RiskMeasures-GaussianKernel.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import modules\n",
    "import numpy as np\n",
    "import csv\n",
    "from scipy import special\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "#helper function to read file\n",
    "def readFile(fileName):\n",
    "    with open(fileName) as f:\n",
    "        reader = csv.reader(f, delimiter=\"\\t\")\n",
    "        d = list(reader)\n",
    "    return d\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This function evaluates a normalized sum of N Gaussian functions with\n",
    "# means specified by the input vector mu and standard deviation equal to s\n",
    "# The function is computed in each point of the input vector x.\n",
    "#Nota que el vector x que le metes abarca el rango de todas las gaussian y se van sumando los valores\n",
    "def sumGaussian(x, mu, s):\n",
    "    N = len(mu)\n",
    "    G = 0\n",
    "    for i in range(N):\n",
    "        G = G + np.exp((-(x-mu[i])**2)/((2*(s**2))))/(np.sqrt(2*np.pi*(s**2)))\n",
    "    G = G/N #Normalization\n",
    "    \n",
    "    return G\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal kernel standard deviation for  bitcoin  =  [0.0070548]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-59-94f29c149ee9>:64: RuntimeWarning: divide by zero encountered in log\n",
      "  aux = np.sum(np.log(p)) #Computing likelihood\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal kernel standard deviation for  Dash  =  [0.02595024]\n",
      "optimal kernel standard deviation for  Ethereum  =  [0.01555676]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/anaconda3/lib/python3.8/site-packages/scipy/optimize/minpack.py:175: RuntimeWarning: The iteration is not making good progress, as measured by the \n",
      "  improvement from the last ten iterations.\n",
      "  warnings.warn(msg, RuntimeWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal kernel standard deviation for  Litecoin  =  [0.02983647]\n",
      "optimal kernel standard deviation for  Monero  =  [0.04977024]\n",
      "optimal kernel standard deviation for  Nem  =  [0.0225702]\n",
      "optimal kernel standard deviation for  Ripple  =  [0.06892612]\n"
     ]
    }
   ],
   "source": [
    "# Al final hacer for loop para todas las crpto!!\"!!!!!!!!!\"\n",
    "\n",
    "file = readFile(\"cryptocurrency_prices.txt\")\n",
    "data = file\n",
    "\n",
    "# Row 1: Bitcoin      (p = 6.14e-13)\n",
    "# Row 2: Dash         (p = 2.17e-02)\n",
    "# Row 3: Ethereum     (p = 6.31e-04)\n",
    "# Row 4: Litecoin     (p = 6.32e-07)\n",
    "# Row 5: Monero       (p = 6.41e-03)\n",
    "# Row 6: Nem          (p = 3.63e-01)\n",
    "# Row 7: Ripple       (p = 1.04e-03)\n",
    "\n",
    "crypto = [\"bitcoin\",\"Dash\",\"Ethereum\",\"Litecoin\",\"Monero\",\"Nem\",\"Ripple\"]\n",
    "\n",
    "# var values becuase we have 7 cryptocurrencies\n",
    "var_hist = np.zeros(7)\n",
    "var_kernel=np.zeros(7)\n",
    "var_test=np.zeros(7)\n",
    "es_hist=np.zeros(7)\n",
    "es_kernel=np.zeros(7)\n",
    "es_test=np.zeros(7)\n",
    "\n",
    "for j in range(7):\n",
    "\n",
    "    b = data[j]\n",
    "\n",
    "    # Log-returns\n",
    "    r = np.zeros((len(b)-1,1))\n",
    "    for i in range(len(b)-1):\n",
    "        den = float(b[i])\n",
    "        num = float(b[i+1])\n",
    "        r[i] = np.log(num/den)\n",
    "\n",
    "    #Separating the data into training / validation / testing sets (one third of the data each)\n",
    "    pt = 0.33 #Fraction of data to use in training set\n",
    "    pv = 0.33 #Fraction of data to use in validation set\n",
    "\n",
    "    # Indexes at 33% and 66% of the data\n",
    "    index33= int(np.round(pt*len(r)))\n",
    "    index66 = int(np.round((pt+pv)*len(r)))\n",
    "\n",
    "    train_set = r[:index33] # [Training set ] first 33% of the data of r\n",
    "    N_T = len(train_set)\n",
    "\n",
    "    val_set = r[index33:index66] # [Validation set ] second 33% of the data of r\n",
    "\n",
    "    test_set = r[index66:] # [Test set ] third 33% of the data of r\n",
    "\n",
    "    # <<<<<<<<<<<<<<<<<<<<<<<<<<.   << Maximum likelihood analysis >>.    >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>\n",
    "\n",
