bluna_pool/amplification_research_bLUNA_LUNA.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ARC-X: Scale Amplification for the bLUNA-LUNA Pool"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Remark. The specific values of A parameter depend on the representation of the function implemented in the pool. In Astroport the amplification parameter is given as a=A*n^(n-1), where n=2 is the number of tokens. For that reason in the functions below the a=2A is used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\tatyana.pashinskaya\\AppData\\Local\\conda\\conda\\envs\\newone\\lib\\site-packages\\numpy\\_distributor_init.py:32: UserWarning: loaded more than 1 DLL from .libs:\n",
      "C:\\Users\\tatyana.pashinskaya\\AppData\\Local\\conda\\conda\\envs\\newone\\lib\\site-packages\\numpy\\.libs\\libopenblas.PYQHXLVVQ7VESDPUVUADXEVJOBGHJPAY.gfortran-win_amd64.dll\n",
      "C:\\Users\\tatyana.pashinskaya\\AppData\\Local\\conda\\conda\\envs\\newone\\lib\\site-packages\\numpy\\.libs\\libopenblas.XWYDX2IKJW2NMTWSFYNGFUWKQU3LYTCZ.gfortran-win_amd64.dll\n",
      "  stacklevel=1)\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from scipy.optimize import fsolve\n",
    "from matplotlib.pyplot import figure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('F:/Scripts/DeFi/Amplification/bLuna_luna.csv', index_col=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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       "       BLOCKCHAIN    CHAIN_ID  BLOCK_ID          BLOCK_TIMESTAMP  \\\n",
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       "...           ...         ...       ...                      ...   \n",
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       "\n",
       "                                    CONTRACT_ADDRESS    TOTAL_SHARE  \\\n",
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       "\n",
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data.price1.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['token0_swap'] = (data.TOKEN_0_AMOUNT - data.TOKEN_0_AMOUNT.shift(1))\n",
    "data['token1_swap'] = (data.TOKEN_1_AMOUNT - data.TOKEN_1_AMOUNT.shift(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_clean = data[data.token0_swap * data.token1_swap<0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>BLOCKCHAIN</th>\n",
       "      <th>CHAIN_ID</th>\n",
       "      <th>BLOCK_ID</th>\n",
       "      <th>BLOCK_TIMESTAMP</th>\n",
       "      <th>CONTRACT_ADDRESS</th>\n",
       "      <th>TOTAL_SHARE</th>\n",
       "      <th>TOKEN_0_CURRENCY</th>\n",
       "      <th>TOKEN_0_AMOUNT</th>\n",
       "      <th>TOKEN_1_CURRENCY</th>\n",
       "      <th>TOKEN_1_AMOUNT</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>seconds</th>\n",
       "      <th>price0</th>\n",
       "      <th>price1</th>\n",
       "      <th>token0_swap</th>\n",
       "      <th>token1_swap</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>271251</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>5846717</td>\n",
       "      <td>2021-12-28 00:00:59.111</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>473405.647350</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>667436.029542</td>\n",
       "      <td>uluna</td>\n",
       "      <td>653375.553630</td>\n",
       "      <td>1.640650e+09</td>\n",
       "      <td>6.133</td>\n",
       "      <td>1.021520</td>\n",
       "      <td>0.978934</td>\n",
       "      <td>233.000000</td>\n",
       "      <td>-227.486431</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>271523</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>5846721</td>\n",
       "      <td>2021-12-28 00:01:26.295</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>473405.647350</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>667330.833028</td>\n",
       "      <td>uluna</td>\n",
       "      <td>653478.860232</td>\n",
       "      <td>1.640650e+09</td>\n",
       "      <td>27.184</td>\n",
       "      <td>1.021197</td>\n",
       "      <td>0.979243</td>\n",
       "      <td>-105.196514</td>\n",
       "      <td>103.306602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>247888</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>5846725</td>\n",
       "      <td>2021-12-28 00:01:52.146</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>473405.647350</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>667328.813342</td>\n",
       "      <td>uluna</td>\n",
       "      <td>653480.843952</td>\n",
       "      <td>1.640650e+09</td>\n",
       "      <td>19.244</td>\n",
       "      <td>1.021191</td>\n",
       "      <td>0.979249</td>\n",
       "      <td>-2.019686</td>\n",
       "      <td>1.983720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>267324</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>5846739</td>\n",
       "      <td>2021-12-28 00:03:26.952</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>473405.647350</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>667264.423861</td>\n",
       "      <td>uluna</td>\n",
       "      <td>653544.199465</td>\n",
       "      <td>1.640650e+09</td>\n",
       "      <td>62.405</td>\n",
       "      <td>1.020994</td>\n",
       "      <td>0.979438</td>\n",
       "      <td>-64.389481</td>\n",
       "      <td>63.355513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>254618</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>5846745</td>\n",
       "      <td>2021-12-28 00:04:14.359</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>473405.647350</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>667564.423861</td>\n",
       "      <td>uluna</td>\n",
