pythoncourse/notebooks/french_elec_fx_vol_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b0494fb0",
   "metadata": {},
   "source": [
    "# FX implied PDF around French presidential election in 2022\n",
    "\n",
    "## Extracting the FX implied PDF from the FX implied volatility surface using Python\n",
    "\n",
    "April 2022 - Saeed Amen - https://www.cuemacro.com - saeed@cuemacro.com"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "358cd4cb",
   "metadata": {},
   "source": [
    "Before a scheduled event, we obviously don't know the outcome of that event. However, we do know that there will be an event. Regular repeated events include central bank meetings and economic data releases. Less common events, include elections. Given that elections occur so rarely, it can be difficult to \"backtest\" any strategy to trade around them. We can obviously look at opinion poll to get an idea of the relative likelihood of any particular winner in an election or at betting markets. Another way is to look at financial markets, such as the FX options market, where traders have skin the in the game. The FX options market is also much bigger than any betting markets we might look at. Furthermore, we might choose to compare the probability distribution from the FX options market to what polls or betting markets are saying.\n",
    "\n",
    "In order to gauge market pricing for an event, we can look at what is priced in FX options markets. Before a large scheduled event, the options market will \"bump\" up the implied volatility around that event (an event vol add on). The skew can also change. We can extract from the FX volatility surface, the implied PDF of price moves over any option tenor we'd like. The implied PDF, will give us a probability distribution for FX spot. If you're interested in this topic, have a look at the paper Iain Clark and I wrote on the implied PDF around Brexit for GBPUSD at https://www.mdpi.com/2227-9091/5/3/35 and also Iain's FX options book, which describes how to interpolate the FX volatility surface using a number of different techniques at https://www.amazon.co.uk/Foreign-Exchange-Option-Pricing-Practitioners/dp/0470683686\n",
    "\n",
    "In this note, we'll show how we can extract the FX implied PDF using Python and market data. If you just want to see the resulting PDF plots, skip to the end!\n",
    "\n",
    "The Python code below:\n",
    "* downloads all the FX data necessary from Bloomberg using findatapy https://github.com/cuemacro/findatapy \n",
    "* fit the FX volatily surface with finmarketpy https://github.com/cuemacro/finmarketpy (& financepy) \n",
    "* plot the extracted implied PDF and vol surface. \n",
    "\n",
    "You can also try running the code over different dates around the French presidential election to see how the implied PDF can change over time, different currency pairs and different tenors. You can also try running around the Brexit vote and using GBPUSD. Note, that you'll need a Bloomberg Terminal with DAPI in order to download the data. However, if you have another FX data data source, you can just replace the code related to `fetch_market` to read data from your alternative data source."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "333e1c50",
   "metadata": {},
   "source": [
    "## How to code it up\n",
    "\n",
    "Let's do a bunch of imports to start."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b177aa92",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-05T14:46:43.983602Z",
     "start_time": "2022-04-05T14:46:43.976600Z"
    }
   },
   "outputs": [],
   "source": [
    "# To make sure our Matplotlib plots are put inside the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "import copy\n",
    "\n",
    "import logging\n",
    "import sys\n",
    "logging.disable(sys.maxsize)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d361d0c",
   "metadata": {},
   "source": [
    "We import from the findatapy library, which will make it easy to download FX data from Bloomberg."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dfae94be",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-05T14:46:44.706685Z",
     "start_time": "2022-04-05T14:46:44.672684Z"
    }
   },
   "outputs": [],
   "source": [
    "# For loading market data\n",
    "from findatapy.market import Market, MarketDataRequest\n",
    "from findatapy.market import MarketDataGenerator\n",
    "market = Market(market_data_generator=MarketDataGenerator())\n",
    "cache_algo = \"cache_algo_return\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b1cbba4",
   "metadata": {},
   "source": [
    "For fitting the vol surface using finmarketpy (& financepy underneath)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1e91e8d0",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-05T14:46:50.115850Z",
     "start_time": "2022-04-05T14:46:45.572641Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "####################################################################\n",
      "# FINANCEPY BETA Version 0.193 - This build:  21 Feb 2021 at 00:47 #\n",
      "#      This software is distributed FREE & WITHOUT ANY WARRANTY    #\n",
      "# For info and disclaimer - https://github.com/domokane/FinancePy  #\n",
      "#      Send any bug reports or comments to quant@financepy.com     #\n",
      "####################################################################\n",
      "\n"
     ]
    },
    {
     "ename": "TypingError",
