AZL LP simulator

Model

• AZL/USD and SOL/USD prices follow correlated geometric Brownian motion with no drift, plus fixed-size, random-sign AZL jumps (news, informed flow).
• The AZL/SOL pool bears the ratio volatility: σ² = σ_AZL² + σ_SOL² − 2ρ σ_AZL σ_SOL. That is the triangle: a SOL move alone is enough to create an arbitrage.
• Diffusion losses: LVR σ²/8 · V (×k for concentrated liquidity), reduced by fees via P_trade = 1 / (1 + γ·√(2λ)/σ), λ = blocks per year (Milionis, Moallemi, Roughgarden).
• Jump losses: L√P · (√r_eff − 1)², where r_eff removes the fee band. A jump smaller than the fee costs nothing.
• Fees: uninformed volume × fee, only while price is in range. Volume = reference volume × (0.30% / fee)^ε.
• Active management: share of arbitrage losses avoided when an operator rebalances before arbitrageurs, minus its cost. Assumes a reliable AZL reference price.

Limits

• No transaction costs or Jito tips for arbitrageurs: on Solana, these would slightly reduce losses.
• Volume is exogenous: the extra depth of concentrated liquidity does not attract more flow in the model.
• Fixed range, no repositioning. Meteora DLMM is approximated as a concentrated range.
• No fee compounding, no JIT liquidity, no reward emissions.
• With 400 ms blocks, fees absorb almost all diffusion. This theoretical result depends on the model; jumps and informed flow then dominate, and their calibration matters more than σ.

Study benchmarks (Solmaz et al., 2026, SOL/USDC on Solana)