# AMM Liquidity and Settlement

> Canonical: https://docs.velocity.exchange/developers/concepts/optimizations

Velocity's AMM is a designated market maker: it quotes both sides of every perp market whether or not an external maker is present, so an order always has a counterparty. That obligation is also its problem. A market maker that cannot step back has to manage depth and inventory through its parameters instead, and those parameters move.

This page covers how the AMM sizes its depth, when it competes for fills, and how the P&L it takes on is settled. It is written for anyone building a maker, a filler, or a risk model that has to account for AMM behavior and not only for DLOB makers.

## Depth comes from `k` and the reserve bounds together

The AMM's liquidity depth is set by `k`, the constant-product invariant, and by how tightly its base reserves are bounded. Raising `k` while narrowing the maximum and minimum base reserves concentrates the same bid and ask liquidity into a narrower price range, which is what `AMM.concentration_coef` controls. An admin moves it with `update_perp_market_concentration_coef`.

The bounds themselves come out of `k` and the coefficient:

```
max_base_asset_reserve = sqrt_k * concentration_coef / CONCENTRATION_PRECISION
min_base_asset_reserve = sqrt_k * CONCENTRATION_PRECISION / concentration_coef
```

A coefficient close to `CONCENTRATION_PRECISION`, meaning 1x, pulls both fences in tight. A larger one, up to `MAX_CONCENTRATION_COEFFICIENT` at about 1.4142x, spreads the same `k` over a wider reserve range. Admins tune this through `concentration_scale` rather than setting the coefficient directly.

Depth available to a single fill is narrower still. `calculate_amm_available_liquidity` additionally caps one step at `base_asset_reserve / max_fill_reserve_fraction`, and then at half the depth available on that side. `max_fill_reserve_fraction` is a per-market, admin-settable field, so the share of reserves one fill can move is whatever the market carries; read it off the market account.

Modeling how much size the AMM absorbs at a given price means reading that market's live `k`, reserve bounds, and fill fraction rather than assuming a fixed depth. All of them drift over time, for the reason in the next section.

## Formulaic `k` adjustments move depth after every funding update

When funding is applied, the AMM adjusts `k` against what that funding cost or earned it. There are three cases and only two of them change anything:

| Condition | Budget | Effect on `k` |
|---|---|---|
| The AMM **received** funding this period, and neither spread has widened past `base_spread` | Half the received amount | `k` increases, more depth |
| The AMM **paid** funding, and the cost exceeded `net_revenue_since_last_funding` | Half the shortfall, negative | `k` decreases, less depth |
| Anything else, including a payment the period's revenue covered | 0 | No change |

Each step is bounded. The scale factor is capped at 10 bps of `sqrt_k` scaled by `AMM.curve_update_intensity`, a per-market value in the range 0 to 100 that an admin sets with `update_perp_market_curve_update_intensity`. At the top of that range one funding update moves `sqrt_k` by at most 0.1%, and a lower intensity scales the step down proportionally. `k` therefore converges toward its target across many funding periods instead of jumping to it. An integration that caches `k` or the reserves should refresh on a cadence that accounts for that drift.

Two gates can switch this off entirely: `AMM.curve_update_intensity` at 0, and the per-market `MarketConfigFlag::DisableFormulaicKUpdate` bit. Read both off the market rather than assuming formulaic updates are running. A `k` increase is also refused once `sqrt_k` reaches `MAX_SQRT_K`, and a decrease is refused when it would take the AMM below the depth its minimum order size needs.

## The AMM competes in the JIT auction

The AMM does not only backstop size that no maker wanted. It can bid in the [JIT auction](/developers/market-makers/jit-auctions.md) itself, to reduce its own inventory, which means a maker bidding into an auction may be quoting against it rather than alongside an empty book.

How much it takes is sized by a chain of caps, set out in [AMM Spread and Quoting](/developers/concepts/amm-spread.md#sizing-its-participation-in-a-jit-auction). One exception matters for fill sizing. When a hard AMM gate is active, meaning a pause, a drawdown, MM-versus-oracle volatility, or an invalid oracle, a DLOB match fills DLOB-only and AMM JIT does not top it up. Fills can be capped to the resting maker's size during those windows, so do not assume the AMM backstops a match.

## Unrealized P&L is settled out of a pool, not minted

A user's unrealized P&L against the AMM is unbounded in principle, because the price it is marked against is a live oracle rather than a bounded curve, because the market can be imbalanced, and because the AMM's maximum spread is capped. A position marked at a price nobody can pay is still marked.

In practice a winning position can only be settled and withdrawn as collateral once an offsetting loss, or enough collected fees, has replenished the market's P&L settlement pool. Until then, winners can be offered discounted margin on their unrealized gains and can withdraw their share of the pool as it grows. [P&L](/protocol/trading/profit-loss.md) owns the full settlement mechanism.

The discount has a boundary worth knowing. If a market's unrealized P&L imbalance exceeds its per-market threshold, the margin system discounts those unrealized gains at the **initial** margin stage only, never at maintenance. That means the discount can block a new position while leaving an existing position's liquidation threshold exactly where it was. See the margin section of [Cross-Collateral Deposits](/protocol/trading/margin.md).

## Terminal state costs nothing when inventory is flat

Repeg and `k`-change operations are priced against the AMM's terminal state, the position it would be left holding. When its inventory is 0, that cost is 0, so those operations are free. The AMM still tracks the market's remaining position imbalance and sizes its spread and depth against it, within the constraints of being a market maker that cannot stop quoting.