Impact‑Based Lending (LTV)

A lending market that adapts borrow limits to the real cost of exiting positions and the current volatility regime.

Why LTV should be slippage‑aware

Static LTVs ignore how much it costs to unwind risk during turbulence. We make borrow limits a function of execution cost and current volatility.

Impact curve

We estimate the slippage to close a position of size q given pool depth & current curve (AMM + orderbook). LTV never exceeds 1 − slippage(q).

Volatility guardrails

Short‑horizon EWMA volatility scales the maximum loan‑to‑value and increases maintenance margin when regimes shift.

Same‑asset debt

Optional debt in the collateral denomination enables delta‑neutral strategies with lower liquidation correlation.

Policy examples

Simple rules that work on‑chain.

Signal	Effect
EWMA volatility ↑	Reduce MaxLTV; raise maintenance buffer
Pool depth ↑	Increase MaxLTV (risk can exit cheaply)
Orderbook tightens	Increase MaxBorrow for smaller trades

Constant‑Product AMM dynamics & price impact

How the invariant and pool depth govern execution price when liquidations sell collateral into the pool.

AMM invariant

We model reserves X (asset A) and Y (asset B) under the constant‑product x·y=k. Current price of A in B is P_A=Y/X. A liquidation that sells ΔX shifts reserves to X′=X+ΔX and Y′=k/X′; the B received is:

\[B_{\text{out}}=Y-\tfrac{k}{X+\Delta X}=\tfrac{Y\,\Delta X}{X+\Delta X}.\]

The execution price is P_exec=B_out/ΔX=Y/(X+ΔX), lower than P_A. The relative impact (slippage) is:

\[\text{Impact}=1-\tfrac{P_{\text{exec}}}{P_A}=\tfrac{\Delta X}{X+\Delta X}.\]

Intuition: Larger trades relative to pool size (ΔX/X) cause greater price impact; if ΔX=0.5X, impact ≈ 33%.

Incorporating realized volatility into LTV

Use a volatility haircut to budget adverse moves during liquidation.

Volatility haircut

Let σ be realized volatility and consider liquidation horizon t. A worst‑case drop fraction δ (e.g., δ=zσ√t) scales down usable collateral. Then the volatility‑adjusted limit obeys:

\[ \text{Loan} \le (1-\delta)\times \text{Collateral Value}. \]

Equivalently, LTV_vol=1−δ. As σ rises, allowable LTV falls.

Combining slippage & volatility for LTV

Safe LTV must respect both AMM depth (slippage) and expected price moves.

Combined limit

Requiring the liquidation proceeds cover debt with a volatility buffer yields:

\[ LTV_{\max}(\Delta X)=\frac{1-\delta}{1+\Delta X/X}. \tag{★}\]

This couples depth and volatility: larger positions (ΔX/X) and higher δ both reduce allowable LTV.

Figure 1: LTV vs Collateral‑to‑Pool Ratio

Dynamic LTV adjustment for utilization & liquidity

As B reserves are borrowed (utilization rises), any new liquidation suffers more impact. LTV must fall with utilization.

Reserve utilization

Define U_B=1−Y_{current}/Y_{initial}. A simple guard is LTV_{allowed}(U_B)=LTV_{max}·(1−U_B).

Figure 2: LTV Heatmap by Volatility and Collateral Size

Preventing excessive drain

Cap single‑loan size (ΔX/X) and enforce minimum post‑trade reserves Y′. Raise rates at high utilization to discourage further borrowing.

Concluding insights

Comparative scenarios

Deep pools → slippage small → volatility dominates: low‑vol assets can support higher LTV than high‑vol assets.

Shallow pool or huge loan → slippage dominates → even stable assets get conservative LTV caps.

Core principle

LTV must be constrained by market depth and asset risk.

As volatility or intended borrow size grows, the safe LTV region shrinks (see Figures 1–2).

Operational tips

Track ΔX/X against pool depth, apply volatility haircuts, and scale LTV down with utilization.