🤖🐮 cowsol, a cow arbitrage solver

tl; dr:

🤖 solvers are a key component in the cow protocol, serving as the matching engines that find the best execution paths for user orders. in this project, i implement a solver from scratch, running certain arbitrage strategies (e.g., running nelder mead simplex optimization).

📚 more details, check my mirror post, on cowsol, an arb solver for CoW protocol.

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current strategies

"no market maker" spread arbitrage

Spread trades are the act of purchasing one security and selling another related security (legs) as a unit.

• One-leg limit price trade.
  • In this type of order (e.g., orders/instance_1.json), we have a limit price and one pool reserve (e.g., A -> C).
• Two-legged limit price trade for a single execution path.
  • In this type of order (e.g., orders/instance_2.json), we have a two-legged trade (e.g., A -> B -> C), with only one option for each leg and it can be solved without any optimization.
• Two-legs limit price trade for multiple execution paths.
  • In this type of order (e.g., orders/instance_3.json), we have a two-legged trade (e.g., A -> B -> C) with multiple pool reserves for each leg (e.g., B1, B2, B3), so the order can be completed dividing it through multiple paths and optimizing for maximum total surplus.

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implemented features

liquidity sources

• Support for constant-product AMMs, such as Uniswap v2 (and its forks), where pools are represented by two token balances.

orders types

• Support for limit price orders for single order instances.
• Support for limit price orders for multiple orders on a single reserve instance.
• Support for limit price orders for multiple orders on multiple reserve instances.

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execution specs

A limit order is an order to buy or sell with a restriction on the maximum price to be paid or the minimum price to be received (the "limit price").

This limit determines when an order can be executed:

limit_price = sell_amount / buy_amount >= executed_buy_amount / executed_sell_amount

a good rule of thumb is that the price impact of your order is about twice the size of your order relative to the pool.

surplus

For multiple execution paths (liquidity sources), we choose the best solution by maximizing the surplus of an order:

surplus = exec_buy_amount  - exec_sell_amount / limit_price

amounts representation

All amounts are expressed by non-negative integer numbers, represented in atoms (i.e., multiples of $10^{18}$). We add an underline (_) to results to denote decimal position, allowing easier reading.

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order specs

User orders describe a trading intent.

User order specs

• sell_token: token to be sold (added to the amm pool).
• buy_token: token to be bought (removed from the amm pool).
• sell_amount: limit amount for tokens to be sold.
• buy_amount: limit amount for tokens to be bought.
• exec_sell_amount: how many tokens get sold after order execution.
• exec_buy_amount: how many tokens get bought after order execution.
• allow_partial_fill: if False, only fill-or-kill orders are executed.
• is_sell_order: if it's sell or buy order.

AMM exec specs

• amm_exec_buy_amount: how many tokens the amm "buys" (gets) from the user, and it's the sum of all exec_sell_amount of each path (leg) in the order execution.
• amm_exec_sell_amount: how many tokens the amm "sells" (gives) to the user, and it's the sum of all exec_buy_amount of each path (leg) in the order execution.
• market_price: the price to buy/sell a token through the user order specs.
• prior_price: the price to buy/sell a token prior to being altered by the order.
• prior_sell_token_reserve: the initial reserve amount of the "sell" token, prior to being altered by the order.
• prior_buy_token_reserve: the initial reserve amount of the "buy" token, prior to being altered by the order.
• updated_sell_token_reserve: the reserve amount of the "sell" token after being altered by the order.
• updated_buy_token_reserve: the reserve amount of the "buy" token after being altered by the order.

