# Theta Vault

Scalable source of liquidity for the volatility tokens
Theta is the change in an instrument's value with the passage of time, all other factors staying constant. As the volatility tokens charge time decay fees and are exposed to Theta, they are designed to be held only for limited amounts of time. However, in order for tokens to have a sustainable source of liquidity on DEXs, there has to be a mechanism which allows them to be paired in a liquidity pool without accounting for time decay. Without such a mechanism it would not make sense for a liquidity provider to add liquidity for such a pool for long periods of time.
Completing this design goal was the key element in CVI v3 with the introduction of the Theta vault, which was built on top of the CVI AMM. The underlying architecture of the vault relies on the following key points:
• The vault is the only gateway for adding and removing liquidity from the CVI AMM
• It utilizes liquidity by depositing it as collateral to the CVI AMM vis-a-vis minting/burning volatility tokens and placing them on DEXs
• As the vault owns both the AMM liquidity and the DEX liquidity, it is the sole beneficiary of time decay fees, thus has no exposure to Theta for the DEX liquidity.This can allow the volatility tokens DEX liquidity to scale up.
The mechanism for splitting the liquidity between the DEX and the AMM:
Splitting the amount being deposited into the theta vault correctly between DEX liquidity and CVI AMM liquidity should hold these requirements:
1. 1.
The CVI AMM liquidity must be P% higher than the liquidity needed as collateral backing them, in order to reserve liquidity for additional minting of CVI tokens to be utilized by arbitrageurs (P to be a parameter, changeable based on market needs).
2. 2.
The vault may add liquidity to the DEX based on its spot price, only in situations where the intrinsic value of CVI in the AMM is close enough to the CVI price on the DEX, otherwise it opens up an arbitrage trade opportunity.
To satisfy all requirements, we create the following 3 variables linear equation system and utilize its solution. The variables are the amount to add as CVI AMM liquidity, and the amount to mint CVI tokens along with the amount of USDC to add to the DEX liquidity.
$1) DepositAmount = a + b + c$
$2) (a+b) * 100 = b *200CVI(t) * (100 + P)$
$3) b/IntrinsicCVIPrice= c/CVIDEXPrice$
With the mechanism above, the vault creates a sustainable source of liquidity for the volatility tokens on DEXs. Overall the volatility tokens allow traders a similar experience to the VIX leveraged ETFs, while the theta vault operates as a structured product: receiving DEX swap fees, mint/burn fees, time decay fees from volatility token owners and P&L from CVI index decrement as counterparty to the volatility tokens long position.