gistfile1.txt

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   "source": [
    "# This program is to implement a function _FX_Volatility()_ to get volatility for Trading Symbol Selection.\n",
    "\n",
    "###Data source here is the MT4 exported csv file with trading time, Open, High, Low, Close and volume. For production, the data source could be from database.\n",
    "\n",
    "###All the language is in Python.\n",
    "\n",
    "\n",
    "#  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### The following is the 1st Input box, only for IPython Notebook, to show plot/chart inside the console"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####The 2nd Input box is for importing data from CSV files.\n",
    "Here only uses EURUSD and USDJPY as example, could be extended to all kinds of Forex symbols."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[['2004.10.20', '18:00', '1.26240', '1.26310', '1.25900', '1.26000', '472'],\n",
       " ['2004.10.20', '19:00', '1.26000', '1.26070', '1.25820', '1.25870', '411'],\n",
       " ['2004.10.20', '20:00', '1.25890', '1.25970', '1.25830', '1.25870', '362'],\n",
       " ['2004.10.20', '21:00', '1.25880', '1.25930', '1.25710', '1.25830', '392'],\n",
       " ['2004.10.20', '22:00', '1.25830', '1.25920', '1.25760', '1.25870', '338'],\n",
       " ['2004.10.20', '23:00', '1.25870', '1.25920', '1.25760', '1.25830', '301'],\n",
       " ['2004.10.21', '00:00', '1.25810', '1.25860', '1.25710', '1.25760', '347'],\n",
       " ['2004.10.21', '01:00', '1.25760', '1.25830', '1.25720', '1.25800', '287'],\n",
       " ['2004.10.21', '02:00', '1.25810', '1.25910', '1.25780', '1.25850', '340'],\n",
       " ['2004.10.21', '03:00', '1.25870', '1.25950', '1.25780', '1.25910', '370']]"
      ]
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     "execution_count": 2,
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   "source": [
    "\"\"\"\n",
    "Volatility with EWMA model, Python\n",
    "\"\"\"\n",
    "\n",
    "# Import some Python standard libraries\n",
    "import csv\n",
    "import math\n",
    "from datetime import datetime\n",
    "\n",
    "# Import data from csv files, read data\n",
    "EURUSDreader = csv.reader(open('EURUSD.csv'))\n",
    "USDJPYreader = csv.reader(open('USDJPY.csv'))\n",
    "\n",
    "EURUSD = []\n",
    "for line in EURUSDreader:\n",
    "\tEURUSD.append(line)\n",
    "\n",
    "USDJPY = []\n",
    "for line in USDJPYreader:\n",
    "\tUSDJPY.append(line)\n",
    "\n",
    "# Show some details about EURUSD\n",
    "EURUSD[0:10]\n",
    "# The following Output box, you will see: Time, Clock, Open_price, High_price, Low_price, Close_price and Trading_Volume."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####The 3rd Input is for data preparation, to get time data series (EURUSD_Time, USDJPY_Time) and Close price data series (EURUSD_Close, USDJPY_Close)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "[datetime.datetime(2004, 10, 20, 18, 0),\n",
       " datetime.datetime(2004, 10, 20, 19, 0),\n",
       " datetime.datetime(2004, 10, 20, 20, 0),\n",
       " datetime.datetime(2004, 10, 20, 21, 0),\n",
       " datetime.datetime(2004, 10, 20, 22, 0),\n",
       " datetime.datetime(2004, 10, 20, 23, 0),\n",
       " datetime.datetime(2004, 10, 21, 0, 0),\n",
       " datetime.datetime(2004, 10, 21, 1, 0),\n",
       " datetime.datetime(2004, 10, 21, 2, 0),\n",
       " datetime.datetime(2004, 10, 21, 3, 0)]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Time data processing\n",
    "EURUSD_Time = []\n",
    "for row in EURUSD:\n",
    "\tEURUSD_Time.append(datetime.strptime((row[0] + \" \" + row[1]), \"%Y.%m.%d %H:%M\"))\n",
    "\n",
    "USDJPY_Time = []\n",
    "for row in USDJPY:\n",
    "\tUSDJPY_Time.append(datetime.strptime((row[0] + \" \" + row[1]), \"%Y.%m.%d %H:%M\"))\n",
    "\n",