---

installing

Install Requirements

python3 -m venv venv
source ./venv/bin/activate
make install_deps

create an .env

cp .env.example .env
vim .env

Install cowsol

make install

Test your installation:

cowsol

---

usage

Listing available pools in an order instance file

cowsol -a <order file>

Example output:

🐮 AMMs available for orders/instance_1.json

{   'AC': {   'reserves': {   'A': '10000_000000000000000000',
                              'C': '10000_000000000000000000'}}}

listing orders in an order instance file

cowsol -o <order file>

Example output:

🐮 Orders for orders/instance_1.json

{   '0': {   'allow_partial_fill': False,
             'buy_amount': '900_000000000000000000',
             'buy_token': 'C',
             'is_sell_order': True,
             'sell_amount': '1000_000000000000000000',
             'sell_token': 'A'}}

solving a trade for one-leg limit price

cowsol -s orders/instance_1.json 

For example, for this user order instance:

{
    "orders": {
        "0": {
            "sell_token": "A",
            "buy_token": "C",
            "sell_amount": "1000_000000000000000000",
            "buy_amount": "900_000000000000000000",
            "allow_partial_fill": false,
            "is_sell_order": true
        }
    },
    "amms": {
        "AC": {
            "reserves": {
                "A": "10000_000000000000000000",
                "C": "10000_000000000000000000"
            }
        }
    }
}

Generates this output (logging set to DEBUG):

🐮 Solving orders/instance_1.json.
🐮 Order 0 is a sell order.
🐮 One-leg trade overview:
🐮 ➖ sell 1000_000000000000000000 of A, amm reserve: 10000_000000000000000000
🐮 ➕ buy 900_000000000000000000 of C, amm reserve: 10000_000000000000000000
🟨   Prior sell reserve: 10000_000000000000000000
🟨   Prior buy reserve: 10000_000000000000000000
🟨   Spot sell price 1.0
🟨   Spot buy price 1.0
🟨   AMM exec sell amount: 1000_000000000000000000
🟨   AMM exec buy amount: 909_090909090909090909
🟨   Updated sell reserve: 11000_000000000000000000
🟨   Updated buy reserve: 9090_909090909090909091
🟨   Market sell price 1.21
🟨   Market buy price 0.8264462809917356
🟨   Can fill: True
🐮 TOTAL SURPLUS: 9_090909090909090909
🐮 Results saved at solutions/solution_1_cowsol.json.

And this solution:

{
    "amms": {
        "AC": {
            "sell_token": "C",
            "buy_token": "A",
            "exec_buy_amount": "1000_000000000000000000",
            "exec_sell_amount": "909_090909090909090909"
        }
    },
    "orders": {
        "0": {
            "allow_partial_fill": false,
            "is_sell_order": true,
            "buy_amount": "900_000000000000000000",
            "sell_amount": "1000_000000000000000000",
            "buy_token": "C",
            "sell_token": "A",
            "exec_buy_amount": "909_090909090909090909",
            "exec_sell_amount": "1000_000000000000000000"
        }
    }
}

Note:

• Input orders are located at orders/.
• Solutions are located at solutions/.

two-legged limit price trade for a single execution path

cowsol -s orders/instance_2.json 

For example, this user order instance:

{
    "orders": {
        "0": {
            "sell_token": "A",
            "buy_token": "C",
            "sell_amount": "1000_000000000000000000",
            "buy_amount": "900_000000000000000000",
            "allow_partial_fill": false,
            "is_sell_order": true
        }
    },
    "amms": {
        "AB2": {
            "reserves": {
                "A": "10000_000000000000000000",
                "B2": "20000_000000000000000000"
            }
        },        
        "B2C": {
            "reserves": {
                "B2": "15000_000000000000000000",
                "C": "10000_000000000000000000"
            }
        }
    }
}

Generates this (DEBUG) output:

🐮 Solving orders/instance_2.json.
🐮 Order 0 is a sell order.
🐮 FIRST LEG trade overview:
🐮 ➖ sell 1000_000000000000000000 of A
🐮 ➕ buy some amount of B2
🟨   Prior sell reserve: 10000_000000000000000000
🟨   Prior buy reserve: 20000_000000000000000000
🟨   Spot sell price 0.5
🟨   Spot buy price 2.0
🟨   AMM exec sell amount: 1000_000000000000000000
🟨   AMM exec buy amount: 1818_181818181818181818
🟨   Updated sell reserve: 11000_000000000000000000
🟨   Updated buy reserve: 18181_818181818181818180
🟨   Market sell price 0.605
🟨   Market buy price 1.6528925619834711
🟨   Can fill: True
🐮 SECOND LEG trade overview:
🐮 ➖ sell 1818_181818181818181818 of B2
🐮 ➕ buy some amount of C
🟨   Prior sell reserve: 15000_000000000000000000
🟨   Prior buy reserve: 10000_000000000000000000
🟨   Spot sell price 1.5
🟨   Spot buy price 0.6666666666666666
🟨   AMM exec sell amount: 1818_181818181818181818
🟨   AMM exec buy amount: 1081_081081081081081081
🟨   Updated sell reserve: 16818_181818181818181820
🟨   Updated buy reserve: 8918_918918918918918919
🟨   Market sell price 1.8856749311294765
🟨   Market buy price 0.5303140978816655
🟨   Can fill: True
🐮 TOTAL SURPLUS: 181_081081081081081081
🐮 Results saved at solutions/solution_2_cowsol.json.

