Optimal execution with a percentage of volume target (Chap 9.2 of Algorithmic and High-Frequency Trading (c) Cartea, Jaimungal, & Penalva 2015 Cambridge University Press)

TargetPercent_MarketSpeed.ipynb

TargetRate_MarketSpeed_Helper.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "with __import__('importnb').Notebook(): \n",
    "    import TargetRate_MarketSpeed_Helper\n",
    "from scipy import interpolate\n",
    "np.random.seed(30)\n",
    "np.seterr(divide='ignore', invalid='ignore')\n",
    "font = {'family': 'serif',\n",
    "        'style': 'italic',\n",
    "        # 'color': 'darkred',\n",
    "        'weight': 1,\n",
    "        'size': 16,\n",
    "        }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot Path Map with respective to Time\n",
    "def PlotPath(t, T, Y, idxfig, title, lw=0.5, midline=None):\n",
    "    fig_1 = plt.figure()\n",
    "    plt.tick_params(direction='in', bottom=True, top=True, left=True, right=True)\n",
    "    axes = fig_1.gca()\n",
    "    axes.set_xlim([0, T])\n",
    "    axes.set_ylim([np.nanmin(Y[idxfig]), np.nanmax(Y[idxfig])*1.1])\n",
    "\n",
    "    for i in range(len(idxfig)):\n",
    "        plt.plot(t, Y[idxfig[i]], linewidth=lw, label=i+1)\n",
    "        \n",
    "    if midline!=None:\n",
    "        plt.plot(t, midline[1], '--k' )\n",
    "\n",
    "    plt.ylabel(title,  fontdict=font)\n",
    "    plt.xlabel('Time ($t$) ',  fontdict=font)\n",
    "    plt.legend()\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot Frequency Map \n",
    "def PlotHist(X, xlabel, bins=50, percentiles=[0.01, 0.1, 0.5, 0.9, 0.99]):\n",
    "    # Visualizing price difference between strategies \n",
    "    fig_7 = plt.figure()\n",
    "    plt.tick_params(direction='in', bottom=True, top=True, left=True, right=True)\n",
    "\n",
    "    n, b, p = plt.hist(X, bins)\n",
    "\n",
    "    q = np.quantile(X, percentiles)\n",
    "    maxHeight = 1.1*np.max(n)\n",
    "    for i in range(len(q)):\n",
    "        plt.plot(q[i]*np.array([1,1]), np.array([0,maxHeight]), '--', label= percentiles[i])\n",
    "\n",
    "    plt.ylabel('Frequency', fontdict=font)\n",
    "    plt.xlabel(xlabel, fontdict=font)\n",
    "    plt.ylim((0,maxHeight))\n",
    "    plt.legend(('qtl=0.01','qtl=0.10','qtl=0.50','qtl=0.90','qtl=0.99'))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  Plot Heat/Density Map\n",
    "def MakeHeatMap(t, y, xlabel, ylabel, fignum=False, nct=20, Nbins=100, Ndt=200, lower_threshold=0.1, upper_threshold=0.48):\n",
    "\n",
    "    miny = np.nanmin(y)\n",
    "    maxy = np.nanmax(y)\n",
    "    dy = (maxy - miny) / Nbins\n",
    "    bins = np.linspace(miny, maxy, 100)\n",
    "\n",
    "\n",
    "    yr = np.full([Ndt, len(bins)], np.nan)\n",
    "\n",
    "    mydt = (t[-1] - t[0]) / (Ndt - 1)\n",
    "\n",
    "    tr = np.full([Ndt, ], np.nan)\n",
    "\n",
    "    for i in range(Ndt):\n",
    "        kk = np.where(t < t[0] + mydt * (i + 1))[-1][-1]\n",
    "        count = np.histogram(y[:, kk], np.arange(miny, maxy + 0.00001, dy))\n",
    "        yr[i, :] = count[0]\n",
    "        tr[i] = t[kk].item()\n",
    "\n",
    "    zr = yr.T / len(y[:, 0])\n",
    "\n",
    "    if not fignum:\n",
    "        fig = plt.figure()\n",
    "    else:\n",
    "        fig = plt.figure(fignum)\n",
    "        \n",
    "    plt.tick_params(direction='in', bottom=True, top=True, left=True, right=True)\n",
    "    axes = fig.gca()\n",
    "    axes.set_xlim(left=0)\n",
    "    axes.set_ylim(bottom=0, top=np.max(maxy))\n",
    "    x_cord_i, y_cord_i = np.meshgrid(tr, bins)\n",
    "    zr[zr < np.max(zr)*lower_threshold] = 0\n",
    "    zr[zr > np.max(zr)*upper_threshold] = np.max(zr)*upper_threshold\n",
    "    cmap = plt.get_cmap('YlOrRd')\n",
    "\n",
    "    plt.contour(x_cord_i, y_cord_i, zr, nct, cmap=cmap, levels=np.linspace(zr.min(), zr.max(), 1000))\n",
    "\n",
    "    lim = np.around(np.max(zr), int(np.around(-(np.log(0.10972799999999999)/np.log(10)))))\n",
    "    plt.colorbar(ticks=np.arange(0, np.max(zr), lim/10))\n",
    "\n",
    "    y_1 = np.quantile(y, 0.05, axis=0)\n",
    "    y_2 = np.quantile(y, 0.5, axis=0)\n",
    "    y_3 = np.quantile(y, 0.95, axis=0)\n",
    "\n",
    "    plt.plot(t, y_1, '--k', linewidth=2)\n",
    "    plt.plot(t, y_2, '--k', linewidth=2)\n",
    "    plt.plot(t, y_3, '--k', linewidth=2)\n",
    "\n",
    "    plt.xlabel(xlabel)\n",
    "    plt.ylabel(ylabel)\n"
   ]
  }
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