     "evalue": "Failed in nopython mode pipeline (step: nopython frontend)\nInternal error at <numba.core.typeinfer.CallConstraint object at 0x0000024B733B3850>.\n\nEnable logging at debug level for details.\n\u001b[1m\nFile \"c:\\Anaconda3\\envs\\py38\\lib\\site-packages\\financepy\\market\\volatility\\FinEquityVolSurface.py\", line 219:\u001b[0m\n\u001b[1mdef _solveForSmileStrike(s, t, r, q,\n    <source elided>\n\n\u001b[1m     K = newton_secant(_deltaFit, x0=initialGuess, args=argtuple,\n\u001b[0m     \u001b[1m^\u001b[0m\u001b[0m\n",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypingError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32me:\\cuemacro\\finmarketpy\\finmarketpy\\curve\\volatility\\fxvolsurface.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     22\u001b[0m \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 23\u001b[1;33m     \u001b[1;32mfrom\u001b[0m \u001b[0mfinancepy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmarket\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvolatility\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mFinFXVolSurfacePlus\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mFinFXVolSurfacePlus\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mFinFXVolSurface\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     24\u001b[0m     \u001b[1;32mfrom\u001b[0m \u001b[0mfinancepy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmarket\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvolatility\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mFinFXVolSurfacePlus\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mFinFXATMMethod\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\financepy\\market\\volatility\\__init__.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mFinEquityVolCurve\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mFinEquityVolSurface\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mFinFXVolSurface\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\financepy\\market\\volatility\\FinEquityVolSurface.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m    201\u001b[0m               float64, float64[:]), fastmath=True)\n\u001b[1;32m--> 202\u001b[1;33m def _solveForSmileStrike(s, t, r, q,\n\u001b[0m\u001b[0;32m    203\u001b[0m                          \u001b[0moptionTypeValue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\decorators.py\u001b[0m in \u001b[0;36mwrapper\u001b[1;34m(func)\u001b[0m\n\u001b[0;32m    225\u001b[0m                 \u001b[1;32mfor\u001b[0m \u001b[0msig\u001b[0m \u001b[1;32min\u001b[0m \u001b[0msigs\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 226\u001b[1;33m                     \u001b[0mdisp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msig\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    227\u001b[0m                 \u001b[0mdisp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdisable_compile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[1;34m(self, sig)\u001b[0m\n\u001b[0;32m    978\u001b[0m                     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 979\u001b[1;33m                         \u001b[0mcres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_compiler\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    980\u001b[0m                     \u001b[1;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mForceLiteralArg\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[1;34m(self, args, return_type)\u001b[0m\n\u001b[0;32m    144\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 145\u001b[1;33m             \u001b[1;32mraise\u001b[0m \u001b[0mretval\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    146\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\dispatcher.py\u001b[0m in \u001b[0;36m_compile_cached\u001b[1;34m(self, args, return_type)\u001b[0m\n\u001b[0;32m    154\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 155\u001b[1;33m             \u001b[0mretval\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_compile_core\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    156\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mTypingError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\dispatcher.py\u001b[0m in \u001b[0;36m_compile_core\u001b[1;34m(self, args, return_type)\u001b[0m\n\u001b[0;32m    167\u001b[0m         \u001b[0mimpl\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_implementation\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m{\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 168\u001b[1;33m         cres = compiler.compile_extra(self.targetdescr.typing_context,\n\u001b[0m\u001b[0;32m    169\u001b[0m                                       \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtargetdescr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtarget_context\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[1;34m(typingctx, targetctx, func, args, return_type, flags, locals, library, pipeline_class)\u001b[0m\n\u001b[0;32m    685\u001b[0m                               args, return_type, flags, locals)\n\u001b[1;32m--> 686\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mpipeline\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcompile_extra\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    687\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[1;34m(self, func)\u001b[0m\n\u001b[0;32m    427\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlifted_from\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 428\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_compile_bytecode\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    429\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36m_compile_bytecode\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    491\u001b[0m         \u001b[1;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfunc_ir\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 492\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_compile_core\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    493\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36m_compile_core\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    470\u001b[0m                     \u001b[1;32mif\u001b[0m \u001b[0mis_final_pipeline\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 471\u001b[1;33m                         \u001b[1;32mraise\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    472\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36m_compile_core\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    461\u001b[0m                 \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 462\u001b[1;33m                     \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    