Hylo Equations

​

Master Equation

The fundamental equation governing hyUSD’s backing in Hylo V2: $$\text{hyUSD Supply} \times \text{hyUSD NAV} = \sum_{i}(\text{vUSD}_i \text{ Supply} \times \text{vUSD}_i \text{ NAV})$$ This means hyUSD is backed 1:1 by the sum of all virtual stablecoins across collateral pools when collateral ratios are healthy (CR > 100%).

​

Per-Asset Invariant

Each collateral pool maintains its own invariant: $$\text{ASSET TVL} = \text{vUSD Supply} \times \text{vUSD Price} + \text{xASSET Supply} \times \text{xASSET Price}$$ Where vUSD is always worth $1.

​

SOL Pool

$$\text{SOL TVL} = \text{vUSD}_{\text{SOL}}\text{ Supply} \times \$1 + \text{xSOL Supply} \times \text{xSOL Price}$$

​

BTC Pool

$$\text{BTC TVL} = \text{vUSD}_{\text{BTC}}\text{ Supply} \times \$1 + \text{xBTC Supply} \times \text{xBTC Price}$$

​

True Asset Value

​

SOL LST Pricing

For SOL LSTs, we use the Sanctum SOL value calculator program to determine the true LST price based on the amount of SOL held in each stake pool, avoiding market manipulation risks: $$\text{True LST Price} = \frac{\text{Amount of SOL in Stake Pool}}{\text{Total LST Supply}}$$

​

BTC Pricing

For wrapped BTC, we use price oracles to determine the true BTC value in USD.

​

Price Oracles

To calculate USD values and maintain pegs, we use price oracles:

• SOL/USD: Pyth SOL/USD price oracle
• BTC/USD: Pyth BTC/USD price oracle
• USDC/USD: Pyth USDC/USD price oracle

​

Net Asset Value (NAV) Calculations

​

vUSD NAV

Virtual stablecoins maintain a $1 NAV in healthy conditions: $$\text{vUSD NAV}_{\text{USD}} = \$1$$ In terms of the underlying asset: $$\text{vUSD NAV}_{\text{ASSET}} = \frac{1}{\text{ASSET Price (USD)}}$$

​

xASSET NAV

The NAV of leverage tokens uses the excess collateral value beyond vUSD backing: $$\text{xASSET NAV}_{\text{USD}} = \frac{\text{ASSET TVL (USD)} - \text{vUSD Supply}}{\text{xASSET Supply}}$$ If xASSET supply is zero, NAV defaults to $1.

​

hyUSD NAV

$$\text{hyUSD NAV}_{\text{USD}} = \$1$$

​

Collateral Ratio Calculations

​

Per-Asset Collateral Ratio

Each asset pool has its own collateral ratio: $$\text{CR} = \frac{\text{Total Collateral} \times \text{Collateral Price}}{\text{vUSD Supply}}$$

​

Max Mintable Stablecoin

The protocol caps stablecoin minting to prevent CR from dropping below a safety threshold: $$\text{Max Mintable} = \frac{\text{TVL} - \text{Target CR} \times \text{Current vUSD Supply}}{\text{Target CR} - 1}$$ Where Target CR is the configured stablecoin mint threshold, which is constrained on-chain to lie within the Neutral zone (135% – 165%). Minting is blocked if it would push the projected CR out of this band.

​

Max Swappable Stablecoin

When converting xASSET to hyUSD within a pool (no TVL change): $$\text{Max Swappable} = \frac{\text{TVL}}{\text{Target CR}} - \text{vUSD Supply}$$

​

Rebalance Zones

Each pool’s CR maps to one of six rebalance zones. The zone determines which rebalancing route is open, how rebalance pricing behaves, and which fee schedule applies. (These zones replace the former “stability mode” thresholds.) Zone boundaries are half-open: the lower bound is inclusive, the upper exclusive.

​

xASSET Effective Leverage

The effective leverage for any xASSET: $$\text{xASSET Effective Leverage} = \frac{\text{ASSET TVL}}{\text{xASSET Market Cap}}$$ Where: $$\text{xASSET Market Cap} = \text{xASSET NAV} \times \text{xASSET Supply}$$ The effective leverage approaches infinity as CR approaches 100%, and approaches 1 as CR increases.