    "# Close_price data processing\\\n",
    "EURUSD_Close = []\t\n",
    "for row in EURUSD:\n",
    "\tEURUSD_Close.append(float(row[5]))\n",
    "\n",
    "USDJPY_Close = []\t\n",
    "for row in USDJPY:\n",
    "\tUSDJPY_Close.append(float(row[5]))\n",
    "    \n",
    "EURUSD_Time[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For production, Input box [1], [2], [3] should be changed. For example, from database."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####4th, we calculate the Return series of the Forex\n",
    "Use Close_price series to calculate **Return series** of the Forex. The volatility calculation is based on Return data series.\n",
    "\n",
    "To calculate Return series data:\n",
    "- create an empty list \"EURUSD_Return\"\n",
    "- loop through EURUSD_Close, each Return is calculated from two agjacent Close_price, formula:\n",
    "\n",
    "###$$Return_i = log_e(Close_{i+1}) - log_e(Close_i)$$\n",
    "\n",
    "- append each Return item into the list EURUSD_Return.\n",
    "\n",
    "Java logarithm calculation reference: \n",
    "_static double  log(double a)_\n",
    "http://docs.oracle.com/javase/7/docs/api/java/lang/Math.html     (search \"natural logarithm\")"
   ]
  },
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   "execution_count": 4,
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   "source": [
    "# Rate of return calculation, using EURUSD as an example\n",
    "EURUSD_Return = []\n",
    "\n",
    "for index in (range(len(EURUSD_Close) - 1)):\n",
    "\ttemp = math.log(EURUSD_Close[index + 1]) - math.log(EURUSD_Close[index])\n",
    "\tEURUSD_Return.append(temp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Finally, implement the _FX_Volatility()_ function \n",
    "\n",
    "#####Use EWMA model to calculate volatility, to show users the latest volatility condition of the Forex product.\n",
    "\n",
    "EWMA model:\n",
    "###$$\\sigma_n^2 = \\lambda\\sigma_{n-1}^2 + (1 - \\lambda)u_{n-1}^2$$\n",
    "\n",
    "- $\\sigma_n$: volatility at day n \n",
    "- $u_{n - 1}$: daily percentage change in the variable\n",
    "- $\\lambda$: the parameter to decide weights,  0 < $\\lambda$ < 1\n",
    "\n",
    "\n",
    "Reference:\n",
    "- $\\lambda$ choice: http://www.investopedia.com/articles/07/ewma.asp\n",
    "- EWMA model for Python Pandas\n",
    "http://pandas.pydata.org/pandas-docs/dev/generated/pandas.stats.moments.ewma.html\n",
    "- EWMA model for Java reference:\n",
    "\n",
    "https://github.com/dropwizard/metrics/blob/master/metrics-core/src/main/java/com/codahale/metrics/EWMA.java\n",
    "http://grepcode.com/file/repo1.maven.org/maven2/com.codahale.metrics/metrics-core/3.0.1/com/codahale/metrics/EWMA.java"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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   "outputs": [],
   "source": [
    "# Volatility using Exponetial Weighted Moving Average model, with the \"Pandas\" package\n",
    "import pandas   # Import a 3rd party package \"Pandas\"\n",
    "\n",
    "\n",
    "# Function of EWMA Volatility - FX_Volatility()\n",
    "def FX_Volatility(FX_Close_raw, FX_Time, starting_time, ending_time):\n",
    "\t\"\"\"\n",
    "\tFor production:\n",
    "    users should choose only starting_time and the name of FX symbol, \n",
    "\tthe ending_time should always be the latest time in our market database,\n",
    "\tand we do the data processing(to generate FX_Close_raw and FX_Time) for users.\n",
    "\n",
    "\t4 input data:\n",
    "\t1-dimension array/list/vector of FX_Close_price series\n",
    "\t1-dimension array/list/vector of FX_Time series\n",
    "\ta time data of starting_time\n",
    "\ta time data of ending_time\n",
    "\t\"\"\"\n",
    "\t\n",
    "\t# Get the Close_price data within a period from starting_time to ending_time\n",
    "\tindex_1 = FX_Time.index(starting_time)\n",
