Execution cost estimation, slippage curve modeling, and optimal trade sizing based on AMM liquidity depth

Slippage Modeling Estimate execution costs, model slippage curves from AMM mechanics and empirical quotes, and determine optimal trade sizes that keep costs within acceptable thresholds. What Is Slippage? Slippage is the difference between the expected price at the time you decide to trade and the actual execution price you receive. On decentralized exchanges, slippage is deterministic and measurable — unlike CEX slippage, which depends on hidden order book dynamics. Example : You expect to buy a token at 0.001 SOL. Your trade executes at 0.00105 SOL. That 5% difference is slippage — it directly reduces your profit and increases your break even threshold. Sources of Slippage 1. AMM Price Impact (Primary Source) Automated market makers use bonding curves that move price as liquidity is consumed. On a constant product AMM ( x y = k ): Where x is the reserve of the input token and Δx is your trade size. A 1 SOL trade against a pool with 100 SOL reserves produces ~1% price impact. Against 10 SOL reserves, it produces ~10%. See references/slippage math.md for full derivations and CLMM adjustments. 2. DEX Fees Every swap incurs a fee taken from the trade: DEX Fee Notes Raydium 0.25% Standard AMM pools Orca 0.30% Whirlpool concentrated pools Meteora 0.1–2.0% Dynamic fees based on volatility PumpFun 1.0% Bonding curve phase 3. Priority Fees Solana validators prioritize transactions with higher compute unit prices. During congestion or for time sensitive trades: Normal: 0.0001 SOL (negligible) Competitive: 0.001–0.01 SOL High congestion: 0.01–0.1 SOL 4. MEV (Sandwich Attacks) Searchers detect pending swaps and sandwich them — buying before your trade (raising the price) and selling after (capturing the difference). MEV cost depends on: Trade size (larger = more attractive target) Token liquidity (thin pools = easier to manipulate) Slippage tolerance setting (higher tolerance = more extractable) Typical MEV cost: 0–200 bps on vulnerable trades. 5. Stale Quotes Between receiving a quote and landing the transaction on chain (0.4–2 seconds on Solana), the price may move. Volatile tokens can shift 50–500 bps in that window. Constant Product Slippage Formula For a pool with reserves (x, y) and invariant k = x y : Buying tokens with SOL (input Δx SOL): Selling tokens for SOL (input Δy tokens): Key insight : Slippage scales with trade size / (reserves + trade size) . This is approximately linear for small trades and accelerates sharply as trade size approaches reserve size. Quick Reference Table Trade / Reserve Ratio Approximate Slippage 0.1% 0.1% (1 bp) 1% 1.0% (100 bps) 5% 4.8% (476 bps) 10% 9.1% (909 bps) 25% 20% (2000 bps) 50% 33% (3333 bps) CLMM Slippage Concentrated Liquidity Market Makers (Orca Whirlpools, Meteora DLMM) concentrate liquidity in specific price ranges: Within the active range: slippage is lower than constant product by a concentration factor Crossing tick boundaries: additional slippage as the next tick's liquidity may be sparse Approximation: clmm slippage ≈ cp slippage / concentration factor Typical concentration factors: 5–50x for well managed positions. Empirical Slippage Measurement Theoretical formulas assume single pool routing. In practice, Jupiter aggregates across multiple pools and routes. Empirical measurement is more accurate: 1. Query Jupiter /quote at multiple trade sizes (0.01, 0.1, 1, 5, 10, 50 SOL) 2. Record output amount and effective price at each size 3. Compute slippage in bps relative to smallest trade (proxy for spot) 4. Fit a power law model: slippage bps = a trade size^b This captures real routing behavior, multi pool splitting, and available liquidity. See scripts/slippage curve.py for the full implementation. Total Execution Cost Model See references/cost model.md for component breakdowns and worked examples. Break Even Analysis For a roundtrip (buy + sell): The token must move more than roundtrip cost bps in your favor to be profitable. For a token with 200 bps entry slippage, 200 bps exit slippage, and 50 bps fees: You need at least a 4.5% price move just to break even. See scripts/execution cost.py for automated cost estimation. Optimal Trade Sizing Maximum Size for Slippage Threshold Given a slippage curve s(q) = a q^b , solve for max trade size: Multi Tranche Execution For large orders, splitting reduces total slippage because each tranche faces a partially reset order book (on CLMMs) or allows arbitrageurs to rebalance between tranches: TWAP Strategy Time Weighted Average Price execution: Divide total order into equal sized tranches Execute one tranche per interval (e.g., every 10 seconds) Total slippage is significantly lower than single execution Tradeoff: price may move against you during execution window Slippage by Token Category Category Typical Pool TVL Slippage for 1 SOL Slippage for 10 SOL Blue chip $10M <5 bps <20 bps Mid cap $100K–$10M 10–50 bps 50–500 bps Small cap $10K–$100K 50–200 bps 500–2000 bps Micro/PumpFun <$10K 200–2000 bps Often impossible Integration Points liquidity analysis : Get pool TVL and reserve data to feed slippage estimates position sizing : Use max trade size from slippage curve as a position size constraint jupiter api : Fetch real quotes for empirical slippage measurement risk management : Include execution costs in risk/reward calculations dex pool analysis : Understand pool mechanics that drive slippage Files References File Description references/slippage math.md AMM slippage derivations, CLMM adjustments, multi pool routing math references/cost model.md Total execution cost components, break even analysis, cost comparison tables Scripts File Description scripts/slippage curve.py Build empirical slippage curves from Jupiter quotes, fit power law model scripts/execution cost.py Estimate total execution cost and break even for a specific trade

slippage-modeling