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Merge branch 'adjust-LRNA-for-fees' into model-LP-fees
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# Conflicts:
#	hydradx/notebooks/Omnipool/LP_fees_analysis.ipynb
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@jepidoptera
jepidoptera committed Jul 13, 2023
2 parents d5cf604 + 4b8c28b commit 16c0f14
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Showing 5 changed files with 379 additions and 44 deletions.
24 changes: 17 additions & 7 deletions hydradx/model/amm/omnipool_amm.py
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Original file line number Diff line number Diff line change
Expand Up @@ -30,6 +30,7 @@ def __init__(self,
remove_liquidity_volatility_threshold: float = 0,
withdrawal_fee: bool = True,
min_withdrawal_fee: float = 0.0001,
lrna_mint_pct: float = 0.0,
):
"""
tokens should be a dict in the form of [str: dict]
Expand Down Expand Up @@ -72,6 +73,7 @@ def __init__(self,
self.max_withdrawal_per_block = max_withdrawal_per_block
self.max_lp_per_block = max_lp_per_block
self.remove_liquidity_volatility_threshold = remove_liquidity_volatility_threshold
self.lrna_mint_pct = lrna_mint_pct
self.withdrawal_fee = withdrawal_fee
if withdrawal_fee:
self.min_withdrawal_fee = min_withdrawal_fee
Expand Down Expand Up @@ -422,8 +424,10 @@ def execute_swap(
)
# lrna_fee = state.last_lrna_fee[tkn_buy]

delta_Qj = -delta_Qi * (1 - lrna_fee)
delta_Rj = state.liquidity[tkn_buy] * -delta_Qj / (state.lrna[tkn_buy] + delta_Qj) * (1 - asset_fee)
delta_Qt = -delta_Qi * (1 - lrna_fee)
delta_Qm = (state.lrna[tkn_buy] + delta_Qt) * delta_Qt * asset_fee / state.lrna[tkn_buy] * state.lrna_mint_pct
delta_Qj = delta_Qt + delta_Qm
delta_Rj = state.liquidity[tkn_buy] * -delta_Qt / (state.lrna[tkn_buy] + delta_Qt) * (1 - asset_fee)
delta_L = min(-delta_Qi * lrna_fee, -state.lrna_imbalance)
delta_QH = -lrna_fee * delta_Qi - delta_L

Expand Down Expand Up @@ -491,11 +495,14 @@ def execute_lrna_swap(
return state.fail_transaction('insufficient lrna in pool', agent)
delta_ra = -state.liquidity[tkn] * delta_qa / (-delta_qa + state.lrna[tkn]) * (1 - asset_fee)

delta_qm = asset_fee * (-delta_qa) / state.lrna[tkn] * (state.lrna[tkn] - delta_qa) * state.lrna_mint_pct
delta_q = delta_qm - delta_qa

if modify_imbalance:
q = state.lrna_total
state.lrna_imbalance += delta_qa * (q + state.lrna_imbalance) / (q - delta_qa) + delta_qa
state.lrna_imbalance += -delta_q * (q + state.lrna_imbalance) / (q + delta_q) - delta_q

state.lrna[tkn] += -delta_qa
state.lrna[tkn] += delta_q
state.liquidity[tkn] += -delta_ra

elif delta_ra > 0:
Expand All @@ -504,13 +511,16 @@ def execute_lrna_swap(
return state.fail_transaction('insufficient assets in pool', agent)
elif delta_ra > agent.holdings[tkn]:
return state.fail_transaction('agent has insufficient assets', agent)
delta_qa = -state.lrna[tkn] * delta_ra / (state.liquidity[tkn] * (1 - asset_fee) - delta_ra)
denom = (state.liquidity[tkn] * (1 - asset_fee) - delta_ra)
delta_qa = -state.lrna[tkn] * delta_ra / denom
delta_qm = - asset_fee * (1 - asset_fee) * (state.liquidity[tkn] / denom) * delta_qa * state.lrna_mint_pct
delta_q = -delta_qa + delta_qm

if modify_imbalance:
q = state.lrna_total
state.lrna_imbalance += delta_qa * (q + state.lrna_imbalance) / (q - delta_qa) + delta_qa
state.lrna_imbalance -= delta_q * (q + state.lrna_imbalance) / (q + delta_q) + delta_q

state.lrna[tkn] += -delta_qa
state.lrna[tkn] += delta_q
state.liquidity[tkn] += -delta_ra