       "      <td>653251.381180</td>\n",
       "      <td>1.640650e+09</td>\n",
       "      <td>6.343</td>\n",
       "      <td>1.021910</td>\n",
       "      <td>0.978559</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>-292.818285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>234186</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>6208570</td>\n",
       "      <td>2022-01-24 23:43:50.979</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>516660.633570</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>737203.519097</td>\n",
       "      <td>uluna</td>\n",
       "      <td>720442.738721</td>\n",
       "      <td>1.643068e+09</td>\n",
       "      <td>50.776</td>\n",
       "      <td>1.023265</td>\n",
       "      <td>0.977264</td>\n",
       "      <td>14.570541</td>\n",
       "      <td>-14.196833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>233236</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>6208580</td>\n",
       "      <td>2022-01-24 23:44:55.107</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>516660.633570</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>737193.406717</td>\n",
       "      <td>uluna</td>\n",
       "      <td>720452.651063</td>\n",
       "      <td>1.643068e+09</td>\n",
       "      <td>38.005</td>\n",
       "      <td>1.023236</td>\n",
       "      <td>0.977291</td>\n",
       "      <td>-10.112380</td>\n",
       "      <td>9.912342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>228267</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>6208588</td>\n",
       "      <td>2022-01-24 23:45:45.693</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>516660.633570</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>737191.819412</td>\n",
       "      <td>uluna</td>\n",
       "      <td>720454.206994</td>\n",
       "      <td>1.643068e+09</td>\n",
       "      <td>44.283</td>\n",
       "      <td>1.023232</td>\n",
       "      <td>0.977295</td>\n",
       "      <td>-1.587305</td>\n",
       "      <td>1.555931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>231742</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>6208604</td>\n",
       "      <td>2022-01-24 23:47:29.122</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>516660.633570</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>737194.612195</td>\n",
       "      <td>uluna</td>\n",
       "      <td>720451.485818</td>\n",
       "      <td>1.643068e+09</td>\n",
       "      <td>31.396</td>\n",
       "      <td>1.023240</td>\n",
       "      <td>0.977288</td>\n",
       "      <td>2.792783</td>\n",
       "      <td>-2.721176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>233291</th>\n",
       "      <td>terra</td>\n",
       "      <td>columbus-5</td>\n",
       "      <td>6208684</td>\n",
       "      <td>2022-01-24 23:56:11.930</td>\n",
       "      <td>terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p</td>\n",
       "      <td>516660.936377</td>\n",
       "      <td>terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp</td>\n",
       "      <td>737433.594255</td>\n",
       "      <td>uluna</td>\n",
       "      <td>720219.550584</td>\n",
       "      <td>1.643069e+09</td>\n",
       "      <td>18.628</td>\n",
       "      <td>1.023901</td>\n",
       "      <td>0.976657</td>\n",
       "      <td>238.550000</td>\n",
       "      <td>-232.357480</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>12300 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       BLOCKCHAIN    CHAIN_ID  BLOCK_ID          BLOCK_TIMESTAMP  \\\n",
       "271251      terra  columbus-5   5846717  2021-12-28 00:00:59.111   \n",
       "271523      terra  columbus-5   5846721  2021-12-28 00:01:26.295   \n",
       "247888      terra  columbus-5   5846725  2021-12-28 00:01:52.146   \n",
       "267324      terra  columbus-5   5846739  2021-12-28 00:03:26.952   \n",
       "254618      terra  columbus-5   5846745  2021-12-28 00:04:14.359   \n",
       "...           ...         ...       ...                      ...   \n",
       "234186      terra  columbus-5   6208570  2022-01-24 23:43:50.979   \n",
       "233236      terra  columbus-5   6208580  2022-01-24 23:44:55.107   \n",
       "228267      terra  columbus-5   6208588  2022-01-24 23:45:45.693   \n",
       "231742      terra  columbus-5   6208604  2022-01-24 23:47:29.122   \n",
       "233291      terra  columbus-5   6208684  2022-01-24 23:56:11.930   \n",
       "\n",
       "                                    CONTRACT_ADDRESS    TOTAL_SHARE  \\\n",
       "271251  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  473405.647350   \n",
       "271523  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  473405.647350   \n",
       "247888  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  473405.647350   \n",
       "267324  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  473405.647350   \n",
       "254618  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  473405.647350   \n",
       "...                                              ...            ...   \n",
       "234186  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  516660.633570   \n",
       "233236  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  516660.633570   \n",
       "228267  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  516660.633570   \n",
       "231742  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  516660.633570   \n",
       "233291  terra1jxazgm67et0ce260kvrpfv50acuushpjsz2y0p  516660.936377   \n",
       "\n",
       "                                    TOKEN_0_CURRENCY  TOKEN_0_AMOUNT  \\\n",