463\u001b[0m                     \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcr\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_machinery.py\u001b[0m in \u001b[0;36mrun\u001b[1;34m(self, state)\u001b[0m\n\u001b[0;32m    342\u001b[0m                 \u001b[0mpatched_exception\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_patch_error\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 343\u001b[1;33m                 \u001b[1;32mraise\u001b[0m \u001b[0mpatched_exception\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    344\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_machinery.py\u001b[0m in \u001b[0;36mrun\u001b[1;34m(self, state)\u001b[0m\n\u001b[0;32m    333\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpass_inst\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mCompilerPass\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 334\u001b[1;33m                     \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_runPass\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0midx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpass_inst\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    335\u001b[0m                 \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_lock.py\u001b[0m in \u001b[0;36m_acquire_compile_lock\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m     34\u001b[0m             \u001b[1;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 35\u001b[1;33m                 \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     36\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0m_acquire_compile_lock\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_machinery.py\u001b[0m in \u001b[0;36m_runPass\u001b[1;34m(self, index, pss, internal_state)\u001b[0m\n\u001b[0;32m    288\u001b[0m         \u001b[1;32mwith\u001b[0m \u001b[0mSimpleTimer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mpass_time\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 289\u001b[1;33m             \u001b[0mmutated\u001b[0m \u001b[1;33m|=\u001b[0m \u001b[0mcheck\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpss\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrun_pass\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minternal_state\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    290\u001b[0m         \u001b[1;32mwith\u001b[0m \u001b[0mSimpleTimer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mfinalize_time\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_machinery.py\u001b[0m in \u001b[0;36mcheck\u001b[1;34m(func, compiler_state)\u001b[0m\n\u001b[0;32m    261\u001b[0m         \u001b[1;32mdef\u001b[0m \u001b[0mcheck\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcompiler_state\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 262\u001b[1;33m             \u001b[0mmangled\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcompiler_state\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    263\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mmangled\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32min\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\typed_passes.py\u001b[0m in \u001b[0;36mrun_pass\u001b[1;34m(self, state)\u001b[0m\n\u001b[0;32m    104\u001b[0m             \u001b[1;31m# Type inference\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 105\u001b[1;33m             typemap, return_type, calltypes, errs = type_inference_stage(\n\u001b[0m\u001b[0;32m    106\u001b[0m                 \u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtypingctx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\typed_passes.py\u001b[0m in \u001b[0;36mtype_inference_stage\u001b[1;34m(typingctx, targetctx, interp, args, return_type, locals, raise_errors)\u001b[0m\n\u001b[0;32m     82\u001b[0m         \u001b[1;31m# return errors in case of partial typing\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 83\u001b[1;33m         \u001b[0merrs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minfer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpropagate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mraise_errors\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mraise_errors\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     84\u001b[0m         \u001b[0mtypemap\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrestype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcalltypes\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minfer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0munify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mraise_errors\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mraise_errors\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\typeinfer.py\u001b[0m in \u001b[0;36mpropagate\u001b[1;34m(self, raise_errors)\u001b[0m\n\u001b[0;32m   1073\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mforce_lit_args\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1074\u001b[1;33m                     \u001b[1;32mraise\u001b[0m \u001b[0merrors\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1075\u001b[0m                 \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypingError\u001b[0m: Failed in nopython mode pipeline (step: nopython frontend)\nInternal error at <numba.core.typeinfer.CallConstraint object at 0x0000024B731543A0>.\n\nEnable logging at debug level for details.\n\u001b[1m\nFile \"c:\\Anaconda3\\envs\\py38\\lib\\site-packages\\financepy\\market\\volatility\\FinEquityVolSurface.py\", line 219:\u001b[0m\n\u001b[1mdef _solveForSmileStrike(s, t, r, q,\n    <source elided>\n\n\u001b[1m     K = newton_secant(_deltaFit, x0=initialGuess, args=argtuple,\n\u001b[0m     \u001b[1m^\u001b[0m\u001b[0m\n",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mTypingError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m~\\DOCUME~1\\MobaXterm\\slash\\var\\log\\xwin/ipykernel_71828/2644763415.