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pool_design.py

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tim
2025-10-24 01:17:40 -04:00
parent 9796a4345f
commit 33aadd333e
1 changed files with 53 additions and 14 deletions
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research/pool_design.py
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@@ -8,6 +8,18 @@ import numpy as np
log = logging.getLogger(__name__) log = logging.getLogger(__name__)
UNISWAP_GAS=115_000
LMSR_GAS=119_000
ETH_PRICE=4500
UNISWAP_GAS_COST=UNISWAP_GAS*ETH_PRICE/1e9
LMSR_GAS_COST=LMSR_GAS*ETH_PRICE/1e9
LMSR_FEE = 0.000010
print(f' LMSR gas: ${LMSR_GAS_COST:.2}')
print(f'Uniswap gas: ${UNISWAP_GAS_COST:.2}')
def lmsr_swap_amount_out( def lmsr_swap_amount_out(
balances, balances,
amount_in, amount_in,
@@ -127,36 +139,63 @@ def lmsr_swap_amount_out(
return float(amount_out) return float(amount_out)
def main(): def compare():
balance0 = 1_000_000 # estimated from the production pool kappa = 10
balance0 = 10_000_000 # estimated from the production pool
balances = [balance0, balance0] balances = [balance0, balance0]
X = np.geomspace(1, 10_000_000, 100) X = np.geomspace(1, 10_000_000, 100)
Y = [1 - Y = [max(0, 1 -
lmsr_swap_amount_out(balances, float(amount_in), 0, 1, 0.000010, 0.8) (lmsr_swap_amount_out(balances, float(amount_in), 0, 1, LMSR_FEE, kappa) - LMSR_GAS_COST)
/ amount_in / amount_in)
for amount_in in X] for amount_in in X]
plt.plot(X / balance0, Y, label='LMSR') plt.plot(X, Y, label=f'LMSR {kappa:.2f}')
d = pd.read_csv('swap_results_block_23640998.csv') d = pd.read_csv('swap_results_block_23640998.csv')
d.columns = ['block', 'price0', 'price1', 'in0', 'out0', 'in1', 'out1'] d.columns = ['block', 'price0', 'price1', 'in0', 'out0', 'in1', 'out1']
uniswap_slippage = 1 - d.out0 / d.in0 / d.iloc[0].price0 uniswap_slippage0 = 1 - (d.out0 - UNISWAP_GAS_COST) / d.in0 / d.iloc[0].price0
plt.plot(d.in0 / balance0, uniswap_slippage, label='CP') plt.plot(d.in0, uniswap_slippage0, label='CP0')
# uniswap_slippage1 = 1 - (d.out1 - UNISWAP_GAS_COST) / d.in1 / d.iloc[0].price1
# plt.plot(d.in1, uniswap_slippage1, label='CP1')
# Interpolate Uniswap slippage to match LMSR x-coordinates # Interpolate Uniswap slippage to match LMSR x-coordinates
interp_uniswap = np.interp(X / balance0, d.in0 / balance0, uniswap_slippage) interp_uniswap = np.interp(X, d.in0, uniswap_slippage0)
mask = Y < interp_uniswap mask = Y < interp_uniswap
plt.fill_between(X / balance0, 0, 1, where=mask, alpha=0.2, color='green') plt.fill_between(X, 0, 1, where=mask, alpha=0.2, color='green')
plt.xscale('log') plt.xscale('log')
plt.yscale('log') plt.yscale('log')
plt.gca().xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _: '{:.2f}'.format(10000*x))) plt.gca().xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _: '{:g}'.format(x)))
plt.gca().yaxis.set_major_formatter(plt.FuncFormatter(lambda y, _: '{:.2f}%'.format(y))) plt.gca().yaxis.set_major_formatter(plt.FuncFormatter(lambda y, _: '{:.2%}'.format(y)))
plt.xlabel('Input Amount (basis points of initial balance)') plt.xlabel('Input Amount')
plt.ylabel('Slippage') plt.ylabel('Slippage')
plt.title('Pool Slippages') plt.title('Pool Slippages')
plt.grid(True) plt.grid(True)
plt.legend() plt.legend()
plt.show() plt.show()
def plot_kappa():
X = np.geomspace(1, 10_000_000, 100)
for kappa in np.geomspace(0.01, 100, 8):
balance0 = 1_000_000 # estimated from the production pool
balances = [balance0, balance0]
Y = [1 -
lmsr_swap_amount_out(balances, float(amount_in), 0, 1, 0.000010, kappa)
/ amount_in
for amount_in in X]
plt.plot(X / balance0, Y, label=f'{kappa:f}')
plt.xscale('log')
plt.yscale('log')
plt.gca().xaxis.set_major_formatter(plt.FuncFormatter(lambda x, _: '{:.2f}'.format(10000*x)))
plt.gca().yaxis.set_major_formatter(plt.FuncFormatter(lambda y, _: '{:.2%}'.format(y)))
plt.xlabel('Input Amount (basis points of initial balance)')
plt.ylabel('Slippage')
plt.title('Pool Slippages by Kappa')
plt.grid(True)
plt.legend()
plt.show()
if __name__ == '__main__': if __name__ == '__main__':
main() compare()
# plot_kappa()