       "271251  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   667436.029542   \n",
       "271523  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   667330.833028   \n",
       "247888  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   667328.813342   \n",
       "267324  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   667264.423861   \n",
       "254618  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   667564.423861   \n",
       "...                                              ...             ...   \n",
       "234186  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   737203.519097   \n",
       "233236  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   737193.406717   \n",
       "228267  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   737191.819412   \n",
       "231742  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   737194.612195   \n",
       "233291  terra1kc87mu460fwkqte29rquh4hc20m54fxwtsx7gp   737433.594255   \n",
       "\n",
       "       TOKEN_1_CURRENCY  TOKEN_1_AMOUNT     timestamp  seconds    price0  \\\n",
       "271251            uluna   653375.553630  1.640650e+09    6.133  1.021520   \n",
       "271523            uluna   653478.860232  1.640650e+09   27.184  1.021197   \n",
       "247888            uluna   653480.843952  1.640650e+09   19.244  1.021191   \n",
       "267324            uluna   653544.199465  1.640650e+09   62.405  1.020994   \n",
       "254618            uluna   653251.381180  1.640650e+09    6.343  1.021910   \n",
       "...                 ...             ...           ...      ...       ...   \n",
       "234186            uluna   720442.738721  1.643068e+09   50.776  1.023265   \n",
       "233236            uluna   720452.651063  1.643068e+09   38.005  1.023236   \n",
       "228267            uluna   720454.206994  1.643068e+09   44.283  1.023232   \n",
       "231742            uluna   720451.485818  1.643068e+09   31.396  1.023240   \n",
       "233291            uluna   720219.550584  1.643069e+09   18.628  1.023901   \n",
       "\n",
       "          price1  token0_swap  token1_swap  \n",
       "271251  0.978934   233.000000  -227.486431  \n",
       "271523  0.979243  -105.196514   103.306602  \n",
       "247888  0.979249    -2.019686     1.983720  \n",
       "267324  0.979438   -64.389481    63.355513  \n",
       "254618  0.978559   300.000000  -292.818285  \n",
       "...          ...          ...          ...  \n",
       "234186  0.977264    14.570541   -14.196833  \n",
       "233236  0.977291   -10.112380     9.912342  \n",
       "228267  0.977295    -1.587305     1.555931  \n",
       "231742  0.977288     2.792783    -2.721176  \n",
       "233291  0.976657   238.550000  -232.357480  \n",
       "\n",
       "[12300 rows x 16 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_clean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\tatyana.pashinskaya\\AppData\\Local\\conda\\conda\\envs\\newone\\lib\\site-packages\\ipykernel_launcher.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "data_clean['balance'] = 1 - abs(data_clean.TOKEN_1_AMOUNT/(data_clean.TOKEN_0_AMOUNT+data_clean.TOKEN_1_AMOUNT) - 0.5) - abs(data_clean.TOKEN_0_AMOUNT/(data_clean.TOKEN_0_AMOUNT+data_clean.TOKEN_1_AMOUNT) - 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x25298ffd808>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data_clean.balance.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x25299423808>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data_clean.token0_swap.values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data_clean.token0_swap.values, density=True, bins=200, log = True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dependence of the fair price location on the A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This function returns the difference between the derivative and a given price s\n",
    "def calculate_derivative(x, A, D, s):\n",
    "    \n",
    "    A = A*2\n",
    "    d = -0.5*(-1+0.5/np.sqrt((D**3/(A*x)+((1-1/A)*D-x)**2)) * (-D**3/(A*x**2)-2*((1-1/A)*D-x))) - s\n",
    "    \n",
    "    return d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This finction returns the amount of y token under a given amount of x token\n",
    "def y_calc(A, D, x):\n",
    "\n",
    "    A = A*2\n",
    "    b = (1 - 1 / A) * D - x\n",
    "    dsc = 4*D * (D/2)**2 / (A*x) + b**2\n",
    "    y = (np.sqrt(dsc) + b) / 2\n",
    "    \n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "649999.9999999999"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Check: for perfectly balanced pool the fsolve should return D/2\n",
    "A = 1\n",
    "D = 650000*2\n",
    "s = 1 \n",
    "x_initial_guess = 600000\n",
    "x_solution = fsolve(calculate_derivative, x_initial_guess, args = (A, D, s))\n",
    "x_solution[0] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "D = 1300000 # approximate current pool size\n",
    "x = []\n",
    "dx_all = []\n",
    "price = 0.98 # target fair market price for bLUNA-LUNA\n",
    "x_amount = D/2\n",
    "\n",
    "x = []\n",
    "y = []\n",
    "\n",
    "A_list = [1, 5, 10, 15, 25, 50]\n",
    "\n",
    "for A in A_list:\n",
    "    \n",
    "    x_solution = fsolve(calculate_derivative, x_initial_guess, args = (A, D, price))[0]\n",
    "    dx = x_solution - x_amount\n",
    "    y_solution = y_calc(A, D, x_solution)\n",
    "\n",
    "    x_amount = x_solution\n",
    "    \n",
    "    x.append(x_solution)\n",
    "    y.append(y_solution)\n",
    "    \n",
    "    dx_all.append(dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(8, 6), dpi=80)\n",
    "\n",
    "A1 = 1\n",