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# For constructing and fitting the vol surface\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mfinmarketpy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcurve\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvolatility\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfxvolsurface\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mFXVolSurface\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32me:\\cuemacro\\finmarketpy\\finmarketpy\\curve\\volatility\\fxvolsurface.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     27\u001b[0m     \u001b[1;32mfrom\u001b[0m \u001b[0mfinancepy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmarket\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvolatility\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mFinFXVolSurfacePlus\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mFinVolFunctionTypes\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     28\u001b[0m \u001b[1;32mexcept\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 29\u001b[1;33m     \u001b[1;32mfrom\u001b[0m \u001b[0mfinancepy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmarket\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvolatility\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mFinFXVolSurface\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mFinFXVolSurface\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     30\u001b[0m     \u001b[1;32mfrom\u001b[0m \u001b[0mfinancepy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmarket\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvolatility\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mFinFXVolSurface\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mFinFXATMMethod\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     31\u001b[0m     \u001b[1;32mfrom\u001b[0m \u001b[0mfinancepy\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmarket\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvolatility\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mFinFXVolSurface\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mFinFXDeltaMethod\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\financepy\\market\\volatility\\__init__.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mFinEquityVolCurve\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mFinEquityVolSurface\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mFinFXVolSurface\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mFinFXVolSurfacePlus\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[1;33m.\u001b[0m\u001b[0mFinIborCapVolCurve\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\financepy\\market\\volatility\\FinEquityVolSurface.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m    200\u001b[0m @njit(float64(float64, float64, float64, float64, int64, int64, float64,\n\u001b[0;32m    201\u001b[0m               float64, float64[:]), fastmath=True)\n\u001b[1;32m--> 202\u001b[1;33m def _solveForSmileStrike(s, t, r, q,\n\u001b[0m\u001b[0;32m    203\u001b[0m                          \u001b[0moptionTypeValue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    204\u001b[0m                          \u001b[0mvolatilityTypeValue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\decorators.py\u001b[0m in \u001b[0;36mwrapper\u001b[1;34m(func)\u001b[0m\n\u001b[0;32m    224\u001b[0m             \u001b[1;32mwith\u001b[0m \u001b[0mtypeinfer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mregister_dispatcher\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdisp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    225\u001b[0m                 \u001b[1;32mfor\u001b[0m \u001b[0msig\u001b[0m \u001b[1;32min\u001b[0m \u001b[0msigs\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 226\u001b[1;33m                     \u001b[0mdisp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msig\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    227\u001b[0m                 \u001b[0mdisp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdisable_compile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    228\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mdisp\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[1;34m(self, sig)\u001b[0m\n\u001b[0;32m    977\u001b[0m                 \u001b[1;32mwith\u001b[0m \u001b[0mev\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtrigger_event\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"numba:compile\"\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mev_details\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    978\u001b[0m                     \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 979\u001b[1;33m                         \u001b[0mcres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_compiler\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcompile\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    980\u001b[0m                     \u001b[1;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mForceLiteralArg\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    981\u001b[0m                         \u001b[1;32mdef\u001b[0m \u001b[0mfolded\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkws\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\dispatcher.py\u001b[0m in \u001b[0;36mcompile\u001b[1;34m(self, args, return_type)\u001b[0m\n\u001b[0;32m    143\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mretval\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    144\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 145\u001b[1;33m             \u001b[1;32mraise\u001b[0m \u001b[0mretval\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    146\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    147\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_compile_cached\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\dispatcher.py\u001b[0m in \u001b[0;36m_compile_cached\u001b[1;34m(self, args, return_type)\u001b[0m\n\u001b[0;32m    153\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    154\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 155\u001b[1;33m             \u001b[0mretval\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_compile_core\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mreturn_type\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    156\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mTypingError\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    157\u001b[0m             \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_failed_cache\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\dispatcher.py\u001b[0m in \u001b[0;36m_compile_core\u001b[1;34m(self, args, return_type)\u001b[0m\n\u001b[0;32m    166\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    167\u001b[0m         \u001b[0mimpl\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_get_implementation\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m{\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 168\u001b[1;33m         cres = compiler.compile_extra(self.targetdescr.typing_context,\n\u001b[0m\u001b[0;32m    169\u001b[0m                                       \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtargetdescr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtarget_context\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    170\u001b[0m                                       \u001b[0mimpl\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[1;34m(typingctx, targetctx, func, args, return_type, flags, locals, library, pipeline_class)\u001b[0m\n\u001b[0;32m    684\u001b[0m     pipeline = pipeline_class(typingctx, targetctx, library,\n\u001b[0;32m    685\u001b[0m                               args, return_type, flags, locals)\n\u001b[1;32m--> 686\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0mpipeline\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcompile_extra\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    687\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    688\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36mcompile_extra\u001b[1;34m(self, func)\u001b[0m\n\u001b[0;32m    426\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlifted\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    427\u001b[0m         \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlifted_from\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 428\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_compile_bytecode\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    429\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    430\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mcompile_ir\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfunc_ir\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlifted\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlifted_from\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mNone\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36m_compile_bytecode\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    490\u001b[0m         \"\"\"\n\u001b[0;32m    491\u001b[0m         \u001b[1;32massert\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfunc_ir\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 492\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_compile_core\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    493\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    494\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_compile_ir\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36m_compile_core\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    469\u001b[0m                     \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstatus\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfail_reason\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    470\u001b[0m                     \u001b[1;32mif\u001b[0m \u001b[0mis_final_pipeline\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 471\u001b[1;33m                         \u001b[1;32mraise\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    472\u001b[0m             \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    473\u001b[0m                 \u001b[1;32mraise\u001b[0m \u001b[0mCompilerError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"All available pipelines exhausted\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler.py\u001b[0m in \u001b[0;36m_compile_core\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    460\u001b[0m                 \u001b[0mres\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    461\u001b[0m                 \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 462\u001b[1;33m                     \u001b[0mpm\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrun\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    463\u001b[0m                     \u001b[1;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcr\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32mNone\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    464\u001b[0m                         \u001b[1;32mbreak\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_machinery.py\u001b[0m in \u001b[0;36mrun\u001b[1;34m(self, state)\u001b[0m\n\u001b[0;32m    341\u001b[0m                     \u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpipeline_name\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpass_desc\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    342\u001b[0m                 \u001b[0mpatched_exception\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_patch_error\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0me\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 343\u001b[1;33m                 \u001b[1;32mraise\u001b[0m \u001b[0mpatched_exception\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    344\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    345\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mdependency_analysis\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_machinery.py\u001b[0m in \u001b[0;36mrun\u001b[1;34m(self, state)\u001b[0m\n\u001b[0;32m    332\u001b[0m                 \u001b[0mpass_inst\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_pass_registry\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpss\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpass_inst\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    