{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Swaption Pricing Part 2: American Monte Carlo for Bermudas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Copyright (c) 2015 Matthias Groncki*\n",
    "\n",
    "\n",
    "Redistribution and use in source and binary forms, with or without\n",
    "modification, are permitted provided that the following conditions are met:\n",
    "\n",
    "    - Redistributions of source code must retain the above copyright notice,\n",
    "    this list of conditions and the following disclaimer.\n",
    "\n",
    "THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\n",
    "AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\n",
    "IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n",
    "DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR CONTRIBUTORS BE LIABLE\n",
    "FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\n",
    "DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\n",
    "SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\n",
    "CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\n",
    "OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\n",
    "OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n",
    "\n",
    "This disclaimer is taken from the QuantLib license"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# import the used libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.api as sm\n",
    "import QuantLib as ql\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Setting evaluation date\n",
    "today = ql.Date(7,4,2015)\n",
    "ql.Settings.instance().setEvaluationDate(today)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Setup Marketdata\n",
    "rate = ql.SimpleQuote(0.03)\n",
    "rate_handle = ql.QuoteHandle(rate)\n",
    "dc = ql.Actual365Fixed()\n",
    "yts = ql.FlatForward(today, rate_handle, dc)\n",
    "yts.enableExtrapolation()\n",
    "hyts = ql.RelinkableYieldTermStructureHandle(yts)\n",
    "t0_curve = ql.YieldTermStructureHandle(yts)\n",
    "euribor6m = ql.Euribor6M(hyts)\n",
    "cal = ql.TARGET()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Setup a dummy portfolio with two Swaps\n",
    "def makeSwap(start, maturity, nominal, fixedRate, index, typ=ql.VanillaSwap.Payer):\n",
    "    \"\"\"\n",
    "    creates a plain vanilla swap with fixedLegTenor 1Y\n",
    "    \n",
    "    parameter:\n",
    "        \n",
    "        start (ql.Date) : Start Date\n",
    "        \n",
    "        maturity (ql.Period) : SwapTenor\n",
    "        \n",
    "        nominal (float) : Nominal\n",
    "        \n",
    "        fixedRate (float) : rate paid on fixed leg\n",
    "        \n",
    "        index (ql.IborIndex) : Index\n",
    "        \n",
    "    return: tuple(ql.Swap, list<Dates>) Swap and all fixing dates\n",
    "    \n",
    "        \n",
    "    \"\"\"\n",
    "    end = ql.TARGET().advance(start, maturity)\n",
    "    fixedLegTenor = ql.Period(\"1y\")\n",
    "    fixedLegBDC = ql.ModifiedFollowing\n",
    "    fixedLegDC = ql.Thirty360(ql.Thirty360.BondBasis)\n",
    "    spread = 0.0\n",
    "    fixedSchedule = ql.Schedule(start,\n",
    "                                end, \n",
    "                                fixedLegTenor, \n",
    "                                index.fixingCalendar(), \n",
    "                                fixedLegBDC,\n",
    "                                fixedLegBDC, \n",
    "                                ql.DateGeneration.Backward,\n",
    "                                False)\n",
    "    floatSchedule = ql.Schedule(start,\n",
    "                                end,\n",
    "                                index.tenor(),\n",
    "                                index.fixingCalendar(),\n",
    "                                index.businessDayConvention(),\n",
    "                                index.businessDayConvention(),\n",
    "                                ql.DateGeneration.Backward,\n",
    "                                False)\n",
    "    swap = ql.VanillaSwap(typ, \n",
    "                          nominal,\n",
    "                          fixedSchedule,\n",
    "                          fixedRate,\n",
    "                          fixedLegDC,\n",
    "                          floatSchedule,\n",
    "                          index,\n",
    "                          spread,\n",
    "                          index.dayCounter())\n",
    "    return swap, [index.fixingDate(x) for x in floatSchedule][:-1]\n",
    "\n",
    "\n",
    "def makeSwaption(swap, callDates, settlement):\n",
    "    if len(callDates) == 1:\n",
    "        exercise = ql.EuropeanExercise(callDates[0])\n",
