Bonding

Bonding is a vital part of the TAO mechanics. Bonders can lock their LP tokens with the protocol indefinitely in return for a Fixed return of TAO at a discount to the market price over the vesting period. This allows the Tao protocol to accumulate its own liquidity.

How does it work?

Bond quotes are a function of the underlying value of the LP share.

RFV=2sqrt(constantProduct)(LP/totalLP)RFV = 2sqrt(constantProduct)*(LP/totalLP)

The Risk Free Value (RFV) is the minimum the protocol can value the LP share in order to protect its reserve requirements. For example, the protocol values TAO equal to BUSD, therefore the protocol only cares about the sum of the assets in the pool. Using the constant product formula x * y = k, the minima of x + y is the risk free value, which is when x = y. The protocol uses the square root of the constant product x * y to determine this minima.

The bond quote is then determined by the following equation:

BondQuote=RFV/PremiumBondQuote = RFV/Premium

The Premium determines the protocol's profits from bonding. A lower premium translates to a higher discount for the bonder and thus incentivizes bonding more, and a higher premium translates to lower discounts and therefore lower incentive to bonders. The premium is a function of the protocols debt and a scaling DAO governed variable called the Bonding Control Variable (BCV), which allows adjusting for more or less inflation.

Premium=1+(debtRatioBCV)Premium = 1 + (debtRatio * BCV)

the Debt Ratio is determined by the following:

debtRatio=bondsOutstanding/taoSupplydebtRatio = bondsOutstanding / taoSupply

This results in an oscillating discount and therefore incentive to bonders. As more participants bond, the debt ratio increases, and therefore the subsequent bonder receives less of a discount. As bonds vest, the debt ratio falls, and the discount returns. The Quoted TAO is returned over a Vested Period, another variable to adjust for more or less inflation.

At the end of every epoch, the treasury recalculates the PCV by summing up its reserve assets (initially BUSD and TAO-BUSD LP shares). It conservatively values the LP shares at their Risk Free Value. Any gains in the treasury's PCV translates to newly minted TAO which are distributed as protocol profits.

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