# buying LRNA
Expand Down
25 changes: 18 additions & 7 deletions hydradx/spec/Swap.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -91,8 +91,10 @@
"$$\n",
"\\begin{align}\n",
"\\Delta Q_i &= Q_i\\frac{- \\Delta R_i}{R_i + \\Delta R_i}\\\\\n",
"\\Delta Q_j' &= -\\Delta Q_i (1 - f_P)\\\\\n",
"\\Delta R_j' &= R_j\\frac{- \\Delta Q_j'}{Q_j + \\Delta Q_j'}\\\\\n",
"\\Delta Q_j^t' &= -\\Delta Q_i (1 - f_P)\\\\\n",
"\\Delta Q_j^m &= \\frac{(Q + \\Delta Q_j^t') \\Delta Q_j^t' f_A}{Q_j}\\\\\n",
"\\Delta Q_j &= \\Delta Q_j^t' + \\Delta Q_j^m\\\\\n",
"\\Delta R_j' &= R_j\\frac{- \\Delta Q_j^t'}{Q_j + \\Delta Q_j^t'}\\\\\n",
"\\Delta R_j &= \\Delta R_j'(1 - f_A)\n",
"\\end{align}\n",
"$$"
Expand Down Expand Up @@ -132,8 +134,10 @@
"$$\n",
"\\begin{align}\n",
"\\Delta Q_i &= Q_i \\frac{-\\Delta R_i}{R_i + \\Delta R_i}\\\\\n",
"\\Delta Q_j &= -\\Delta Q_i(1 - f_P)\\\\\n",
"\\Delta R_j &= R_j \\frac{-\\Delta Q_j}{Q_j + \\Delta Q_j}(1 - f_A)\\\\\n",
"\\Delta Q_j^t &= -\\Delta Q_i(1 - f_P)\\\\\n",
"\\Delta Q_j^m &= \\frac{(Q_j + \\Delta Q_j^t)\\Delta Q_j^t f_A}{Q_j}\\\\\n",
"\\Delta Q_j &= \\Delta Q_j^t + \\Delta Q_j^m\\\\\n",
"\\Delta R_j &= R_j \\frac{-\\Delta Q_j^t}{Q_j^t + \\Delta Q_j^t}(1 - f_A)\\\\\n",
"\\Delta L &= min(-\\Delta Q_i f_P, -L)\\\\\n",
"\\Delta Q_H &= -\\Delta Q_i f_P - \\Delta L\n",
"\\end{align}\n",
Expand All @@ -148,8 +152,10 @@
"### $\\Delta R_j < 0$ provided\n",
"$$\n",
"\\begin{align}\n",
"\\Delta Q_j &= Q_j\\frac{-\\Delta R_j}{R_j(1 - f_A) + \\Delta R_j}\\\\\n",
"\\Delta Q_i &= -\\frac{\\Delta Q_j}{1 - f_P}\\\\\n",
"\\Delta Q_j^t &= Q_j\\frac{-\\Delta R_j}{R_j(1 - f_A) + \\Delta R_j}\\\\\n",
"\\Delta Q_j^m &= \\frac{f_A(1 - f_A) R_j}{R_j(1 - f_A) + \\Delta R_j}\\Delta Q_j^t\\\\\n",
"\\Delta Q_j &= \\Delta Q_j^t + \\Delta Q_j^m\\\\\n",
"\\Delta Q_i &= -\\frac{\\Delta Q_j^t}{1 - f_P}\\\\\n",
"\\Delta R_i &= R_i\\frac{-\\Delta Q_i}{Q_i + \\Delta Q_i}\\\\\n",
"\\Delta L &= min(-\\Delta Q_i f_P, -L)\\\\\n",
"\\Delta Q_H &= -\\Delta Q_i f_P - \\Delta L\n",
Expand Down Expand Up @@ -181,7 +187,12 @@
"cell_type": "code",
"execution_count": null,
"id": "b2e739d5-22a0-4a72-a479-1337339b5d04",
"metadata": {},
"metadata": {
"ExecuteTime": {
"end_time": "2023-06-16T17:39:54.078367641Z",
"start_time": "2023-06-16T17:39:54.067954002Z"
}
},
"outputs": [],
"source": []
}
Expand Down
70 changes: 44 additions & 26 deletions hydradx/spec/SwapLRNA.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -13,7 +13,12 @@
"cell_type": "code",
"execution_count": 5,
"id": "74c2097f-82ff-45a3-90d5-37dcea976d40",
"metadata": {},
"metadata": {
"ExecuteTime": {
"end_time": "2023-06-16T17:38:58.073637337Z",
"start_time": "2023-06-16T17:38:58.044598411Z"
}
},
"outputs": [],
"source": [
"import os\n",
Expand Down Expand Up @@ -88,8 +93,10 @@
"source": [
"$$\n",
"\\begin{align}\n",
"\\Delta Q_i &= -\\Delta q^\\alpha\\\\\n",
"\\Delta R_i &= R_i\\frac{- \\Delta Q_i}{Q_i + \\Delta Q_i}(1 - f_A)\\\\\n",
"\\Delta Q_i^t &= -\\Delta q^\\alpha\\\\\n",
"\\Delta Q_i^m &= f_A \\left(Q + \\Delta Q_i^t\\right)\\frac{\\Delta Q_i^t}{Q}\\\\\n",
"\\Delta Q_i &= \\Delta Q_i^t + \\Delta Q_i^m\\\\\n",
"\\Delta R_i &= R_i\\frac{- \\Delta Q_i^t}{Q_i + \\Delta Q_i^t}(1 - f_A)\\\\\n",
"\\Delta L &= -\\frac{\\Delta Q_i (Q + L)}{Q + \\Delta Q_i} - \\Delta Q_i\\\\\n",
"\\Delta r_i^\\alpha &= - \\Delta R_i\\\\\n",
"\\end{align}\n",
Expand All @@ -100,14 +107,19 @@