    "    else:\n",
    "        exercise = ql.BermudanExercise(callDates)\n",
    "    return ql.Swaption(swap, exercise, settlement)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lets start with an european swaption"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a forward starting plain vanilla swap using the helper function above and create a european swaption which allows us to to enter the swap in one year from today."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "settlementDate = today + ql.Period(\"1Y\")\n",
    "\n",
    "swaps = [makeSwap(settlementDate,\n",
    "                  ql.Period(\"5Y\"),\n",
    "                  1e6,\n",
    "                  0.03047096,\n",
    "                  euribor6m)\n",
    "        ]\n",
    "\n",
    "calldates = [euribor6m.fixingDate(settlementDate), euribor6m.valueDate(ql.Date(5,4,2017))]\n",
    " \n",
    "swaptions = [makeSwaption(swap, \n",
    "                          calldates, \n",
    "                          ql.Settlement.Physical) \n",
    "             for swap, fd in swaps]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pricing of the underlying at time 0 using the QuantLib pricing engine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Swap NPV at time 0: 0.0091\n"
     ]
    }
   ],
   "source": [
    "#%%timeit\n",
    "# Setup pricing engine and calculate the npv of the underlying swap\n",
    "engine = ql.DiscountingSwapEngine(hyts)\n",
    "for swap, fixingDates in swaps:\n",
    "    swap.setPricingEngine(engine)\n",
    "    print(\"Swap NPV at time 0: %.4f\" % swap.NPV())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Setup the Gaussian Shortrate model (a.k.a Hull White model)\n",
    "\n",
    "Don't worry about calibration, assume we know the calbriated model parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Stochastic Process "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Assume the model is already calibrated either historical or market implied\n",
    "volas = [ql.QuoteHandle(ql.SimpleQuote(0.0075)),\n",
    "         ql.QuoteHandle(ql.SimpleQuote(0.0075))]\n",
    "meanRev = [ql.QuoteHandle(ql.SimpleQuote(0.002))]\n",
    "model = ql.Gsr(t0_curve, [today+100], volas, meanRev, 16.)\n",
    "process = model.stateProcess()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Calculate the swaption price using an integral pricing engine"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "swaptionEngine = ql.Gaussian1dSwaptionEngine(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Swaption NPV : 17068.93\n"
     ]
    }
   ],
   "source": [
    "for swaption in swaptions:\n",
    "    swaption.setPricingEngine(swaptionEngine)\n",
    "    print(\"Swaption NPV : %.2f\" % swaption.NPV())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "###Pricing with an Monte Carlo method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "####Create a swap path pricer in Python \n",
    "\n",
    "Convert all Dates into times in years (using the same DayCounter as in the yieldTermStructure and store all fix cashflows in a numpy array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mcDC = yts.dayCounter()\n",
    "\n",
    "def timeFromReferenceFactory(daycounter, ref):\n",
    "    \"\"\"\n",
    "    returns a function, that calculate the time in years\n",
    "    from a the reference date *ref* to date *dat* \n",
    "    with respect to the given DayCountConvention *daycounter*\n",
    "    \n",
    "    Parameter:\n",
    "        dayCounter (ql.DayCounter)\n",
    "        ref (ql.Date)\n",
    "        \n",
    "    Return:\n",
    "    \n",
    "        f(np.array(ql.Date)) -> np.array(float)\n",
    "    \"\"\"\n",
    "    def impl(dat):\n",
    "        return daycounter.yearFraction(ref, dat)\n",
    "    return np.vectorize(impl)\n",
    "\n",
    "timeFromReference = timeFromReferenceFactory(mcDC, today)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def getFixedLeg(swap, t):\n",
    "    \"\"\"\n",
    "    returns all future payment times and amount of the fixed leg of the underlying swap\n",
    "    \n",
    "    Parameter:\n",
    "        swap (ql.Swap)\n",
    "        t (float) \n",
    "        \n",
    "    Return:\n",
    "        (np.array, np.array) (times, amounts)\n",
    "\n",
    "    \"\"\"\n",
    "    fixed_leg = swap.leg(0)\n",
    "    n = len(fixed_leg)\n",
    "    fixed_times=[]\n",
    "    fixed_amounts=[]\n",
    "    npv = 0\n",
    "    for i in range(n):\n",
    "        cf = fixed_leg[i]\n",
    "        t_i = timeFromReference(cf.date())\n",
    "        if t_i > t:\n",
    "            fixed_times.append(t_i)\n",
