Check the bonding section above to see how it is calculated.
FIDLDAO=FIDLbondersFIDL_{DAO} = FIDL_{bonders}FIDLDAO​=FIDLbonders​
The DAO receives the same amount of FIDL as the bonder. This represents the DAO profit.
FIDLtfidlExercise=tFIDL+BUSDFIDL_{tfidlExercise} = tFIDL + BUSDFIDLtfidlExercise​=tFIDL+BUSD
The individual would supply 1 tFIDL along with 1 BUSD to mint 1 FIDL. The tFIDL is subsequently burned.
Backing per FIDL
FIDLbacking=treasuryBalancestablecoin+treasuryBalanceotherAssetsFIDL_{backing} = treasuryBalance_{stablecoin} + treasuryBalance_{otherAssets}FIDLbacking​=treasuryBalancestablecoin​+treasuryBalanceotherAssets​
Every FIDL in circulation is backed by the Trapeza treasury. The assets in the treasury can be divided into two categories: stablecoin and non-stablecoin.
treasuryBalancestablecoin=RFVreserveBond+RFVlpBondtreasuryBalance_{stablecoin} = RFV_{reserveBond} + RFV_{lpBond}treasuryBalancestablecoin​=RFVreserveBond​+RFVlpBond​
The stablecoin balance in the treasury grows when bonds are sold. RFV(Risk Free Value) is calculated differently for different bond types.
RFVreserveBond=assetSuppliedRFV_{reserveBond} = assetSuppliedRFVreserveBond​=assetSupplied
For reserve bonds such as BUSD bond, the RFV simply equals to the amount of the underlying asset supplied by the bonder.
RFVlpBond=2sqrt(constantProduct)∗(% ownership of the pool)RFV_{lpBond} = 2sqrt(constantProduct) * (\%\ ownership\ of\ the\ pool)RFVlpBond​=2sqrt(constantProduct)∗(% ownership of the pool)
For LP bonds such as FIDL-BUSD bond, the RFV is calculated differently because the protocol needs to mark down its value. Why? The LP token pair consists of FIDL, and each FIDL in circulation will be backed by these LP tokens - there is a cyclical dependency. To safely guarantee all circulating FIDL are backed, the protocol marks down the value of these LP tokens, hence the name risk-free value (RFV).
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