VT Swap

VT liquidity is provided through an Automated Market Maker (AMM) pool with a specially designed price formula, aimed at achieving less gap between the prices of VT and T as the vesting period nears its end.

Price Formula:

$$\text{price}(t) = \frac{1}{\text{rateScalar}(t) }\times \ln \left( \frac{p(t)}{(1 - p(t))*R} \right) + \text{rateAnchor}(t)$$

• Normalized time ( t ) ranges from 0 (Vesting End) to 1.

• P(t) is a metric that measures the proportion of VT in the pool. Calculated by the formula: P(t) = Amount of VT / (Amount of VT + Amount of T)

• rateScalar: rateScalar(t)=ScalarRoot/t, adjusts dynamically to maintain capital efficiency.

• rateAnchor: rateAnchor(t) = 1 + (InitialAnchor-1) * t, adjusts the expected discount between VT and T.

• R: Initial Liquidity Rate of VT/T

Example:

Alice wants to swap 100 T for VT.

Given $\text{rateScalar} =100$, $\text{rateAnchor} = 1.1$，R=1 Initial VT proportion $( p_{\text{before}} = 0.6 )$

$$\text{price}_{\text{before}} = \frac{1}{100} \times \ln\left(\frac{0.6}{0.4}\right) + 1.1 = 1.104055$$

After swapping 100 T for VT, assuming $p_{\text{after}} = 0.55$

$$\text{price}_{\text{after}} = \frac{1}{100} \times \ln\left(\frac{0.55}{0.45}\right) + 1.1 = 1.102007$$

$$dVT = 100 \times \frac{1.104055 + 1.102007}{2} = 110.3031$$

Alice received 110.3031 VT