Bonding Curve

Hypers.fun uses a constant product bonding curve with virtual reserves to determine token prices.

Why bonding curve?

Traditional AMM	Hypers.fun bonding curve
Needs external LPs	No LP required
Liquidity can be pulled	Always available liquidity
Price depends on pool depth	Price anchored to NAV
Slippage varies wildly	Predictable price impact

The formula

Token pricing follows the constant product formula (x × y = k):

Buy:  tokensOut = virtualTokens × usdcIn / (virtualBase + usdcIn)
Sell: usdcOut   = virtualBase × tokensIn / (virtualTokens + tokensIn)

Example

Assume:

• virtualBase = 2,000,000 USDC

• virtualTokens = 2,000,000 tokens

• You buy with 10,000 USDC

tokensOut = 2,000,000 × 10,000 / (2,000,000 + 10,000)
         = 20,000,000,000 / 2,010,000
         ≈ 9,950.25 tokens

Average execution premium ≈ 0.5%
Post-trade spot price ≈ +1.0%

Virtual reserve mechanism

Virtual reserves simulate deep liquidity even for small vaults. This prevents extreme price swings when TVL is low.

Parameter	Default	Meaning
virtualBase	2,000,000	Virtual USDC reserve
virtualTokens	2,000,000	Virtual token reserve

How it works:

Actual Price = NAV × (virtualBase / virtualTokens)

The virtual reserves don't represent real assets. They are parameters that control the curve shape.

Dynamic scaling

Fixed virtual reserves break at extremes:

• Small vault → price impact too high

• Large vault → price impact too low

So we scale virtual reserves proportionally with TVL:

function getEffectiveVirtualTokens() public view returns (uint256) {
    uint256 assets = getEstimatedAssets();
    if (assets <= initialAssets) return virtualTokens;
    return (virtualTokens * assets) / initialAssets;
}

function getEffectiveVirtualBase() public view returns (uint256) {
    uint256 assets = getEstimatedAssets();
    if (assets <= initialAssets) return virtualBase;
    return (virtualBase * assets) / initialAssets;
}

Example:

Vault TVL	Effective virtual reserves	$10K buy impact
$1,000 (initial)	2M / 2M	~0.5%
$100,000	200M / 200M	~0.5%
$10,000,000	20B / 20B	~0.5%

Result: consistent price impact regardless of vault size.

Maximum purchase limit

To prevent single trades from manipulating prices, each transaction is capped:

maxBuyBps = 100; // max 1% of total assets per transaction

Vault TVL	Max single buy
$100,000	$1,000
$1,000,000	$10,000
$10,000,000	$100,000

If you want to buy more, split into multiple transactions.

Price boundaries

Prices are capped to prevent extreme deviations from NAV:

Boundary	Limit	Meaning
Max premium	+100%	Price cannot exceed 2× NAV
Max discount	-50%	Price cannot fall below 0.5× NAV

uint256 maxPrice = (nav * (BPS + maxPremiumBps)) / BPS;  // 2× NAV
uint256 minPrice = (nav * (BPS - maxDiscountBps)) / BPS; // 0.5× NAV

Summary

Base price     = NAV (Total Assets / Total Supply)
Actual price   = NAV × (virtualBase / virtualTokens)
Virtual reserves scale with TVL (dynamic scaling)
Boundaries     = 0.5× NAV to 2× NAV
Max buy        = 1% of TVL per transaction