augmented-tbc-design/math-translation-for-z.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "##########################################\n",
    "# This block is a literal translation of #\n",
    "# src/math.ts                            #\n",
    "##########################################\n",
    "\n",
    "# Computes the price at a specific reserve `R`\n",
    "def getPriceR(R, V0, k):\n",
    "    return (k * R ** ((k - 1) / k)) / V0 ** (1 / k)\n",
    "\n",
    "# Compute slippage at a point `R`, given a `deltaR`\n",
    "def getSlippage(R, deltaR, V0, k):\n",
    "    S = (V0 * R) ** (1 / k)\n",
    "    deltaS = (V0 * (R + deltaR)) ** (1 / k) - S\n",
    "    realizedPrice = deltaR / deltaS\n",
    "    spotPrice = getPriceR(R, V0, k)\n",
    "    return abs(realizedPrice - spotPrice) / spotPrice\n",
    "\n",
    "# Get deltaR for a given price growth factor\n",
    "def getDeltaR_priceGrowth(R, k, priceGrowth):\n",
    "    return -R + (priceGrowth * R ** (1 - 1 / k)) ** (k / (-1 + k))\n",
    "\n",
    "# Computes a tx distribution using a normal distribution,\n",
    "# Given a sum of tx value and a number of transactions\n",
    "# Demo: https://codepen.io/anon/pen/mNqJjv?editors=0010#0\n",
    "def getTxDistribution(_sum, num):\n",
    "    mean = _sum / num\n",
    "    off = mean * 4\n",
    "    x = []\n",
    "    for i in range(0, int(num)):\n",
    "        x.append(randn_bm(mean - off, mean + off))\n",
    "    return x\n",
    "\n",
    "# Random variable uniformly distributed\n",
    "def rv_U(min, max):\n",
    "    return random.random() * (max - min) + min\n",
    "\n",
    "\n",
    "# Standard Normal variate using Box-Muller transform.\n",
    "# by https://stackoverflow.com/questions/25582882/javascript-math-random-normal-distribution-gaussian-bell-curve/36481059#36481059\n",
    "def randn_bm(min, max):\n",
    "    u = 0\n",
    "    v = 0\n",
    "    while (u == 0):\n",
    "        u = random.random() # Converting [0,1) to (0,1)\n",
    "    while (v == 0):\n",
    "        v = random.random()\n",
    "    num = math.sqrt(-2.0 * math.log(u)) * math.cos(2.0 * math.pi * v)\n",
    "    \n",
    "    num = num / 10.0 + 0.5; # Translate to 0 -> 1\n",
    "    if (num > 1) or (num < 0):\n",
    "        num = randn_bm(min, max) # resample between 0 and 1 if out of range\n",
    "    num *= max - min # Stretch to fill range\n",
    "    num += min # offset to min\n",
    "    return num\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "##########################################\n",
    "# This block represent the user choices  #\n",
    "# src/App.ts                             #\n",
    "##########################################\n",
    "\n",
    "# Given data\n",
    "d0 = 1e6\n",
    "theta = 0.35\n",
    "p0 = 0.1\n",
    "p1 = 0.3\n",
    "wFee = 0.05\n",
    "\n",
    "# Initial params\n",
    "k = p1 / p0 / (1 - theta)\n",
    "R0 = (1 - theta) * d0\n",
    "S0 = d0 / p0\n",
    "V0 = S0 ** k / R0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "##########################################\n",
    "# Literal translation of the price walk  #\n",
    "# in src/App.ts                          #\n",
    "##########################################\n",
    "\n",
    "# Price walk\n",
    "R_t = [R0]\n",
    "p_t = [getPriceR(R0, V0, k)]\n",
    "wFee_t = [0]\n",
    "slippage_t = []\n",
    "avgTxSize_t = []\n",
    "\n",
    "numSteps = 52\n",
    "\n",
    "for t in range(0, numSteps):\n",
    "    txsWeek = rv_U(5, 2 * t + 5)\n",
    "    priceGrowth = rv_U(0.99, 1.03)\n",
    "\n",
    "    R = R_t[-1]\n",
    "    deltaR = getDeltaR_priceGrowth(R, k, priceGrowth)\n",
    "\n",
    "    R_next = R + deltaR\n",
    "    txs = getTxDistribution(deltaR, txsWeek)\n",
    "    # Compute slippage\n",
    "    slippage_txs = [getSlippage(R, txR, V0, k) for txR in txs]\n",
    "    slippage = np.mean(slippage_txs)\n",
    "    \n",
    "    txsWithdraw = filter(lambda tx: tx < 0, txs)\n",
    "    wFees = -wFee * sum(txsWithdraw)\n",
    "\n",
    "    # Store variables\n",
    "    R_t.append(R_next)\n",
    "    p_t.append(getPriceR(R_next, V0, k))\n",
    "    slippage_t.append(slippage)\n",
    "    wFee_t.append(wFees)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Price')"
      ]
     },
     "execution_count": 56,
     "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": [
    "##########################################\n",
    "# Same graph as the one showed after     #\n",
    "# clicking \"Run simulation\"              #\n",
    "##########################################\n",
    "\n",
    "plt.plot(p_t)\n",
    "plt.xlabel('Weeks')\n",
    "plt.ylabel('Price')"
   ]
  },
  {
   "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}