And this solution:

{
    "amms": {
        "AB2": {
            "sell_token": "B2",
            "buy_token": "A",
            "exec_buy_amount": "1000_000000000000000000",
            "exec_sell_amount": "1818_181818181818181818"
        },
        "B2C": {
            "sell_token": "C",
            "buy_token": "B2",
            "exec_buy_amount": "1818_181818181818181818",
            "exec_sell_amount": "1081_081081081081081081"
        }
    },
    "orders": {
        "0": {
            "allow_partial_fill": false,
            "is_sell_order": true,
            "buy_amount": "900_000000000000000000",
            "sell_amount": "1000_000000000000000000",
            "buy_token": "C",
            "sell_token": "A",
            "exec_buy_amount": "1081_081081081081081081",
            "exec_sell_amount": "1000_000000000000000000"
        }
    }
}

two-legged limit price trade for multiple execution paths

cowsol -s orders/instance_3.json 

For example, this user order instance:

{
    "orders": {
        "0": {
            "sell_token": "A",
            "buy_token": "C",
            "sell_amount": "1000_000000000000000000",
            "buy_amount": "900_000000000000000000",
            "allow_partial_fill": false,
            "is_sell_order": true
        }
    },
    "amms": {
        "AB1": {
            "reserves": {
                "A": "10000_000000000000000000",
                "B1": "20000_000000000000000000"
            }
        },
        "AB2": {
            "reserves": {
                "A": "20000_000000000000000000",
                "B2": "10000_000000000000000000"
            }
        },        
        "AB3": {
            "reserves": {
                "A": "12000_000000000000000000",
                "B3": "12000_000000000000000000"
            }
        },        
        "B1C": {
            "reserves": {
                "B1": "23000_000000000000000000",
                "C": "15000_000000000000000000"
            }
        },
        "B2C": {
            "reserves": {
                "B2": "10000_000000000000000000",
                "C": "15000_000000000000000000"
            }
        },
        "B3C": {
            "reserves": {
                "B3": "10000_000000000000000000",
                "C": "15000_000000000000000000"
            }
        }
    }
}

Generates this (DEBUG) output:

🐮 Solving orders/instance_3.json.
🐮 Order 0 is a sell order.
🐮 Using the best two execution simulations by surplus yield.
🐮 FIRST LEG trade overview:
🐮 ➖ sell 289_073705673240477696 of A
🐮 ➕ buy some amount of B1
🟨   Prior sell reserve: 10000_000000000000000000
🟨   Prior buy reserve: 20000_000000000000000000
🟨   Spot sell price 0.5
🟨   Spot buy price 2.0
🟨   AMM exec sell amount: 289_073705673240477696
🟨   AMM exec buy amount: 561_904237334502880476
🟨   Updated sell reserve: 10289_073705673240477700
🟨   Updated buy reserve: 19438_095762665497119520
🟨   Market sell price 0.5293251886038823
🟨   Market buy price 1.8891978343927718
🟨   Can fill: True
🐮 SECOND LEG trade overview:
🐮 ➖ sell 561_904237334502880476 of B1
🐮 ➕ buy some amount of C
🟨   Prior sell reserve: 23000_000000000000000000
🟨   Prior buy reserve: 15000_000000000000000000
🟨   Spot sell price 1.5333333333333334
🟨   Spot buy price 0.6521739130434783
🟨   AMM exec sell amount: 561_904237334502880476
🟨   AMM exec buy amount: 357_719965038404924081
🟨   Updated sell reserve: 23561_904237334502880480
🟨   Updated buy reserve: 14642_280034961595075920
🟨   Market sell price 1.609169076200932
🟨   Market buy price 0.6214387380354636
🟨   Can fill: True
🐮 FIRST LEG trade overview:
🐮 ➖ sell 710_926294326759522304 of A
🐮 ➕ buy some amount of B3
🟨   Prior sell reserve: 12000_000000000000000000
🟨   Prior buy reserve: 12000_000000000000000000
🟨   Spot sell price 1.0
🟨   Spot buy price 1.0
🟨   AMM exec sell amount: 710_926294326759522304
🟨   AMM exec buy amount: 671_163952522389243203
🟨   Updated sell reserve: 12710_926294326759522300
🟨   Updated buy reserve: 11328_836047477610756800
🟨   Market sell price 1.1219975504153292
🟨   Market buy price 0.8912675429904732
🟨   Can fill: True
🐮 SECOND LEG trade overview:
🐮 ➖ sell 671_163952522389243203 of B3
🐮 ➕ buy some amount of C
🟨   Prior sell reserve: 10000_000000000000000000
🟨   Prior buy reserve: 15000_000000000000000000
🟨   Spot sell price 0.6666666666666666
🟨   Spot buy price 1.5
🟨   AMM exec sell amount: 671_163952522389243203
🟨   AMM exec buy amount: 943_426540218806186671
🟨   Updated sell reserve: 10671_163952522389243200
🟨   Updated buy reserve: 14056_573459781193813330
🟨   Market sell price 0.7591582673440884
🟨   Market buy price 1.317248382868167
🟨   Can fill: True
🐮 TOTAL SURPLUS: 401_146505257211110752
🐮 Results saved at solutions/solution_3_cowsol.json.

And this solution:

{
    "amms": {
        "AB1": {
            "sell_token": "B1",
            "buy_token": "A",
            "exec_sell_amount": "561_904237334502880476",
            "exec_buy_amount": "289_073705673240477696"
        },
        "B1C": {
            "sell_token": "C",
            "buy_token": "B1",
            "exec_sell_amount": "357_719965038404924081",
            "exec_buy_amount": "561_904237334502880476"
        },
        "AB3": {
            "sell_token": "B3",
            "buy_token": "A",
            "exec_sell_amount": "671_163952522389243203",
            "exec_buy_amount": "710_926294326759522304"
        },
        "B3C": {
            "sell_token": "C",
            "buy_token": "B3",
            "exec_sell_amount": "943_426540218806186671",
            "exec_buy_amount": "671_163952522389243203"
        }
    },
    "orders": {
        "0": {
            "allow_partial_fill": false,
            "is_sell_order": true,
            "buy_amount": "900_000000000000000000",
            "sell_amount": "1000_000000000000000000",
            "buy_token": "C",
            "sell_token": "A",
            "exec_buy_amount": "1301_146505257211110752",
            "exec_sell_amount": "1000_000000000000000000"
        }
    }
}

Note: the derivation for the optimization equation for this strategy can be seen here.

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features to be added some day

strategies

• Add support for more than two legs.
• Add support for more than two pools on two-legged trade.
• Add multiple path graph weighting and cyclic arbitrage detection using the Bellman-Ford algorithm, so that we can optimize by multiple paths without necessarily dividing the order through them. This would allow obtaining arbitrage profit through finding profitable negative cycles (e.g., A -> B -> C -> D -> A).

liquidity sources

• Add support for Balancer's weighted pools.
• Add support for Uniswap v3 and forks.
• Add support for stable pools.

code improvement

• Implement support for AMM fees.
• Add support for concurrency (async), so tasks could run in parallel adding temporal advantage to the solver.
• Benchmark and possibly add other optimization algorithms options.
• Add an actual execution class (through CoW server or directly to the blockchains).
• Finish implementing end-to-end BUY limit orders.
• Add unit tests.
• add the bot server (on docker).

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resources

• cow.fi

• solver specs

• cow protocol support to ERC-1271

• useful CowSwap resources