"cell_type": "code",
"execution_count": 6,
"id": "f33e16b1-0277-4288-be82-6c289631c224",
"metadata": {},
"metadata": {
"ExecuteTime": {
"end_time": "2023-06-16T17:38:58.096588049Z",
"start_time": "2023-06-16T17:38:58.068489841Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"def swap_lrna_delta_Ri(state: OmnipoolState, delta_qi: float, i: str) -> float:\n",
" return state.liquidity[i] * (- delta_qi / (state.lrna[i] + delta_qi))\n",
"def swap_lrna_delta_Qi(state: OmnipoolState, delta_ri: float, i: str) -> float:\n",
" return state.lrna[i] * (- delta_ri / (state.liquidity[i] + delta_ri))\n",
"\n"
]
}
Expand All @@ -132,9 +144,11 @@
"$$\n",
"\\begin{align}\n",
"\\Delta R_i &= -\\Delta r_i^\\alpha\\\\\n",
"\\Delta Q_i &= Q_i\\frac{-\\Delta R_i}{R_i(1 - f_A) + \\Delta R_i}\\\\\n",
"\\Delta Q_i^t &= Q_i\\frac{-\\Delta R_i}{R_i(1 - f_A) + \\Delta R_i}\\\\\n",
"\\Delta Q_i^m &= \\frac{f_A (1 - f_A) R_i}{R_i(1 - f_A) + \\Delta R_i} \\Delta Q_i^t\\\\\n",
"\\Delta Q_i &= \\Delta Q_i^t + \\Delta Q_i^m\\\\\n",
"\\Delta L &= -\\frac{\\Delta Q_i (Q + L)}{Q + \\Delta Q_i} - \\Delta Q_i\\\\\n",
"\\Delta q^\\alpha &= - \\Delta Q_i\\\\\n",
"\\Delta q^\\alpha &= - \\Delta Q_i^t\\\\\n",
"\\end{align}\n",
"$$\n",
"\n",
Expand All @@ -145,14 +159,20 @@
"cell_type": "code",
"execution_count": 7,
"id": "6f056d9c-4982-4d82-9748-8d2e6cb5b2a2",
"metadata": {},
"metadata": {
"ExecuteTime": {
"end_time": "2023-06-16T17:38:58.143398075Z",
"start_time": "2023-06-16T17:38:58.074524296Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"def swap_lrna_delta_Qi(state: OmnipoolState, delta_ri: float, i: str) -> float:\n",
" return state.lrna[i] * (- delta_ri / (state.liquidity[i] + delta_ri))\n",
"def asset_invariant(state: OmnipoolState, i: str) -> float:\n",
" \"\"\"Invariant for specific asset\"\"\"\n",
" return state.liquidity[i] * state.lrna[i]\n",
"\n"
]
}
Expand All @@ -165,25 +185,19 @@
"cell_type": "code",
"execution_count": 8,
"id": "bd16beca-63b8-4864-bc1d-3decce681cb8",
"metadata": {},
"metadata": {
"ExecuteTime": {
"end_time": "2023-06-16T17:38:58.144059900Z",
"start_time": "2023-06-16T17:38:58.116900980Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"def swap_lrna(\n",
" old_state: OmnipoolState,\n",
" old_agent: Agent,\n",
" delta_ra: float = 0,\n",
" delta_qa: float = 0,\n",
" tkn: str = ''\n",
") -> tuple[OmnipoolState, Agent]:\n",
" \"\"\"Compute new state after LRNA swap\"\"\"\n",
"\n",
" new_state = old_state.copy()\n",
" new_agent = old_agent.copy()\n",
"\n",
" return new_state.execute_lrna_swap(new_agent, delta_ra, delta_qa, tkn)\n",
"def weight_i(state: OmnipoolState, i: str) -> float:\n",
" return state.lrna[i] / state.lrna_total\n",
"\n"
]
}
Expand All @@ -198,7 +212,11 @@
"outputs": [],
"source": [],
"metadata": {
"collapsed": false
"collapsed": false,
"ExecuteTime": {
"end_time": "2023-06-16T17:38:58.144273343Z",
"start_time": "2023-06-16T17:38:58.117260530Z"
}
}
}
],
Expand Down
2 changes: 1 addition & 1 deletion hydradx/tests/test_omnipool_agents.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -93,7 +93,7 @@ def test_omnipool_arbitrager_feeless(omnipool: oamm.OmnipoolState, market: list,

# Trading should be profitable
if old_value > new_value:
if new_value != pytest.approx(old_value, rel=1e-15):
if new_value != pytest.approx(old_value, rel=1e-12):
raise


Expand Down
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