333\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpass_inst\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mCompilerPass\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 334\u001b[1;33m                     \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_runPass\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0midx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpass_inst\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mstate\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    335\u001b[0m                 \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    336\u001b[0m                     \u001b[1;32mraise\u001b[0m \u001b[0mBaseException\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Legacy pass in use\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_lock.py\u001b[0m in \u001b[0;36m_acquire_compile_lock\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m     33\u001b[0m         \u001b[1;32mdef\u001b[0m \u001b[0m_acquire_compile_lock\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     34\u001b[0m             \u001b[1;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 35\u001b[1;33m                 \u001b[1;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     36\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0m_acquire_compile_lock\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     37\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_machinery.py\u001b[0m in \u001b[0;36m_runPass\u001b[1;34m(self, index, pss, internal_state)\u001b[0m\n\u001b[0;32m    287\u001b[0m             \u001b[0mmutated\u001b[0m \u001b[1;33m|=\u001b[0m \u001b[0mcheck\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpss\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrun_initialization\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minternal_state\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    288\u001b[0m         \u001b[1;32mwith\u001b[0m \u001b[0mSimpleTimer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mpass_time\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 289\u001b[1;33m             \u001b[0mmutated\u001b[0m \u001b[1;33m|=\u001b[0m \u001b[0mcheck\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpss\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrun_pass\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minternal_state\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    290\u001b[0m         \u001b[1;32mwith\u001b[0m \u001b[0mSimpleTimer\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mfinalize_time\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    291\u001b[0m             \u001b[0mmutated\u001b[0m \u001b[1;33m|=\u001b[0m \u001b[0mcheck\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mpss\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrun_finalizer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minternal_state\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\compiler_machinery.py\u001b[0m in \u001b[0;36mcheck\u001b[1;34m(func, compiler_state)\u001b[0m\n\u001b[0;32m    260\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    261\u001b[0m         \u001b[1;32mdef\u001b[0m \u001b[0mcheck\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcompiler_state\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 262\u001b[1;33m             \u001b[0mmangled\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcompiler_state\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    263\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mmangled\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[1;32min\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;32mFalse\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    264\u001b[0m                 msg = (\"CompilerPass implementations should return True/False. \"\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\typed_passes.py\u001b[0m in \u001b[0;36mrun_pass\u001b[1;34m(self, state)\u001b[0m\n\u001b[0;32m    103\u001b[0m                               % (state.func_id.func_name,)):\n\u001b[0;32m    104\u001b[0m             \u001b[1;31m# Type inference\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 105\u001b[1;33m             typemap, return_type, calltypes, errs = type_inference_stage(\n\u001b[0m\u001b[0;32m    106\u001b[0m                 \u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtypingctx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    107\u001b[0m                 \u001b[0mstate\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtargetctx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\typed_passes.py\u001b[0m in \u001b[0;36mtype_inference_stage\u001b[1;34m(typingctx, targetctx, interp, args, return_type, locals, raise_errors)\u001b[0m\n\u001b[0;32m     81\u001b[0m         \u001b[0minfer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbuild_constraint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     82\u001b[0m         \u001b[1;31m# return errors in case of partial typing\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 83\u001b[1;33m         \u001b[0merrs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minfer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpropagate\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mraise_errors\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mraise_errors\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     84\u001b[0m         \u001b[0mtypemap\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrestype\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcalltypes\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0minfer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0munify\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mraise_errors\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mraise_errors\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     85\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mc:\\Anaconda3\\envs\\py38\\lib\\site-packages\\numba\\core\\typeinfer.py\u001b[0m