Below you’ll see the terms
x-token and y-token. These refer to the token that you bring to the
pool (x-token) and the collateral token that is used to purchase it (y-token). Said another way,
the x-token is your custom ERC-20 and the y-token is typically something like USDC or USDT.Parameter Overview
| Parameter | What it controls |
|---|---|
x_add | Initial supply of x-tokens deposited into the curve |
p_lower | Y-intercept of the initial price curve |
V | Volatility sensitivity that governs how quickly slope changes as x moves |
C | Initial concentration parameter that shifts the curve horizontally |
x_min | Starting x-position |
C and x_add, which move only when you explicitly add liquidity according to the rules in the math spec.
Parameter Details
x_add — Initial Inventory
- Definition: Total amount of token X you transfer into the Token Bonding Curve (TBC) during deployment.
- Effect: Sets the ceiling on cumulative sales; once the curve dispenses
x_addtokens, the AMM cannot sell more unless you add liquidity. Largerx_addstretches the curve over more supply, creating a smoother price climb. - Calibration hints: Start from the number of tokens you expect to sell via the AMM.
p_lower — Initial Price Floor
- Definition: Price intercept when
x = 0on the initial price curve. - Effect: Establishes the minimum price; even if demand is low, the curve will not fall below
p_lower. Raisingp_lowerguarantees higher opening revenue but can discourage initial adoption.
V — Volatility Sensitivity
- Definition: Measures how aggressively the curve responds to a given trade size once you’re at a specific point on the inventory axis.
- Effect: At the same inventory position, higher
Vvalues make each trade move price more sharply, which translates into greater volatility and higher marginal costs; lowerVsoftens the response so prices adjust more gently. - Calibration hints: Set
Vhigher when you want speculation or scarcity premiums; set it lower when prioritizing predictable fills for market makers or retail buyers. This value can only be set during pool creation and is not adjustable later.
C — Initial Concentration
- Definition: Horizontal shift that influences the “density” of the curve near the start of trading.
- Effect: Larger
Csmooths early trades by reducing slope sensitivity nearx_min; smaller values produce a sharper bend.Cwill update after liquidity additions using the same formula, so a well-chosenCgives you a predictable baseline.
x_min — Starting Position
- Definition: Lower bound of the trading region. You can think of it as the amount of x-tokens that have already been “synthetically sold” before the pool opens.
- Effect: Controls the initial slope and therefore the opening spot price. Increasing
x_minmoves you further along the curve before the first trade occurs, which reduces the initial slope and price. - Calibration hints: Pick a non-zero value high enough to avoid a near-infinite slope when combined with small
C.
Calibrating for Real Launches
- Revenue targeting: Work backward from the total y-tokens you hope to collect.
- Market depth: Low
x_addpaired with highVcan create runaway prices.