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add Impermanent loss calculator python code
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,140 @@ | ||
| { | ||
| "cells": [ | ||
| { | ||
| "cell_type": "code", | ||
| "execution_count": 1, | ||
| "metadata": {}, | ||
| "outputs": [], | ||
| "source": [ | ||
| "# Uniswap math functions\n", | ||
| "# https://youtu.be/_asFkMz4zhw?t=25 - Uniswap V3 - Liquidity | DeFi\n", | ||
| "\n", | ||
| "def get_liquidity_0(x, sp, sb):\n", | ||
| " return x * sp * sb / (sb - sp)\n", | ||
| "\n", | ||
| "def get_liquidity_1(y, sp, sa):\n", | ||
| " return y / (sp - sa)\n", | ||
| "\n", | ||
| "def get_liquidity(x, y, sp, sa, sb):\n", | ||
| " if sp <= sa:\n", | ||
| " liquidity = get_liquidity_0(x, sp, sb)\n", | ||
| " elif sp < sb:\n", | ||
| " liquidity0 = get_liquidity_0(x, sp, sb)\n", | ||
| " liquidity1 = get_liquidity_1(y, sp, sa)\n", | ||
| " liquidity = min(liquidity0, liquidity1)\n", | ||
| " else:\n", | ||
| " liquidity = get_liquidity_1(y, sp, sa)\n", | ||
| " return liquidity\n", | ||
| "\n", | ||
| "\n", | ||
| "#\n", | ||
| "# Calculate x and y given liquidity and price range\n", | ||
| "#\n", | ||
| "def calculate_x(L, sp, sa, sb):\n", | ||
| " sp = max(min(sp, sb), sa) # if the price is outside the range, use the range endpoints instead\n", | ||
| " return L * (sb - sp) / (sp * sb)\n", | ||
| "\n", | ||
| "def calculate_y(L, sp, sa, sb):\n", | ||
| " sp = max(min(sp, sb), sa) # if the price is outside the range, use the range endpoints instead\n", | ||
| " return L * (sp - sa)\n", | ||
| "\n", | ||
| "def calculate_a1(L, sp, sb, x, y):\n", | ||
| " # https://www.wolframalpha.com/input/?i=solve+L+%3D+y+%2F+%28sqrt%28P%29+-+a%29+for+a\n", | ||
| " # sqrt(a) = sqrt(P) - y / L\n", | ||
| " return (sp - y / L) ** 2\n", | ||
| "\n", | ||
| "def calculate_a2(sp, sb, x, y):\n", | ||
| " # https://www.wolframalpha.com/input/?i=solve+++x+sqrt%28P%29+sqrt%28b%29+%2F+%28sqrt%28b%29++-+sqrt%28P%29%29+%3D+y+%2F+%28sqrt%28P%29+-+a%29%2C+for+a\n", | ||
| " # sqrt(a) = (y/sqrt(b) + sqrt(P) x - y/sqrt(P))/x\n", | ||
| " # simplify:\n", | ||
| " # sqrt(a) = y/(sqrt(b) x) + sqrt(P) - y/(sqrt(P) x)\n", | ||
| " sa = y / (sb * x) + sp - y / (sp * x)\n", | ||
| " return sa ** 2\n", | ||
| "\n", | ||
| "#\n", | ||
| "# Two different ways how to calculate p_b. calculate_b1() uses liquidity as an input, calculate_b2() does not.\n", | ||
| "#\n", | ||
| "def calculate_b1(L, sp, sa, x, y):\n", | ||
| " # https://www.wolframalpha.com/input/?i=solve+L+%3D+x+sqrt%28P%29+sqrt%28b%29+%2F+%28sqrt%28b%29+-+sqrt%28P%29%29+for+b\n", | ||
| " # sqrt(b) = (L sqrt(P)) / (L - sqrt(P) x)\n", | ||