    "x1 = np.linspace(200000, 1300000, 500)\n",
    "y1 = y_calc(A1, D, x1)\n",
    "\n",
    "A2 = 50\n",
    "x2 = x1\n",
    "y2 = y_calc(A2, D, x2)\n",
    "\n",
    "plt.plot(x1, y1, label = f\"A={A1}\")\n",
    "plt.plot(x2, y2, '--', color='brown', label = f\"A={A2}\")\n",
    "\n",
    "for xs, ys, A in zip(x,y,A_list):\n",
    "\n",
    "    labelA = f\"A={A}\"\n",
    "    plt.scatter(xs,ys, label = labelA);\n",
    "    plt.text(xs,ys, \"P=0.98\", fontsize=8)\n",
    "\n",
    "plt.title('Curve Function', fontsize=20, fontweight=\"bold\")\n",
    "plt.xlabel(\"x token\")\n",
    "plt.ylabel(\"y token\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dependence of the pool balance on A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Loop over all prices\n",
    "D = data_clean.TOKEN_0_AMOUNT.values[0] + data_clean.TOKEN_1_AMOUNT.values[0] \n",
    "\n",
    "df_x = pd.DataFrame()\n",
    "df_y = pd.DataFrame()\n",
    "df_dx = pd.DataFrame()\n",
    "\n",
    "df_balance = pd.DataFrame()\n",
    "x_initial_guess = D/2\n",
    "\n",
    "A_range = [1] + list(np.arange(5,200,5))\n",
    "\n",
    "for A in A_range:\n",
    "    \n",
    "    x = []\n",
    "    y = []\n",
    "    balance = []\n",
    "    dx_all = []\n",
    "    x_amount = data_clean.TOKEN_1_AMOUNT.values[0]\n",
    "    \n",
    "    for price in data_clean.price1.values:\n",
    "\n",
    "        x_solution = fsolve(calculate_derivative, x_initial_guess, args = (A, D, price))[0]\n",
    "        y_solution = y_calc(A, D, x_solution)\n",
    "                \n",
    "        bal = 1 - abs(x_solution / (x_solution + y_solution) - 1/2) - abs(y_solution / (x_solution + y_solution) - 1/2)\n",
    "        \n",
    "        dx = x_solution - x_amount\n",
    "        x_amount = x_solution\n",
    "\n",
    "        x.append(x_solution)\n",
    "        y.append(y_solution)\n",
    "        balance.append(bal)\n",
    "        dx_all.append(dx)\n",
    "    \n",
    "    df_x[A] = x\n",
    "    df_y[A] = y\n",
    "    df_balance[A] = balance\n",
    "    df_dx[A] = dx_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>5</th>\n",
       "      <th>10</th>\n",
       "      <th>15</th>\n",
       "      <th>20</th>\n",
       "      <th>25</th>\n",
       "      <th>30</th>\n",
       "      <th>35</th>\n",
       "      <th>40</th>\n",
       "      <th>45</th>\n",
       "      <th>...</th>\n",
       "      <th>150</th>\n",
       "      <th>155</th>\n",
       "      <th>160</th>\n",
       "      <th>165</th>\n",
       "      <th>170</th>\n",
       "      <th>175</th>\n",
       "      <th>180</th>\n",
       "      <th>185</th>\n",
       "      <th>190</th>\n",
       "      <th>195</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-210.580483</td>\n",
       "      <td>-621.806962</td>\n",
       "      <td>-1087.466672</td>\n",
       "      <td>-1472.220372</td>\n",
       "      <td>-1767.741121</td>\n",
       "      <td>-1981.522717</td>\n",
       "      <td>-2128.191902</td>\n",
       "      <td>-2223.288177</td>\n",
       "      <td>-2280.303147</td>\n",
       "      <td>-2309.868743</td>\n",
       "      <td>...</td>\n",
       "      <td>-1820.442934</td>\n",
       "      <td>-1798.062189</td>\n",
       "      <td>-1776.364819</td>\n",
       "      <td>-1755.327879</td>\n",
       "      <td>-1734.927838</td>\n",
       "      <td>-1715.141020</td>\n",
       "      <td>-1695.943921</td>\n",
       "      <td>-1677.313439</td>\n",
       "      <td>-1659.227040</td>\n",
       "      <td>-1641.662866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-4.043011</td>\n",
       "      <td>-11.941131</td>\n",
       "      <td>-20.897680</td>\n",
       "      <td>-28.317943</td>\n",
       "      <td>-34.037327</td>\n",
       "      <td>-38.191963</td>\n",
       "      <td>-41.056296</td>\n",
       "      <td>-42.925023</td>\n",
       "      <td>-44.055801</td>\n",
       "      <td>-44.652764</td>\n",
       "      <td>...</td>\n",
       "      <td>-35.314188</td>\n",
       "      <td>-34.881471</td>\n",
       "      <td>-34.461872</td>\n",
       "      <td>-34.054960</td>\n",
       "      <td>-33.660294</td>\n",
       "      <td>-33.277425</td>\n",
       "      <td>-32.905908</td>\n",
       "      <td>-32.545304</td>\n",
       "      <td>-32.195184</td>\n",
       "      <td>-31.855131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-129.004304</td>\n",
       "      <td>-381.072977</td>\n",
       "      <td>-667.176660</td>\n",
       "      <td>-904.598604</td>\n",
       "      <td>-1087.996553</td>\n",
       "      <td>-1221.562264</td>\n",
       "      <td>-1313.925737</td>\n",
       "      <td>-1374.416198</td>\n",
       "      <td>-1411.226022</td>\n",
       "      <td>-1430.867781</td>\n",
       "      <td>...</td>\n",
       "      <td>-1134.114553</td>\n",
       "      <td>-1120.247239</td>\n",
       "      <td>-1106.798354</td>\n",
       "      <td>-1093.754424</td>\n",
       "      <td>-1081.101505</td>\n",
       "      <td>-1068.825467</td>\n",
       "      <td>-1056.912210</td>\n",
       "      <td>-1045.347820</td>\n",
       "      <td>-1034.118677</td>\n",
       "      <td>-1023.211531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>598.728776</td>\n",
       "      <td>1767.697332</td>\n",
       "      <td>3090.295225</td>\n",
       "      <td>4181.429040</td>\n",
       "      <td>5017.852133</td>\n",
       "      <td>5621.535959</td>\n",
       "      <td>6034.595648</td>\n",
       "      <td>6301.502419</td>\n",
       "      <td>6460.714499</td>\n",
       "      <td>6542.448191</td>\n",
       "      <td>...</td>\n",