in \u001b[0;36mpropagate\u001b[1;34m(self, raise_errors)\u001b[0m\n\u001b[0;32m   1072\u001b[0m                                   if isinstance(e, ForceLiteralArg)]\n\u001b[0;32m   1073\u001b[0m                 \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mforce_lit_args\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1074\u001b[1;33m                     \u001b[1;32mraise\u001b[0m \u001b[0merrors\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1075\u001b[0m                 \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1076\u001b[0m                     \u001b[1;32mraise\u001b[0m \u001b[0mreduce\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0moperator\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mor_\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mforce_lit_args\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypingError\u001b[0m: Failed in nopython mode pipeline (step: nopython frontend)\nInternal error at <numba.core.typeinfer.CallConstraint object at 0x0000024B733B3850>.\n\nEnable logging at debug level for details.\n\u001b[1m\nFile \"c:\\Anaconda3\\envs\\py38\\lib\\site-packages\\financepy\\market\\volatility\\FinEquityVolSurface.py\", line 219:\u001b[0m\n\u001b[1mdef _solveForSmileStrike(s, t, r, q,\n    <source elided>\n\n\u001b[1m     K = newton_secant(_deltaFit, x0=initialGuess, args=argtuple,\n\u001b[0m     \u001b[1m^\u001b[0m\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "# For constructing and fitting the vol surface \n",
    "from finmarketpy.curve.volatility.fxvolsurface import FXVolSurface"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e431ce23",
   "metadata": {},
   "source": [
    "Our last imports are for plotting using plotly and chartpy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "030a6708",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-03T21:21:30.468765Z",
     "start_time": "2022-04-03T21:21:30.444766Z"
    }
   },
   "outputs": [],
   "source": [
    "# For plotting\n",
    "import plotly.offline as py_offline\n",
    "\n",
    "import plotly.io as pio\n",
    "pio.renderers.default = \"notebook\" # larger notebook files, but interactive plots\n",
    "# pio.renderers.default = \"svg\"\n",
    "# pio.renderers.default = \"png\" # smaller notebook files\n",
    "\n",
    "from chartpy import Chart, Style\n",
    "\n",
    "chart = Chart(engine='plotly')\n",
    "style_template = Style(width=900, height=500, scale_factor=-1, plotly_plot_mode=\"dash\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed7eb1ad",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-03T19:05:18.631607Z",
     "start_time": "2022-04-03T19:05:18.617609Z"
    }
   },
   "source": [
    "## Download FX data from Bloomberg and fit FX volatility surface\n",
    "\n",
    "We write a function `construct_vol_surface`, which downloads the New York closing prices from Bloomberg for FX spot, FX volatility surface, rates etc. for a user specfied date with findatapy. It only take 2 lines of code to download all the necessary data to fit an FX vol surface!\n",
    "\n",
    "It then uses this data to construct the vol surface with finmarketpy (underneath all the fitting is done using Dominic O'Kane's financepy library at https://github.com/domokane/FinancePy). We then extract the vol surface for strikes which are -15%/15% of the spot price."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "5d029c8c",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-03T21:28:52.542914Z",
     "start_time": "2022-04-03T21:28:52.526912Z"
    }
   },
   "outputs": [],
   "source": [
    "def construct_vol_surface(cross, horizon_date):\n",
    "    # Download the whole all market data for pricing options (vol surface)\n",
    "    md_request = MarketDataRequest(start_date=horizon_date, finish_date=horizon_date,\n",
    "                                   data_source='bloomberg', cut='BGN', category='fx-vol-market',\n",
    "                                   tickers=cross,\n",
    "                                   cache_algo=cache_algo)\n",
    "\n",
    "    df = market.fetch_market(md_request)\n",
    "\n",
    "    fx_vol_surface = FXVolSurface(market_df=df, vol_function_type='BBG', asset=cross)\n",
    "\n",
    "    fx_vol_surface.build_vol_surface(horizon_date)\n",
    "    \n",
    "    spot = df[cross + '.close'][horizon_date]\n",
    "    low_spot = spot * 0.85\n",
    "    high_spot = spot * 1.15\n",
    "    \n",
    "    # Note for unstable vol surface dates (eg. over Brexit date) you may need to increase tolerance in FinancePy\n",
    "    # FinFXVolSurface.buildVolSurface method to get it to fill, or choose different vol_function_type (eg. 'CLARK5')\n",
    "    return df, low_spot, high_spot, fx_vol_surface.extract_vol_surface(\n",
    "        low_K_pc=low_spot, high_K_pc=high_spot, num_strike_intervals=120)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0f56454",
   "metadata": {},
   "source": [
    "## Create functions for plotting the implied PDF and vol surface"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "id": "3fa72de4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-04T10:05:25.695153Z",
     "start_time": "2022-04-04T10:05:25.689151Z"
    }
   },
   "outputs": [],
   "source": [
    "# Plot implied PDF in strike space (all interpolated)\n",
    "# x_axis = strike - index\n",
    "# y_axis = tenor - columns\n",
    "# z_axis = implied PDF - values\n",
    "def plot_implied_pdf(df_vol_dict, style_c, low_spot, high_spot, tenor, title=\"\", df_plot=None):\n",
    "    style = copy.copy(style_c)\n",
    "    style.title = 'Plotting implied PDF in strike space ' + str(tenor) + ' ' + title\n",
    "    style.x_axis_range = [low_spot, high_spot]\n",
    "    \n",
    "    if df_plot is None:\n",
    "        df_plot = df_vol_dict['vol_surface_implied_pdf'][tenor]\n",
    "        \n",
    "    # Plot the implied PDF for ON only versus strikes\n",
    "    fig = chart.plot(df_plot, chart_type='line', style=style)\n",
    "    \n",