    "    # Vector of different standard deviations from 1^(-3) to 1^(-1) in log scales with 100 values\n",
    "    h = np.logspace(-3,-1,100) \n",
    "    L = np.zeros((len(h),1))\n",
    "\n",
    "    #Literal itera con todos los diferentes values de S.D para saber Mac Likelihood\n",
    "    #En otras ocaciones usabamos funciones de maximizacion y no era tan facil porque habia que maximizar\n",
    "    # multiples variables\n",
    "    for i in range(len(h)):\n",
    "        #Computing log-likelihood for Gaussian kernel evaluated on the\n",
    "        #validation set (using the training set as fixed parameters)\n",
    "\n",
    "        p = sumGaussian(val_set,train_set,h[i]) #Vector of Gaussian kernel values calculated in each point of validation set\n",
    "        aux = np.sum(np.log(p)) #Computing likelihood\n",
    "\n",
    "        L[i] = aux\n",
    "    h_opt = h[np.where(L == max(L))[0]] #agarra el valor de h en el indice donde esta el max L\n",
    "    print(\"optimal kernel standard deviation for \",crypto[j],\" = \", h_opt)\n",
    "\n",
    "    # <<<<<<<<<<<<<<<<<<<<<<<<<<.   << Kernel Random Numbers >>.    >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>\n",
    "\n",
    "    f = lambda x, u: sum(1+scipy.special.erf((x-train_set)/np.sqrt(2*h_opt**2)))/(2*N_T) - u\n",
    "    n_rand = 5000\n",
    "    kernel_random_numbers = np.zeros(n_rand)\n",
    "\n",
    "    for i in range(n_rand):\n",
    "        u = np.random.uniform()\n",
    "        y = scipy.optimize.fsolve(f,0,args = (u))\n",
    "        kernel_random_numbers[i] = y\n",
    "\n",
    "    # In Kernel_Gaussian notebook this variable is train_val (combination of train set and validation set)\n",
    "    historical = np.concatenate((train_set,val_set), axis=0);\n",
    "\n",
    "    alpha = 0.95\n",
    "    \n",
    "    # VaR [Value at Risk]\n",
    "    var_hist[j] = np.absolute(np.quantile(historical,1-alpha))\n",
    "    var_kernel[j] = np.absolute(np.quantile(kernel_random_numbers,1-alpha))\n",
    "    # ES [Expected Shortfall]\n",
    "    es_hist[j] =np.absolute(np.mean([[v]  for v in historical if v < -var_hist[j]])) # Used list comprehension\n",
    "    es_kernel[j] =np.absolute(np.mean([[m]  for m in kernel_random_numbers if m < -var_kernel[j]]))\n",
    "\n",
    "    #VaR and ES for Test set\n",
    "    var_test[j] = np.absolute(np.quantile(test_set,1-alpha))\n",
    "    es_test[j] =np.absolute(np.mean([[k]  for k in historical if k < -var_test[j]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f851d38cf40>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "\n",
    "plot1 = plt.figure(1,figsize=(4,4), dpi=100)\n",
    "for i in range(6):\n",
    "    plt.plot(i+1,var_hist[i],\"g.\")\n",
    "    plt.plot(i+1,var_kernel[i],\"bx\")\n",
    "    plt.plot(i+1,var_test[i], \"rx\")\n",
    "    plt.ylabel(\"VaR\")\n",
    "    plt.tight_layout()\n",
    "plt.plot(7,var_hist[i],\"g.\",label = \"historical\")\n",
    "plt.plot(7,var_kernel[i],\"bx\",label = \"kernel\")\n",
    "plt.plot(7,var_test[i], \"rx\",label = \"realized\")\n",
    "plt.legend()\n",
    "\n",
    "\n",
    "plot2 = plt.figure(2,figsize=(4,4), dpi=100)\n",
    "for i in range(6):\n",
    "    plt.plot(i+1,es_hist[i],\"g.\")\n",
    "    plt.plot(i+1,es_kernel[i],\"bx\")\n",
    "    plt.plot(i+1,es_test[i],\"rx\")\n",
    "    plt.ylabel(\"Expected Shortfall\")\n",
    "    plt.tight_layout()\n",
    "\n",
    "plt.plot(7,es_hist[i],\"g.\",label = \"historical\")\n",
    "plt.plot(7,es_kernel[i],\"bx\",label = \"kernel\")\n",
    "plt.plot(7,es_test[i],\"rx\",label = \"realized\")\n",
    "plt.legend()\n",
    "\n",
    "# 1: Bitcoin\n",
    "# 2: Dash \n",
    "# 3: Ethereum \n",
    "# 4: Litecoin  \n",
    "# 5: Monero  \n",
    "# 6: Nem    \n",
    "# 7: Ripple "
   ]
  },
  {
   "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
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
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  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "nbTranslate": {
   "displayLangs": [
    "*"
   ],
   "hotkey": "alt-t",
   "langInMainMenu": true,
   "sourceLang": "en",
   "targetLang": "fr",
   "useGoogleTranslate": true
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}