    "            fixed_amounts.append(cf.amount())\n",
    "    return np.array(fixed_times), np.array(fixed_amounts)\n",
    "\n",
    "\n",
    "def getFloatingLeg(swap, t):\n",
    "    \n",
    "    float_leg = swap.leg(1)\n",
    "    n = len(float_leg)\n",
    "    float_times = []\n",
    "    float_dcf = []\n",
    "    accrual_start_time = []\n",
    "    accrual_end_time = []\n",
    "    nominals = []\n",
    "    for i in range(n):\n",
    "        # convert base classiborstart_idx Cashflow to\n",
    "        # FloatingRateCoupon\n",
    "        cf = ql.as_floating_rate_coupon(float_leg[i])\n",
    "        value_date = cf.referencePeriodStart()\n",
    "        t_fix_i = timeFromReference(value_date)\n",
    "        t_i = timeFromReference(cf.date()) \n",
    "        if t_fix_i >= t:\n",
    "            iborIndex = cf.index()\n",
    "            \n",
    "            index_mat = cf.referencePeriodEnd()\n",
    "            # year fraction\n",
    "            float_dcf.append(cf.accrualPeriod())\n",
    "            # calculate the start and end time\n",
    "            accrual_start_time.append(t_fix_i)\n",
    "            accrual_end_time.append(timeFromReference(index_mat))\n",
    "            # payment time\n",
    "            float_times.append(t_i)\n",
    "            # nominals \n",
    "            nominals.append(cf.nominal())\n",
    "    return np.array(float_times), np.array(float_dcf), np.array(accrual_start_time), np.array(accrual_end_time), np.array(nominals)\n",
    "\n",
    "\n",
    "def swapPathNPV(swap, t):\n",
    "    fixed_times, fixed_amounts = getFixedLeg(swap, t)\n",
    "    float_times, float_dcf, accrual_start_time, accrual_end_time, nominals = getFloatingLeg(swap, t)\n",
    "    df_times = np.concatenate([fixed_times, \n",
    "                           accrual_start_time, \n",
    "                           accrual_end_time, \n",
    "                           float_times])\n",
    "    df_times = np.unique(df_times)\n",
    "    # Store indices of fix leg payment times in \n",
    "    # the df_times array\n",
    "    fix_idx = np.in1d(df_times, fixed_times, True)\n",
    "    fix_idx = fix_idx.nonzero()\n",
    "    # Indices of the floating leg payment times \n",
    "    # in the df_times array\n",
    "    float_idx = np.in1d(df_times, float_times, True)\n",
    "    float_idx = float_idx.nonzero()\n",
    "    # Indices of the accrual start and end time\n",
    "    # in the df_times array\n",
    "    accrual_start_idx = np.in1d(df_times, accrual_start_time, True)\n",
    "    accrual_start_idx = accrual_start_idx.nonzero()\n",
    "    accrual_end_idx = np.in1d(df_times, accrual_end_time, True)\n",
    "    accrual_end_idx = accrual_end_idx.nonzero()\n",
    "    # Calculate NPV\n",
    "    def calc(x_t):\n",
    "        discount = np.vectorize(lambda T: model.zerobond(T, t, x_t))\n",
    "        dfs = discount(df_times)\n",
    "        # Calculate fixed leg npv\n",
    "        fix_leg_npv = np.sum(fixed_amounts * dfs[fix_idx])\n",
    "        # Estimate the index fixings\n",
    "        index_fixings = (dfs[accrual_start_idx] / dfs[accrual_end_idx] - 1) \n",
    "        index_fixings /= float_dcf\n",
    "        # Calculate the floating leg npv\n",
    "        float_leg_npv = np.sum(nominals * index_fixings * float_dcf * dfs[float_idx])\n",
    "        npv = float_leg_npv - fix_leg_npv\n",
    "        return npv\n",
    "    return calc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.99726027,  2.00273973])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert call date to time\n",
    "callTimes = timeFromReference(calldates)\n",
    "callTimes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "####Test the t0 Swap Pricing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Swap NPV at time 0: 0.0091\n",
      "Error : 0.00000000\n"
     ]
    }
   ],
   "source": [
    "npv = swapPathNPV(swap, 0.)(0)\n",
    "print(\"Swap NPV at time 0: %.4f\" % npv)\n",
    "print(\"Error : %.8f\" % (npv - swap.NPV()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Monte Carlo Simulation\n",
    "\n",
    "#### Generate time grid and paths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def fixingdates(swap):\n",
    "    leg = swap.leg(1)\n",
    "    n = len(leg)\n",
    "    fixing_dates = []\n",
    "    for i in range(0, n):\n",
    "        cf = ql.as_floating_rate_coupon(float_leg[i])\n",
    "        value_date = cf.referencePeriodStart()\n",
    "        fixing_dates.append(value_date)\n",
    "    return fixing_dates\n",
    "\n",
    "# Define evaluation grid\n",
    "\n",
    "date_grid = [today] + calldates \n",
    "\n",