    "\tindex_2 = FX_Time.index(ending_time) + 1\n",
    "\tFX_Close = FX_Close_raw[index_1 : index_2]\n",
    "\n",
    "\t# Get the Return_series of the FX symbol\n",
    "\tFX_Return = []\n",
    "\n",
    "\tfor index in (range(len(FX_Close) - 1)):\n",
    "\t\ttemp = math.log(FX_Close[index + 1]) - math.log(FX_Close[index])\n",
    "\t\tFX_Return.append(temp)\n",
    "\n",
    "\t# Use the built-in function in the Pandas package to calculate volatility series\n",
    "\tFX_ReturnSeries = pandas.Series(FX_Return)\n",
    "\tEWMA_Volatility = pandas.stats.moments.ewma(FX_ReturnSeries, (1/0.94-1))\n",
    "        \n",
    "\t# The returned value is the last value of the volatility series\n",
    "\treturn EWMA_Volatility[len(EWMA_Volatility)-1]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####The last box: we show some example here to call the function and see the output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000337875882614\n",
      "0.000665365109227\n"
     ]
    }
   ],
   "source": [
    "# Some examples to call the function\n",
    "Volatility_example_1 = FX_Volatility(EURUSD_Close, EURUSD_Time, datetime(2014, 01, 01, 23, 0), datetime(2015, 04, 01, 07, 0))\n",
    "print Volatility_example_1\n",
    "\n",
    "Volatility_example_2 = FX_Volatility(USDJPY_Close, USDJPY_Time, datetime(2014, 01, 01, 23, 0), datetime(2015, 04, 23, 23, 0))\n",
    "print Volatility_example_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
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   "outputs": [],
   "source": [
    "# Function of EWMA Volatility - FX_Volatility()\n",
    "def FX_Volatility_2(FX_Close_raw, FX_Time, starting_time, ending_time):\n",
    "\t\"\"\"\n",
    "\tFor production:\n",
    "    users should choose only starting_time and the name of FX symbol, \n",
    "\tthe ending_time should always be the latest time in our market database,\n",
    "\tand we do the data processing(to generate FX_Close_raw and FX_Time) for users.\n",
    "\n",
    "\t4 input data:\n",
    "\t1-dimension array/list/vector of FX_Close_price series\n",
    "\t1-dimension array/list/vector of FX_Time series\n",
    "\ta time data of starting_time\n",
    "\ta time data of ending_time\n",
    "\t\"\"\"\n",
    "\t\n",
    "\t# Get the Close_price data within a period from starting_time to ending_time\n",
    "\tindex_1 = FX_Time.index(starting_time)\n",
    "\tindex_2 = FX_Time.index(ending_time) + 1\n",
    "\tFX_Close = FX_Close_raw[index_1 : index_2]\n",
    "\n",
    "\t# Get the Return_series of the FX symbol\n",
    "\tFX_Return = []\n",
    "\n",
    "\tfor index in (range(len(FX_Close) - 1)):\n",
    "\t\ttemp = math.log(FX_Close[index + 1]) - math.log(FX_Close[index])\n",
    "\t\tFX_Return.append(temp)\n",
    "\n",
    "    # Calculate EWMA model and get the volatility\n",
    "\tLAMBDA = 0.94\n",
    "\tVolatility = []\n",
    "\tVolatility.append(FX_Return[0])\n",
    "\n",
    "\tfor i in range(len(FX_Return)):\n",
    "\t\ttemp_Volatility = math.sqrt(LAMBDA * Volatility[i] ** 2 + (1 - LAMBDA) * FX_Return[i] ** 2)\n",
    "\t\tVolatility.append(temp_Volatility)\n",
    "\n",
    "\t# The returned value is the last value of the volatility series\n",
    "\treturn [Volatility[len(Volatility) - 1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.0011404647627206502]\n",
      "[0.0007958705970447617]\n"
     ]
    }
   ],
   "source": [
    "# Some examples to call the function\n",
    "Volatility_example_1 = FX_Volatility_2(EURUSD_Close, EURUSD_Time, datetime(2014, 01, 01, 23, 0), datetime(2015, 04, 01, 07, 0))\n",
    "print Volatility_example_1\n",
    "\n",
    "Volatility_example_2 = FX_Volatility_2(USDJPY_Close, USDJPY_Time, datetime(2014, 01, 01, 23, 0), datetime(2015, 04, 23, 23, 0))\n",
    "print Volatility_example_2"
   ]
  },
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