    "    return fig, df_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "700516c2",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-04T10:05:27.949257Z",
     "start_time": "2022-04-04T10:05:27.943262Z"
    }
   },
   "outputs": [],
   "source": [
    "# Plot vol surface in strike space (all interpolated)\n",
    "# x_axis = strike - index\n",
    "# y_axis = tenor - columns\n",
    "# z_axis = implied vol - values\n",
    "def plot_vol_surface(df_vol_dict, style_c, title=\"\", df_plot=None):\n",
    "    style = copy.copy(style_c)\n",
    "    style.title = 'Plotting vol surface ' + title\n",
    "    \n",
    "    if df_plot is None:\n",
    "        df_plot = df_vol_dict['vol_surface_strike_space'].iloc[:, ::-1]\n",
    "        \n",
    "    # Plot the implied PDF for ON only versus strikes\n",
    "    fig = chart.plot(df_plot, chart_type='surface', style=style)\n",
    "    \n",
    "    return fig, df_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94345e86",
   "metadata": {},
   "source": [
    "## Run computation for French presidential elections in 2017 and 2022\n",
    "\n",
    "We'll now download FX data around the 2017 and 2022 French presidential elections. The vol surface will then be fit, and we'll get figures for the vol surface and the implied PDFs. The 2W implied vol date will cover the first round election whilst the 1M implied vol date will cover the second round election in both instances\n",
    "\n",
    "* For the 2017 election, we'll use 14 Apr 2017 as our reference date  (23 Apr 2017 for the first round election and 07 May 2017 for the second round election). \n",
    "* For the 2022 election, we'll use 01 Apr 2022 as our reference date  (10 Apr 2022 for the first round election and 24 Apr 2017 for the second round election). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "id": "7b0230fb",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-04T10:51:33.592952Z",
     "start_time": "2022-04-04T10:51:33.392952Z"
    }
   },
   "outputs": [],
   "source": [
    "date = \"14 Apr 2017\"; tenor = \"2W\"; cross = \"EURUSD\"\n",
    "df, low_spot, high_spot, df_vol_dict = construct_vol_surface(cross, date)\n",
    "fig_vol_surface_2017_2W, df_plot = plot_vol_surface(df_vol_dict, style_copy, title=date)\n",
    "fig_implied_pdf_2017_2W, df_plot = plot_implied_pdf(df_vol_dict, style_copy, low_spot, high_spot, tenor, title=date)\n",
    "\n",
    "tenor = \"1M\"\n",
    "df, low_spot, high_spot, df_vol_dict = construct_vol_surface(cross, date)\n",
    "fig_vol_surface_2017_1M, df_plot = plot_vol_surface(df_vol_dict, style_copy, title=date)\n",
    "fig_implied_pdf_2017_1M, df_plot = plot_implied_pdf(df_vol_dict, style_copy, low_spot, high_spot, tenor, title=date)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "id": "9b33a122",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-04T10:51:34.237949Z",
     "start_time": "2022-04-04T10:51:34.044954Z"
    }
   },
   "outputs": [],
   "source": [
    "date = \"01 Apr 2022\"; tenor = \"2W\"; cross = \"EURUSD\"\n",
    "df, low_spot, high_spot, df_vol_dict = construct_vol_surface(cross, date)\n",
    "fig_vol_surface_2022_2W, df_plot = plot_vol_surface(df_vol_dict, style_copy, title=date)\n",
    "fig_implied_pdf_2022_2W, df_plot = plot_implied_pdf(df_vol_dict, style_copy, low_spot, high_spot, tenor, title=date)\n",
    "\n",
    "tenor = \"1M\"\n",
    "df, low_spot, high_spot, df_vol_dict = construct_vol_surface(cross, date)\n",
    "fig_vol_surface_2022_1M, df_plot = plot_vol_surface(df_vol_dict, style_copy, title=date)\n",
    "fig_implied_pdf_2022_1M, df_plot = plot_implied_pdf(df_vol_dict, style_copy, low_spot, high_spot, tenor, title=date)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "479c4a99",
   "metadata": {},
   "source": [
    "## How does the volatility surface look like before a big event..?\n",
    "\n",
    "Earlier we talked about how an FX volatility surface will be \"bumped\" before a big scheduled event, as traders expect more vol around the event (even if they don't know the actual outcome). Below, we plot the vol surface from 01 Apr 2022. We see that the very short dates have implied vol much lower. As soon as we get to dates which cover the first round of the French presidential election, we can see a massive jump. You would obvserve something similar for equity options where they cover scheduled events like earnings annoucements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "id": "2fb8101d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-04-04T11:02:41.459384Z",
     "start_time": "2022-04-04T11:02:41.445386Z"
    }
   },
   "outputs": [
    {
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    "## Comparing implied vol only over the first round French presidential elections\n",
    "\n",
    "Let's now show the implied PDF for the 2W date in 2017 and 2022. The most obvious difference in 2017 versus 2022, is that there is much fatter left hand tail in 2017 (ie. for EURUSD downside in the event of a far right win) compared to 2022. In a sense, we could argue (with a lot of hindsight!) that the left hand tail in 2017 was too big (ie. downside EURUSD options were too expensive), because ultimately, it would have been very unlikely that any candidate would win in the first round."
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     "start_time": "2022-04-04T10:30:50.595931Z"
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    "## Comparing implied vol covering both the first and second rounds of the French presidential elections\n",
    "\n",
    "For the 2017 and 2022, when looking the 1M tenor which covers both the first and second rounds of the French presidential election, we again see a much bigger left hand tail (ie. EURUSD downside) in 2017. "
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    "## Conclusion\n",
    "\n",
    "We have seen that how to calculate the FX implied PDF from the FX implied volatility surface. This type of analysis can be useful in understanding what is priced into the market for large scheduled events."
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