​

Dynamic Collateral Routing

​

Piecewise-Linear Fee Curves

Hylo uses two independent fee curves for hyUSD minting and redemption. Each curve is defined as a set of (CR, fee) control points with linear interpolation between them. Mint fee curve:

• Domain: CR range bounded below by the Neutral zone threshold
• Shape: monotonically decreasing; fee is highest at the lower CR bound, falling to zero at the upper bound
• Below domain: minting is blocked (no valid fee)
• Above domain: fee clamps to zero

Redeem fee curve:

• Domain: wider CR range extending down toward the Destabilized threshold
• Shape: monotonically increasing; fee is zero at the lower CR bound, rising to maximum at the upper bound
• Below domain: fee clamps to zero
• Above domain: fee clamps to maximum

​

Projected CR for Fee Computation

Fees are evaluated at the projected CR, the CR after the operation: Mint projected CR: $$\text{CR}_{\text{projected}} = \frac{(\text{Total Collateral} + \text{Deposit}) \times \text{Price}}{\text{vUSD Supply} + \text{New vUSD}}$$ Redeem projected CR: $$\text{CR}_{\text{projected}} = \frac{(\text{Total Collateral} - \text{Withdrawal}) \times \text{Price}}{\text{vUSD Supply} - \text{Burned vUSD}}$$

​

xASSET Fees

xASSET (levercoin) fees use a discrete table indexed by rebalance zone, with separate mint / redeem rates per zone: See Anti-Destabilization Fees for why this schedule rarely binds in normal operation.

​

Collateral Rebalancing

​

Max Sellable Collateral (Low CR)

When a pool’s CR drops into the sell zone, the maximum collateral available for sale targets the sell zone inner bound (135% CR): $$\text{Max Sellable} = \frac{\text{Sell Zone CR} \cdot \text{vUSD Supply} - \text{Price} \cdot \text{Total Collateral}}{\text{Price} \cdot (\text{Sell Zone CR} - 1)}$$

​

Max Buyable Collateral (High CR)

When a pool’s CR rises into the buy zone, the maximum buyable collateral targets the buy zone inner bound (165% CR): $$\text{Max Buyable} = \frac{\text{Price} \cdot \text{Total Collateral} - \text{Buy Zone CR} \cdot \text{vUSD Supply}}{\text{Price} \cdot (\text{Buy Zone CR} - 1)}$$

​

Rebalance Pricing

Rebalance prices apply a signed percentage spread to the oracle spot price: $$\text{Rebalance Price} = \text{Spot} \times (1 + \delta(\text{CR}))$$ Where $\delta(\text{CR})$ interpolates linearly between two per-asset configured spreads of opposite sign (one at the inner bound, one at the outer bound), so it crosses zero (the unadjusted oracle price) partway through the zone. See Rebalance Pricing for which side each bound favors and why. Both endpoint percentages are configurable per asset, determining how aggressively the protocol prices rebalancing activity for each pool. The schedule is a fixed set of percentages rather than a function of live market data, so prices are deterministic across the zone.

​

Borrow Rate for Non-Yield Assets

For collateral pools without native yield (e.g., BTC), a per-epoch borrow rate is harvested: $$\text{Collateral Harvested} = \text{Vault Balance} \times \text{Rate Per Epoch}$$ The harvested collateral is converted to hyUSD and distributed between the Earn Pool and treasury according to configurable allocation parameters.

​

Yield Sources by Asset Type

​

Earn Pool

​

LP Token NAV

$$\text{eHYUSD NAV} = \frac{\text{hyUSD in Pool}}{\text{eHYUSD Supply}}$$ Returns $1 if eHYUSD supply is zero.

​

Deposit

$$\text{eHYUSD Out} = \frac{\text{hyUSD In}}{\text{eHYUSD NAV}}$$

​

Withdrawal

Pro-rata share of both hyUSD and any xASSET in the pool, with a configurable withdrawal fee applied to the hyUSD portion.

​

Average Reserve Yield (SOL Pool)

$$\text{Average SOL Reserve Yield} = \frac{\sum_{j=1}^{n} (\text{Supply}_{\text{LST}_j} \times \text{Price}_{\text{LST}_j} \times \text{APY}_{\text{LST}_j})}{\text{Total SOL In Reserve}}$$