       "      <td>5146.733489</td>\n",
       "      <td>5083.349625</td>\n",
       "      <td>5021.908383</td>\n",
       "      <td>4962.343694</td>\n",
       "      <td>4904.587996</td>\n",
       "      <td>4848.573447</td>\n",
       "      <td>4794.232807</td>\n",
       "      <td>4741.500074</td>\n",
       "      <td>4690.310931</td>\n",
       "      <td>4640.603046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-203.914186</td>\n",
       "      <td>-601.774716</td>\n",
       "      <td>-1050.713393</td>\n",
       "      <td>-1419.241248</td>\n",
       "      <td>-1699.894786</td>\n",
       "      <td>-1900.881885</td>\n",
       "      <td>-2037.133124</td>\n",
       "      <td>-2124.123734</td>\n",
       "      <td>-2175.070613</td>\n",
       "      <td>-2200.257910</td>\n",
       "      <td>...</td>\n",
       "      <td>-1719.882317</td>\n",
       "      <td>-1698.573043</td>\n",
       "      <td>-1677.925348</td>\n",
       "      <td>-1657.915755</td>\n",
       "      <td>-1638.520473</td>\n",
       "      <td>-1619.715772</td>\n",
       "      <td>-1601.478260</td>\n",
       "      <td>-1583.785071</td>\n",
       "      <td>-1566.613999</td>\n",
       "      <td>-1549.943591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12295</th>\n",
       "      <td>26.346779</td>\n",
       "      <td>77.576795</td>\n",
       "      <td>134.594210</td>\n",
       "      <td>180.231065</td>\n",
       "      <td>213.860826</td>\n",
       "      <td>237.021566</td>\n",
       "      <td>251.997937</td>\n",
       "      <td>260.968508</td>\n",
       "      <td>265.690097</td>\n",
       "      <td>267.469852</td>\n",
       "      <td>...</td>\n",
       "      <td>203.228319</td>\n",
       "      <td>200.643971</td>\n",
       "      <td>198.144249</td>\n",
       "      <td>195.725649</td>\n",
       "      <td>193.384723</td>\n",
       "      <td>191.118117</td>\n",
       "      <td>188.922583</td>\n",
       "      <td>186.794997</td>\n",
       "      <td>184.732367</td>\n",
       "      <td>182.731831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12296</th>\n",
       "      <td>-18.340446</td>\n",
       "      <td>-54.002023</td>\n",
       "      <td>-93.689941</td>\n",
       "      <td>-125.452852</td>\n",
       "      <td>-148.855682</td>\n",
       "      <td>-164.970506</td>\n",
       "      <td>-175.388684</td>\n",
       "      <td>-181.627202</td>\n",
       "      <td>-184.909099</td>\n",
       "      <td>-186.144209</td>\n",
       "      <td>...</td>\n",
       "      <td>-141.420227</td>\n",
       "      <td>-139.621684</td>\n",
       "      <td>-137.882047</td>\n",
       "      <td>-136.198875</td>\n",
       "      <td>-134.569769</td>\n",
       "      <td>-132.992390</td>\n",
       "      <td>-131.464479</td>\n",
       "      <td>-129.983862</td>\n",
       "      <td>-128.548453</td>\n",
       "      <td>-127.156261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12297</th>\n",
       "      <td>-2.878839</td>\n",
       "      <td>-8.476735</td>\n",
       "      <td>-14.707618</td>\n",
       "      <td>-19.695704</td>\n",
       "      <td>-23.372258</td>\n",
       "      <td>-25.904979</td>\n",
       "      <td>-27.543252</td>\n",
       "      <td>-28.525008</td>\n",
       "      <td>-29.042187</td>\n",
       "      <td>-29.237642</td>\n",
       "      <td>...</td>\n",
       "      <td>-22.219271</td>\n",
       "      <td>-21.936766</td>\n",
       "      <td>-21.663509</td>\n",
       "      <td>-21.399116</td>\n",
       "      <td>-21.143213</td>\n",
       "      <td>-20.895432</td>\n",
       "      <td>-20.655418</td>\n",
       "      <td>-20.422831</td>\n",
       "      <td>-20.197344</td>\n",
       "      <td>-19.978643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12298</th>\n",
       "      <td>5.049976</td>\n",
       "      <td>14.869602</td>\n",
       "      <td>25.799418</td>\n",
       "      <td>34.548948</td>\n",
       "      <td>40.997697</td>\n",
       "      <td>45.439942</td>\n",
       "      <td>48.313220</td>\n",
       "      <td>50.034936</td>\n",
       "      <td>50.941792</td>\n",
       "      <td>51.284368</td>\n",
       "      <td>...</td>\n",
       "      <td>38.972622</td>\n",
       "      <td>38.477095</td>\n",
       "      <td>37.997789</td>\n",
       "      <td>37.534034</td>\n",
       "      <td>37.085169</td>\n",
       "      <td>36.650552</td>\n",
       "      <td>36.229560</td>\n",
       "      <td>35.821595</td>\n",
       "      <td>35.426083</td>\n",
       "      <td>35.042476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12299</th>\n",
       "      <td>431.341434</td>\n",
       "      <td>1269.411009</td>\n",
       "      <td>2199.257782</td>\n",
       "      <td>2939.297312</td>\n",
       "      <td>3480.644336</td>\n",
       "      <td>3850.227864</td>\n",
       "      <td>4086.649681</td>\n",
       "      <td>4226.111981</td>\n",
       "      <td>4297.467987</td>\n",
       "      <td>4321.989402</td>\n",
       "      <td>...</td>\n",
       "      <td>3265.417419</td>\n",
       "      <td>3223.683369</td>\n",
       "      <td>3183.329538</td>\n",
       "      <td>3144.297256</td>\n",
       "      <td>3106.529131</td>\n",
       "      <td>3069.969482</td>\n",
       "      <td>3034.564619</td>\n",
       "      <td>3000.263010</td>\n",
       "      <td>2967.015372</td>\n",
       "      <td>2934.774696</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>12299 rows × 40 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              1            5            10           15           20   \\\n",