    "date_grid = np.unique(np.sort(date_grid))\n",
    "time_grid = np.vectorize(lambda x: ql.Actual365Fixed().yearFraction(today, x))(date_grid)\n",
    "dt = time_grid[1:] - time_grid[:-1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([Date(7,4,2015), Date(5,4,2016), Date(7,4,2017)], dtype=object)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "date_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.99726027,  2.00273973])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Random number generator\n",
    "seed = 1\n",
    "urng = ql.MersenneTwisterUniformRng(seed)\n",
    "usrg = ql.MersenneTwisterUniformRsg(len(time_grid)-1,urng)\n",
    "generator = ql.InvCumulativeMersenneTwisterGaussianRsg(usrg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#%%timeit\n",
    "# Generate N paths\n",
    "M = 100000\n",
    "m = len(time_grid)\n",
    "x = np.zeros((M, m))\n",
    "y = np.zeros((M, m))\n",
    "numeraires = np.zeros((M, m))\n",
    "                      \n",
    "for n in range(0, M):\n",
    "    numeraires[n, 0] = model.numeraire(0, 0)\n",
    "    \n",
    "for n in range(0,M):\n",
    "    dWs = generator.nextSequence().value()\n",
    "    j = 1\n",
    "    for i in range(1, len(time_grid)):\n",
    "        t0 = time_grid[i-1]\n",
    "        t1 = time_grid[i]\n",
    "        e = process.expectation(t0, \n",
    "                                x[n,i-1], \n",
    "                                dt[i-1])\n",
    "        std = process.stdDeviation(t0,\n",
    "                                   x[n,i-1],\n",
    "                                   dt[i-1])\n",
    "        x[n,i] = e + dWs[i-1] * std \n",
    "        e_0_0 = process.expectation(0,0,t1)\n",
    "        std_0_0 = process.stdDeviation(0,0,t1)\n",
    "        y[n,i] = (x[n,i] - e_0_0) / std_0_0\n",
    "        numeraires[n, i] = model.numeraire(t1, y[n,i])\n",
    "        #df_times_temp = df_times.copy()\n",
    "        #df_times_temp[df_times_temp <= t1] = t1\n",
    "        #dfs[n,i] = np.vectorize(lambda T: model.zerobond(T, t1, y[n,i]))(df_times_temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "                         \n",
    "pricer = np.vectorize(swapPathNPV(swap, time_grid[-1]))\n",
    "\n",
    "cont_value = pricer(y[:,-1]) / numeraires[:,-1]\n",
    "cont_value[cont_value < 0] = 0\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.99726027,  2.00273973])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pricer = np.vectorize(swapPathNPV(swap, time_grid[-2]))\n",
    "exercise_values = pricer(y[:,-2]) / numeraires[:,-2]\n",
    "exercise_values[exercise_values < 0] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "states = y[:, -2]\n",
    "Y = np.column_stack((states, states**2, states**3, states**4))\n",
    "Y = sm.add_constant(Y)\n",
    "ols = sm.OLS(cont_value, Y)\n",
    "ols_result = ols.fit()\n",
    "cont_value_hat = np.sum(ols_result.params * Y, axis=1)\n",
    "npv_amc = np.maximum(cont_value_hat, exercise_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 15476.68970108,  22203.99784323,   9906.4788144 ,    589.72935045,\n",
       "         -282.14303658])"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ols_result.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "npv_amc = np.mean(npv_amc) * numeraires[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17011.521601274337"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npv_amc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MC NPV: 17011.5216\n",
      "Error : -57.4077 \n",
      "Rel. Error in bps: -0.5741 \n"
     ]
    }
   ],
   "source": [
    "print(\"MC NPV: %.4f\" % npv_amc)\n",
    "print(\"Error : %.4f \" % (npv_amc-swaption.NPV()))\n",
    "print(\"Rel. Error in bps: %.4f \" % ((npv_amc-swaption.NPV()) / 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11be52588>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bAwcOxOjRo3HppZdGHGPSpEmYMGECTjvtNPTp0wderxePPvpozPMJ/0xHHhaX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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bdf9a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8.5,8.5))\n",
    "plt.scatter(states, cont_value)\n",
    "plt.scatter(states, cont_value_hat, marker='x', c='red')\n",
    "plt.legend([\"continuation values at t+1\", \"regression\"])\n",
    "plt.title(\"Regression Bermudan Swaption\")\n",
    "plt.xlabel(\"State at t\")\n",
    "plt.ylabel(\"NPV\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.65652302,  0.60137971,  0.96419477, ...,  0.58020483,\n",
       "        0.62947565,  0.62142583])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numeraires[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}