| " return ((L * sp) / (L - sp * x)) ** 2\n", | ||
| "\n", | ||
| "def calculate_b2(sp, sa, x, y):\n", | ||
| " # find the square root of b:\n", | ||
| " # https://www.wolframalpha.com/input/?i=solve+++x+sqrt%28P%29+b+%2F+%28b++-+sqrt%28P%29%29+%3D+y+%2F+%28sqrt%28P%29+-+sqrt%28a%29%29%2C+for+b\n", | ||
| " # sqrt(b) = (sqrt(P) y)/(sqrt(a) sqrt(P) x - P x + y)\n", | ||
| " P = sp ** 2\n", | ||
| " return (sp * y / ((sa * sp - P) * x + y)) ** 2\n", | ||
| "\n", | ||
| "\n", | ||
| "\n", | ||
| "def calculate_P(x,y,sa,sb):\n", | ||
| " p = sb*x\n", | ||
| " q = y-x*sa*sb\n", | ||
| " r = -sb*y\n", | ||
| " return (math.pow(-1*q+(q**2 - 4*p*r),0.5)/(2*p) )\n", | ||
| "\n", | ||
| "def tick_price(t):\n", | ||
| " return 1.0001**t\n", | ||
| "\n", | ||
| "def price_tick(p):\n", | ||
| " return math.log(p,1.0001)\n", | ||
| "\n", | ||
| "def getYFromX(x,sa,sb,sp):\n", | ||
| " return x * (sp - sa) * sp *sb /(sb - sp)\n", | ||
| "\n", | ||
| "# ? P is Y/X\n", | ||
| "def simulator_calc_L(x,pa,pb,p):\n", | ||
| " sa = pa ** 0.5\n", | ||
| " sb = pb ** 0.5\n", | ||
| " sp = p ** 0.5\n", | ||
| " if p >= pb:\n", | ||
| " y=x\n", | ||
| " x=0\n", | ||
| " L = get_liquidity(x, y, sp, sa, sb)\n", | ||
| " elif p <= pa:\n", | ||
| " y = 0\n", | ||
| " else:\n", | ||
| " print(\"sim2\", sa, sb, sp, x)\n", | ||
| " y = getYFromX(x, sa, sb, sp)\n", | ||
| " L = get_liquidity(x, y, sp, sa, sb)\n", | ||
| "\n", | ||
| " return L,y\n", | ||
| "\n", | ||
| "# ! Requires X token to be a stable token\n", | ||
| "def getXY(capitalDollar, token0Decimals, token1Decimals, Pxusd, Pyusd, sp, sa, sb):\n", | ||
| " # captal = x * Pxusd / xdecimals + y * Pyusd / yDecimals ----- eq1\n", | ||
| " # replace y with x from getYFromX\n", | ||
| "\n", | ||
| " factor1 = Pxusd / (10 ** token0Decimals)\n", | ||
| " factor2 = Pyusd / (10 ** token1Decimals)\n", | ||
| " factor3 = (sp - sa) * sp * sb / (sb - sp)\n", | ||
| "\n", | ||
| " x = capitalDollar / (factor1 + factor3 * factor2)\n", | ||
| " y = getYFromX(x, sa, sb, sp)\n", | ||
| " return x, y" | ||
| ] | ||
| } | ||
| ], | ||
| "metadata": { | ||
| "kernelspec": { | ||
| "display_name": "Python 3", | ||
| "language": "python", | ||
| "name": "python3" | ||
| }, | ||
| "language_info": { | ||
| "codemirror_mode": { | ||
| "name": "ipython", | ||
| "version": 3 | ||
| }, | ||
| "file_extension": ".py", | ||
| "mimetype": "text/x-python", | ||
| "name": "python", | ||
| "nbconvert_exporter": "python", | ||
| "pygments_lexer": "ipython3", | ||
| "version": "3.10.11" | ||
| } | ||
| }, | ||
| "nbformat": 4, | ||
| "nbformat_minor": 2 | ||
| } |
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