       "1     -210.580483  -621.806962 -1087.466672 -1472.220372 -1767.741121   \n",
       "2       -4.043011   -11.941131   -20.897680   -28.317943   -34.037327   \n",
       "3     -129.004304  -381.072977  -667.176660  -904.598604 -1087.996553   \n",
       "4      598.728776  1767.697332  3090.295225  4181.429040  5017.852133   \n",
       "5     -203.914186  -601.774716 -1050.713393 -1419.241248 -1699.894786   \n",
       "...           ...          ...          ...          ...          ...   \n",
       "12295   26.346779    77.576795   134.594210   180.231065   213.860826   \n",
       "12296  -18.340446   -54.002023   -93.689941  -125.452852  -148.855682   \n",
       "12297   -2.878839    -8.476735   -14.707618   -19.695704   -23.372258   \n",
       "12298    5.049976    14.869602    25.799418    34.548948    40.997697   \n",
       "12299  431.341434  1269.411009  2199.257782  2939.297312  3480.644336   \n",
       "\n",
       "               25           30           35           40           45   ...  \\\n",
       "1     -1981.522717 -2128.191902 -2223.288177 -2280.303147 -2309.868743  ...   \n",
       "2       -38.191963   -41.056296   -42.925023   -44.055801   -44.652764  ...   \n",
       "3     -1221.562264 -1313.925737 -1374.416198 -1411.226022 -1430.867781  ...   \n",
       "4      5621.535959  6034.595648  6301.502419  6460.714499  6542.448191  ...   \n",
       "5     -1900.881885 -2037.133124 -2124.123734 -2175.070613 -2200.257910  ...   \n",
       "...            ...          ...          ...          ...          ...  ...   \n",
       "12295   237.021566   251.997937   260.968508   265.690097   267.469852  ...   \n",
       "12296  -164.970506  -175.388684  -181.627202  -184.909099  -186.144209  ...   \n",
       "12297   -25.904979   -27.543252   -28.525008   -29.042187   -29.237642  ...   \n",
       "12298    45.439942    48.313220    50.034936    50.941792    51.284368  ...   \n",
       "12299  3850.227864  4086.649681  4226.111981  4297.467987  4321.989402  ...   \n",
       "\n",
       "               150          155          160          165          170  \\\n",
       "1     -1820.442934 -1798.062189 -1776.364819 -1755.327879 -1734.927838   \n",
       "2       -35.314188   -34.881471   -34.461872   -34.054960   -33.660294   \n",
       "3     -1134.114553 -1120.247239 -1106.798354 -1093.754424 -1081.101505   \n",
       "4      5146.733489  5083.349625  5021.908383  4962.343694  4904.587996   \n",
       "5     -1719.882317 -1698.573043 -1677.925348 -1657.915755 -1638.520473   \n",
       "...            ...          ...          ...          ...          ...   \n",
       "12295   203.228319   200.643971   198.144249   195.725649   193.384723   \n",
       "12296  -141.420227  -139.621684  -137.882047  -136.198875  -134.569769   \n",
       "12297   -22.219271   -21.936766   -21.663509   -21.399116   -21.143213   \n",
       "12298    38.972622    38.477095    37.997789    37.534034    37.085169   \n",
       "12299  3265.417419  3223.683369  3183.329538  3144.297256  3106.529131   \n",
       "\n",
       "               175          180          185          190          195  \n",
       "1     -1715.141020 -1695.943921 -1677.313439 -1659.227040 -1641.662866  \n",
       "2       -33.277425   -32.905908   -32.545304   -32.195184   -31.855131  \n",
       "3     -1068.825467 -1056.912210 -1045.347820 -1034.118677 -1023.211531  \n",
       "4      4848.573447  4794.232807  4741.500074  4690.310931  4640.603046  \n",
       "5     -1619.715772 -1601.478260 -1583.785071 -1566.613999 -1549.943591  \n",
       "...            ...          ...          ...          ...          ...  \n",
       "12295   191.118117   188.922583   186.794997   184.732367   182.731831  \n",
       "12296  -132.992390  -131.464479  -129.983862  -128.548453  -127.156261  \n",
       "12297   -20.895432   -20.655418   -20.422831   -20.197344   -19.978643  \n",
       "12298    36.650552    36.229560    35.821595    35.426083    35.042476  \n",
       "12299  3069.969482  3034.564619  3000.263010  2967.015372  2934.774696  \n",
       "\n",
       "[12299 rows x 40 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_dx[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>0.659886</td>\n",
       "      <td>0.633850</td>\n",
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       "      <th>2</th>\n",
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       "      <td>0.839845</td>\n",
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       "      <td>0.756680</td>\n",
       "      <td>0.720964</td>\n",
       "      <td>0.688842</td>\n",
       "      <td>0.659951</td>\n",
       "      <td>0.633917</td>\n",
       "      <td>...</td>\n",
       "      <td>0.382897</td>\n",
       "      <td>0.377115</td>\n",
       "      <td>0.371585</td>\n",
       "      <td>0.366288</td>\n",
       "      <td>0.361209</td>\n",
       "      <td>0.356333</td>\n",
       "      <td>0.351648</td>\n",
       "      <td>0.347140</td>\n",
       "      <td>0.342801</td>\n",
       "      <td>0.338619</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.979230</td>\n",
       "      <td>0.938022</td>\n",
       "      <td>0.888143</td>\n",
       "      <td>0.841197</td>\n",
       "      <td>0.797901</td>\n",
       "      <td>0.758504</td>\n",
       "      <td>0.722924</td>\n",
       "      <td>0.690892</td>\n",
       "      <td>0.662055</td>\n",
       "      <td>0.636050</td>\n",
       "      <td>...</td>\n",
       "      <td>0.384582</td>\n",
       "      <td>0.378780</td>\n",
       "      <td>0.373229</td>\n",
       "      <td>0.367913</td>\n",
