LBTC/LBTCv

This page gives a high-level explanation for how the value LBTCv is calculated.

The Lombard DeFi Vault accepts deposits of LBTC, WBTC, and cbBTC, and issues its liquid provisioning (LP) token LBTCv to represent users' underlying portion of the pool. LBTCv is only redeemable for LBTC, so users depositing WBTC or cbBTC will receive LBTC upon redemption.

Suppose 2 LBTC, 1 cbBTC, and 1 WBTC was deposited into the vault, and that the current market price determines 1 LBTC = $90,000, 1 cbBTC = $89,000 and 1 WBTC = $ 88,000. (Note: values are just examples.) Then,

\begin{align} \text{TVL (Total Value Locked) of Vault} &= 2\cdot \text{LBTC} + \text{cbBTC} + \text{WBTC} \\ &= 2\cdot 90,000$ + 89,000$ + 88,000$\\ &= $357,000 \end{align}

There is no fee for depositing LBTC and cbBTC into the vault. There is a fee of 40bps for depositing WBTC into the vault. A user depositing into the vault will receive the following amount of LBTCv,

$$2\cdot\text{LBTC} \rightarrow 2\cdot \text{LBTCv}\\ \text{cbBTC} \rightarrow \text{LBTCv}\\ \text{WBTC} \rightarrow (1-40\text{bps})\cdot \text{LBTCv} = 0.996 \text{LBTCv}$$

At any given point, the value of LBTCv is the TVL of the Vault divided by the number of LBTCv in circulation. In this example,

\text{LBTCv}= \frac{$357,000}{(2+1+0.996)}\approx $89339.34

The vault has a three day withdrawal period for security and to ensure economic stability.

Example of Vault Activity for LBTCv Calculation

Day 1:

Suppose 3 deposits are made as described above, and assume the vault was previously empty.

Day 2:

Suppose the vault made a yield of 1%, and the prices of LBTC, cbBTC, and WBTC are unchanged. Then,

\text{TVL} = $357,000 \cdot (1.01) = $ 357,357

This means that 1 LBTCv is now redeemable for 1.01 worth of LBTC, and given there was no change in price of LBTC since deposit, this means LBTCv is now redeemable for 1.01 LBTC, or $90,900 worth of LBTC.

Day 3:

Suppose the vault made no profit, the prices of LBTC, cbBTC and WBTC are unchanged, and an additional 1 LBTC is deposited into the vault. Then, given the current value of LBTCv, a deposit of 1 LBTC on day 3 would be worth 0.99 LBTCv. That is,

$$\text{LBTC} \rightarrow \frac{1}{1.01}\text{LBTCv} = 0.99 \cdot \text{LBTCv}\\$$

Currently, the amount of LBTCv in circulation is 3.966 + 0.99 = 4.956, and vault's TVL is $357,357 + $90,000 = $447,357.

Day 4:

Suppose the vault makes a yield of 1%, and the prices of LBTC, cbBTC and WBTC are unchanged. Then,

\text{TVL} = $451,831

Day 5:

Suppose the vault made no profit, and the prices of LBTC, cbBTC and WBTC are unchanged.

A user wants to withdraw 1 LBTCv. Given the total circulation of LBTCv is 4.956, and the vault's TVL is $451,831 then,

\text{LBTCv}\rightarrow \frac{1}{4.96}\cdot $447,357 \approx $90,192.94

that is, they would receive $91,168, or redeem approximately 1.01298 LBTC.

Note on Impermentant loss for the Lombard DeFi Vault:

Lombard reservers the right to change the balance of assets held in the Lombard DeFi Vault pending on a variety of factors, including maintaining a majority of LBTC in the vault and providing adequate collateral for the positions taken up the vault to earn yield.