Curve AMM plots.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### StableSwap Invariant\n",
    "\\begin{equation}\n",
    "An^n\\sum x_i + D = DAn^n + \\frac{D^{n+1}}{n^n\\prod x_i}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizations of Curves with various Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = [7.50, 4.50]\n",
    "plt.rcParams[\"figure.autolayout\"] = True\n",
    "delta = 2\n",
    "xrange = np.arange(0.1, 2000.0, delta)\n",
    "yrange = np.arange(0.1, 2000.0, delta)\n",
    "x, y = np.meshgrid(xrange, yrange)\n",
    "\n",
    "N = 2\n",
    "D = 1000\n",
    "A = 10\n",
    "\n",
    "Ann = A*N**N\n",
    "equation = Ann*(x+y) + D - Ann*D - (D**(N+1))/(N**N*x*y)\n",
    "plt.contour(x, y, equation, [0], colors='orange')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect of varying Ann, amplification coefficient, on stable swap invariant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = [7.50, 4.50]\n",
    "plt.rcParams[\"figure.autolayout\"] = True\n",
    "delta = 2\n",
    "xrange = np.arange(0.1, 2000.0, delta)\n",
    "yrange = np.arange(0.1, 2000.0, delta)\n",
    "x, y = np.meshgrid(xrange, yrange)\n",
    "N = 2\n",
    "D = 1000\n",
    "A = 10\n",
    "\n",
    "Ann_1 = A*N**N\n",
    "equation = Ann_1*(x+y) + D - Ann_1*D - (D**(N+1))/(N**N*x*y)\n",
    "cntr1 = plt.contour(x, y, equation, [0], colors='orange')\n",
    "\n",
    "Ann_2 = A*N\n",
    "equation = Ann_2*(x+y) + D - Ann_2*D - (D**(N+1))/(N**N*x*y)\n",
    "cntr2 = plt.contour(x, y, equation, [0], colors='green')\n",
    "\n",
    "Ann_3 = A\n",
    "equation = Ann_3*(x+y) + D - Ann_3*D - (D**(N+1))/(N**N*x*y)\n",
    "cntr3 = plt.contour(x, y, equation, [0], colors='blue')\n",
    "\n",
    "h1,_ = cntr1.legend_elements()\n",
    "h2,_ = cntr2.legend_elements()\n",
    "h3,_ = cntr3.legend_elements()\n",
    "plt.legend([h1[0], h2[0], h3[0]], ['Ann = A*N**N = {}'.format(Ann_1), 'Ann = A*N = {}'.format(Ann_2), 'Ann = A = {}'.format(Ann_3)])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CurveCrypto Invariant \n",
    "\\begin{equation}\n",
    "KD^{N-1}\\sum x_i + \\prod x_i = KD^N + \\Big(\\frac{D}{N}\\Big)^N\n",
    "\\end{equation}\n",
    "where,\n",
    "\\begin{equation}\n",
    "K_0 = \\frac{\\prod x_i N^N}{D^N},\\hskip{2em} K = AK_0\\frac{\\gamma^2}{\\big(\\gamma+1-K_0\\big)^2}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = [7.50, 4.5]\n",
    "plt.rcParams[\"figure.autolayout\"] = True\n",
    "delta = 2\n",
    "xrange = np.arange(0.1, 4000.0, delta)\n",
    "yrange = np.arange(0.1, 4000.0, delta)\n",
    "x, y = np.meshgrid(xrange, yrange)\n",
    "N = 2\n",
    "D = 1000\n",
    "A = 100\n",
    "Ann = A*N**N\n",
    "\n",
    "gamma_1 = 10**(-4)\n",
    "K0 = x*y*N**N/D**N\n",
    "K = (Ann*x*y*gamma_1**2)/(D**N*(gamma_1 + 1 - K0)**2)\n",
    "equation = K*D**(N-1)*(x+y) + x*y - K*D**N - (D/N)**N\n",
    "\n",
    "cntr1 = plt.contour(x, y, equation, [0], colors='orange')\n",
    "\n",
    "gamma_2 = 10**(-1)\n",
    "K0 = x*y*N**N/D**N\n",
    "K = (A*K0*gamma_2**2)/(gamma_2 + 1 - K0)**2\n",
    "equation = K*D**(N-1)*(x+y) + x*y - K*D**N - (D/N)**N\n",
    "\n",
    "cntr2 = plt.contour(x, y, equation, [0], colors='green')\n",
    "\n",
    "h1,_ = cntr1.legend_elements()\n",
    "h2,_ = cntr2.legend_elements()\n",
    "plt.legend([h1[0], h2[0]], ['gamma = {}'.format(gamma_1), 'gamma = {}'.format(gamma_2)])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effect of varying A on CurveCrypto Invariant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = [7.50, 4.5]\n",