       "      <td>0.362815</td>\n",
       "      <td>0.357921</td>\n",
       "      <td>0.353218</td>\n",
       "      <td>0.348693</td>\n",
       "      <td>0.344337</td>\n",
       "      <td>0.340138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.978333</td>\n",
       "      <td>0.935376</td>\n",
       "      <td>0.883521</td>\n",
       "      <td>0.834948</td>\n",
       "      <td>0.790407</td>\n",
       "      <td>0.750114</td>\n",
       "      <td>0.713922</td>\n",
       "      <td>0.681496</td>\n",
       "      <td>0.652426</td>\n",
       "      <td>0.626302</td>\n",
       "      <td>...</td>\n",
       "      <td>0.376937</td>\n",
       "      <td>0.371229</td>\n",
       "      <td>0.365771</td>\n",
       "      <td>0.360543</td>\n",
       "      <td>0.355531</td>\n",
       "      <td>0.350720</td>\n",
       "      <td>0.346098</td>\n",
       "      <td>0.341652</td>\n",
       "      <td>0.337372</td>\n",
       "      <td>0.333248</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12295</th>\n",
       "      <td>0.977011</td>\n",
       "      <td>0.931480</td>\n",
       "      <td>0.876749</td>\n",
       "      <td>0.825852</td>\n",
       "      <td>0.779577</td>\n",
       "      <td>0.738071</td>\n",
       "      <td>0.701081</td>\n",
       "      <td>0.668164</td>\n",
       "      <td>0.638825</td>\n",
       "      <td>0.612586</td>\n",
       "      <td>...</td>\n",
       "      <td>0.366419</td>\n",
       "      <td>0.360844</td>\n",
       "      <td>0.355514</td>\n",
       "      <td>0.350411</td>\n",
       "      <td>0.345520</td>\n",
       "      <td>0.340826</td>\n",
       "      <td>0.336317</td>\n",
       "      <td>0.331981</td>\n",
       "      <td>0.327807</td>\n",
       "      <td>0.323786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12296</th>\n",
       "      <td>0.977038</td>\n",
       "      <td>0.931561</td>\n",
       "      <td>0.876889</td>\n",
       "      <td>0.826039</td>\n",
       "      <td>0.779799</td>\n",
       "      <td>0.738317</td>\n",
       "      <td>0.701342</td>\n",
       "      <td>0.668435</td>\n",
       "      <td>0.639100</td>\n",
       "      <td>0.612863</td>\n",
       "      <td>...</td>\n",
       "      <td>0.366629</td>\n",
       "      <td>0.361051</td>\n",
       "      <td>0.355719</td>\n",
       "      <td>0.350613</td>\n",
       "      <td>0.345719</td>\n",
       "      <td>0.341023</td>\n",
       "      <td>0.336511</td>\n",
       "      <td>0.332173</td>\n",
       "      <td>0.327997</td>\n",
       "      <td>0.323974</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12297</th>\n",
       "      <td>0.977042</td>\n",
       "      <td>0.931574</td>\n",
       "      <td>0.876911</td>\n",
       "      <td>0.826068</td>\n",
       "      <td>0.779833</td>\n",
       "      <td>0.738355</td>\n",
       "      <td>0.701383</td>\n",
       "      <td>0.668477</td>\n",
       "      <td>0.639143</td>\n",
       "      <td>0.612906</td>\n",
       "      <td>...</td>\n",
       "      <td>0.366662</td>\n",
       "      <td>0.361084</td>\n",
       "      <td>0.355751</td>\n",
       "      <td>0.350645</td>\n",
       "      <td>0.345750</td>\n",
       "      <td>0.341054</td>\n",
       "      <td>0.336542</td>\n",
       "      <td>0.332203</td>\n",
       "      <td>0.328027</td>\n",
       "      <td>0.324004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12298</th>\n",
       "      <td>0.977035</td>\n",
       "      <td>0.931551</td>\n",
       "      <td>0.876872</td>\n",
       "      <td>0.826017</td>\n",
       "      <td>0.779772</td>\n",
       "      <td>0.738288</td>\n",
       "      <td>0.701311</td>\n",
       "      <td>0.668402</td>\n",
       "      <td>0.639067</td>\n",
       "      <td>0.612830</td>\n",
       "      <td>...</td>\n",
       "      <td>0.366604</td>\n",
       "      <td>0.361027</td>\n",
       "      <td>0.355694</td>\n",
       "      <td>0.350589</td>\n",
       "      <td>0.345695</td>\n",
       "      <td>0.341000</td>\n",
       "      <td>0.336488</td>\n",
       "      <td>0.332150</td>\n",
       "      <td>0.327975</td>\n",
       "      <td>0.323952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12299</th>\n",
       "      <td>0.976389</td>\n",
       "      <td>0.929654</td>\n",
       "      <td>0.873587</td>\n",
       "      <td>0.821631</td>\n",
       "      <td>0.774582</td>\n",
       "      <td>0.732551</td>\n",
       "      <td>0.695226</td>\n",
       "      <td>0.662113</td>\n",
       "      <td>0.632674</td>\n",
       "      <td>0.606403</td>\n",
       "      <td>...</td>\n",
       "      <td>0.361763</td>\n",
       "      <td>0.356248</td>\n",
       "      <td>0.350976</td>\n",
       "      <td>0.345929</td>\n",
       "      <td>0.341091</td>\n",
       "      <td>0.336450</td>\n",
       "      <td>0.331991</td>\n",
       "      <td>0.327704</td>\n",
       "      <td>0.323578</td>\n",
       "      <td>0.319603</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>12300 rows × 40 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            1         5         10        15        20        25        30   \\\n",
       "0      0.978715  0.936503  0.885487  0.837602  0.793585  0.753666  0.717727   \n",
       "1      0.979031  0.937434  0.887114  0.839802  0.796225  0.756623  0.720902   \n",
       "2      0.979037  0.937452  0.887145  0.839845  0.796276  0.756680  0.720964   \n",
       "3      0.979230  0.938022  0.888143  0.841197  0.797901  0.758504  0.722924   \n",
       "4      0.978333  0.935376  0.883521  0.834948  0.790407  0.750114  0.713922   \n",
       "...         ...       ...       ...       ...       ...       ...       ...   \n",
       "12295  0.977011  0.931480  0.876749  0.825852  0.779577  0.738071  0.701081   \n",
       "12296  0.977038  0.931561  0.876889  0.826039  0.779799  0.738317  0.701342   \n",
       "12297  0.977042  0.931574  0.876911  0.826068  0.779833  0.738355  0.701383   \n",
       "12298  0.977035  0.931551  0.876872  0.826017  0.779772  0.738288  0.701311   \n",
       "12299  0.976389  0.929654  0.873587  0.821631  0.774582  0.732551  0.695226   \n",
       "\n",
       "            35        40        45   ...       150       155       160  \\\n",
       "0      0.685462  0.656487  0.630409  ...  0.380140  0.374393  0.368895   \n",
       "1      0.688778  0.659886  0.633850  ...  0.382844  0.377064  0.371534   \n",
       "2      0.688842  0.659951  0.633917  ...  0.382897  0.377115  0.371585   \n",
       "3      0.690892  0.662055  0.636050  ...  0.384582  0.378780  0.373229   \n",
       "4      0.681496  0.652426  0.626302  ...  0.376937  0.371229  0.365771   \n",
       "...         ...       ...       ...  ...       ...       ...       ...   \n",
       "12295  0.668164  0.638825  0.612586  ...  0.366419  0.360844  0.355514   \n",
       "12296  0.668435  0.639100  0.612863  ...  0.366629  0.361051  0.355719   \n",
       "12297  0.668477  0.639143  0.612906  ...  0.366662  0.361084  0.355751   \n",
       "12298  0.668402  0.639067  0.612830  ...  0.366604  0.361027  0.355694   \n",
       "12299  0.662113  0.632674  0.606403  ...  0.361763  0.356248  0.350976   \n",
       "\n",
       "            165       170       175       180       185       190       195  \n",
       "0      0.363630  0.358582  0.353736  0.349080  0.344601  0.340289  0.336133  \n",
       "1      0.366237  0.361159  0.356284  0.351599  0.347092  0.342753  0.338571  \n",
       "2      0.366288  0.361209  0.356333  0.351648  0.347140  0.342801  0.338619  \n",
       "3      0.367913  0.362815  0.357921  0.353218  0.348693  0.344337  0.340138  \n",
       "4      0.360543  0.355531  0.350720  0.346098  0.341652  0.337372  0.333248  \n",
       "...         ...       ...       ...       ...       ...       ...       ...  \n",
       "12295  0.350411  0.345520  0.340826  0.336317  0.331981  0.327807  0.323786  \n",
       "12296  0.350613  0.345719  0.341023  0.336511  0.332173  0.327997  0.323974  \n",
       "12297  0.350645  0.345750  0.341054  0.336542  0.332203  0.328027  0.324004  \n",
       "12298  0.350589  0.345695  0.341000  0.336488  0.332150  0.327975  0.323952  \n",
       "12299  0.345929  0.341091  0.336450  0.331991  0.327704  0.323578  0.319603  \n",
       "\n",
       "[12300 rows x 40 columns]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_balance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Optimal A\n",
    "A_opt = 30\n",
    "\n",
    "x_opt = []\n",
    "y_opt = []\n",
    "balance_opt = []\n",
    "dx_all_opt = []\n",
    "x_amount_opt = data_clean.TOKEN_1_AMOUNT.values[0]\n",
    "\n",
    "for price in data_clean.price1.values:\n",
    "\n",
    "    x_solution = fsolve(calculate_derivative, x_initial_guess, args = (A_opt, D, price))[0]\n",
    "    \n",
    "    y_solution = y_calc(A_opt, D, x_solution)\n",
    "        \n",
    "    bal = 1 - abs(x_solution / (x_solution + y_solution) - 1/2) - abs(y_solution / (x_solution + y_solution) - 1/2)\n",
    "        \n",
    "    dx = x_solution - x_amount_opt\n",
    "    x_amount_opt = x_solution\n",
    "\n",
    "    x_opt.append(x_solution)\n",
    "    y_opt.append(y_solution)\n",
    "    balance_opt.append(bal)\n",
    "    dx_all_opt.append(dx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(8, 6), dpi=80)\n",
    "\n",
    "A_orig = A_opt # due to the representation used in Astro\n",
    "\n",
    "plt.plot(df_balance.columns.values, df_balance.mean(), label = 'Average');\n",
    "plt.plot(df_balance.columns.values, df_balance.min(), label = 'Minimum');\n",
    "\n",
    "xx = [A_orig,  A_orig, 0]\n",
    "yy = [0, np.mean(balance_opt), np.mean(balance_opt)]\n",
    "plt.plot(xx,yy,'--')\n",
    "\n",
    "bal_avg = int(np.round(np.mean(balance_opt), 1)*100)\n",
    "bal_min = int(np.round(np.min(balance_opt), 1)*100)\n",
    "\n",
    "plt.text(A_orig,np.mean(balance_opt), f\"Avg balance={bal_avg}%, A={A_orig}\", fontsize=15)\n",
    "plt.text(A_orig,np.min(balance_opt), f\"Min balance={bal_min}%, A={A_orig}\", fontsize=15)\n",
    "\n",
    "plt.scatter(A_orig, np.mean(balance_opt))\n",
    "plt.scatter(A_orig, np.min(balance_opt))\n",
    "\n",
    "title = \"Average and Minimum Balance\"\n",
    "\n",
    "plt.title(title, fontsize=20, fontweight=\"bold\")\n",
    "plt.xlabel(\"Amplification\")\n",
    "plt.ylabel(\"Balance\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(8, 6), dpi=80)\n",
    "plt.plot(df_dx.iloc[1:,6], label = 'A=30');\n",
    "plt.plot(df_dx.iloc[1:,1], label = 'A=5');\n",
    "plt.plot(data_clean.token0_swap.values, label = 'A=0')\n",
    "plt.title('Swap Amounts', fontsize=20, fontweight=\"bold\")\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"x token\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(8, 6), dpi=80)\n",
    "plt.plot(df_balance.iloc[:,6], label = 'A=30')\n",
    "plt.plot(df_balance.iloc[:,1], label = 'A=5')\n",
    "plt.plot(data_clean.balance.values, label = 'A=0')\n",
    "\n",
    "plt.title('Pool Balance', fontsize=20, fontweight=\"bold\")\n",
    "plt.ylim(ymax = 1.04, ymin = 0.3)\n",
    "#plt.title('Pool Balance')\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Balance\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}