    "plt.rcParams[\"figure.autolayout\"] = True\n",
    "delta = 2\n",
    "xrange = np.arange(0.1, 4000.0, delta)\n",
    "yrange = np.arange(0.1, 4000.0, delta)\n",
    "x, y = np.meshgrid(xrange, yrange)\n",
    "N = 2\n",
    "D = 1000\n",
    "A = 100000000\n",
    "gamma = 10**(-4)\n",
    "K0 = x*y*N**N/D**N\n",
    "\n",
    "Ann_1 = A*N**N\n",
    "K = (Ann_1*x*y*gamma**2)/(D**N*(gamma + 1 - K0)**2)\n",
    "equation = K*D**(N-1)*(x+y) + x*y - K*D**N - (D/N)**N\n",
    "cntr1 = plt.contour(x, y, equation, [0], colors='orange')\n",
    "\n",
    "Ann_2 = A*N\n",
    "K = (Ann_2*x*y*gamma**2)/(D**N*(gamma + 1 - K0)**2)\n",
    "equation = K*D**(N-1)*(x+y) + x*y - K*D**N - (D/N)**N\n",
    "cntr2 = plt.contour(x, y, equation, [0], colors='green')\n",
    "\n",
    "Ann_3 = A\n",
    "K = (Ann_3*x*y*gamma**2)/(D**N*(gamma + 1 - K0)**2)\n",
    "equation = K*D**(N-1)*(x+y) + x*y - K*D**N - (D/N)**N\n",
    "cntr3 = plt.contour(x, y, equation, [0], colors='blue')\n",
    "\n",
    "h1,_ = cntr1.legend_elements()\n",
    "h2,_ = cntr2.legend_elements()\n",
    "h3,_ = cntr3.legend_elements()\n",
    "plt.legend([h1[0], h2[0], h3[0]], ['Ann = A*N**N = {}'.format(Ann_1), 'Ann = A*N = {}'.format(Ann_2), 'Ann = A = {}'.format(Ann_3)])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot current stETH-ETH Pool composition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x324 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = [7.50, 4.50]\n",
    "plt.rcParams[\"figure.autolayout\"] = True\n",
    "delta = 2\n",
    "xrange = np.arange(0.1, 2000.0, delta)\n",
    "yrange = np.arange(0.1, 2000.0, delta)\n",
    "x, y = np.meshgrid(xrange, yrange)\n",
    "\n",
    "N = 2\n",
    "D = 1010\n",
    "A = 50\n",
    "\n",
    "Ann = A*N**N\n",
    "equation = Ann*(x+y) + D - Ann*D - (D**(N+1))/(N**N*x*y)\n",
    "plt.contour(x, y, equation, [0], colors='orange')\n",
    "\n",
    "plt.plot(704, 306, 'x', markersize = 20)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Basic Price derivation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.0\n"
     ]
    }
   ],
   "source": [
    "A = 85\n",
    "x_point = 1000000\n",
    "y_point = 1000000\n",
    "D = x_point + y_point\n",
    "N = 2\n",
    "\n",
    "chi = (A * x_point * y_point) / (D / N)**N\n",
    "\n",
    "x_point_delta = 1\n",
    "y_deriv = -1 * (chi + x_point)**-1 * (chi + (chi*D + D**N * N**(-N) - chi*x_point)*(chi+x_point)**-1)\n",
    "\n",
    "print(y_deriv)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TODO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specific Price for stETH - ETH pool"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 2\n",
    "D = 1010\n",
    "A = 50\n",
    "\n",
    "current_a = 704\n",
    "current_b = 306\n",
    "\n",
    "\n",
    "to_be_sold_a = 0.1 * current_a\n",
    "new_a = current_a + to_be_sold_a\n",
    "\n",
    "\n",
    "new_b = (1 + new_a)**-1 * (D + D**N * N**(-N) - new_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3860739.3465909087"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A*D*N**N + D ** (N + 1) / (N**N * to_be_sold_a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_point = 306\n",
    "y_point = 704"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi = (A * x_point * y_point) / (D / N)**N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42.2358592294873"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "844.7171845897461"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1000 * x_point * y_point) / (D / N)**N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}