{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5894bc31",
   "metadata": {},
   "source": [
    "# Overview of BasicHullWhite\n",
    "\n",
    "The [Hull-White model](https://en.wikipedia.org/wiki/Hull%E2%80%93White_model) is a short rate model represented by the stochastic differential equiation:\n",
    "\n",
    " $$dr(t) = (\\theta(t) - a r(t))dt + \\sigma dW$$\n",
    "\n",
    "\n",
    "`BasicHullWhite` in the **economic** library is a simple implementation of the Hull-White model built using [modelx](https://github.com/fumitoh/modelx).\n",
    "\n",
    "`BasicHullWhite` preforms Monte-Carlo simulations and generates paths of the instantaneous short rate based on the Hull-White model. It also inclues formulas to calculate various properties of the Hull-White model.\n",
    "\n",
    "[Gouthaman Balaraman] presents some tests performed on a Hull-White model. He uses QuantLib to build his model, but the `BasicHullWhite` does not use QuantLib, and its Monte-Carlo simulations are generated from first principles using random numbers following the standard normal distribution. \n",
    "In addition, `BasicHullWhite` generates values of stochastic variable at each time step at once as a numpy array based on the vector modeling approach.\n",
    "\n",
    "This notebook aims to perform analyses similar to Balaraman's using `BasicHullWhite`.  \n",
    "\n",
    "\n",
    "[Gouthaman Balaraman]: http://gouthamanbalaraman.com/blog/hull-white-simulation-quantlib-python.html\n",
    "\n",
    "\n",
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "**References**\n",
    "\n",
    "* [Gouthaman Balaraman. Hull White Term Structure Simulations with QuantLib Python](http://gouthamanbalaraman.com/blog/hull-white-simulation-quantlib-python.html)\n",
    "* [Gouthaman Balaraman. On the Convergence of Hull White Monte Carlo Simulations](http://gouthamanbalaraman.com/blog/hull-white-simulation-monte-carlo-convergence.html)    \n",
    "* [Damiano Brigo, Fabio Mercurio (2006). Interest Rate Models - Theory and Practice with Smile, Inflation and Credit, 2nd ed.](https://link.springer.com/book/10.1007/978-3-540-34604-3)\n",
    "* [Paul Glasserman (2003). Monte Carlo Methods in Financial Engineering](https://link.springer.com/book/10.1007/978-0-387-21617-1)\n",
    "\n",
    "\n",
    "</div>\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e70ecf0",
   "metadata": {},
   "source": [
    "## Overview of the model\n",
    "\n",
    "`HullWiteModel` include only one space, which is named `HullWhite`, and all the definitions are in that space. The `HullWhite` space is assined to `HW` in this notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bd39830d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import modelx as mx\n",
    "\n",
    "model = mx.read_model('BasicHullWhite')\n",
    "HW = model.HullWhite"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0856413a",
   "metadata": {},
   "source": [
    "All the input parameters except for the initial curve are given as *References* (names starting with \"_\" are default names defined by modelx). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "da0a349b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{__builtins__,\n",
       " _self,\n",
       " _space,\n",
       " np,\n",
       " step_size,\n",
       " time_len,\n",
       " a,\n",
       " sigma,\n",
       " seed1,\n",
       " seed2,\n",
       " scen_size}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.refs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80e9824f",
   "metadata": {},
   "source": [
    "The defalut values for the number of scenarios, length of time ($T$), number of steps, $a$, $\\sigma$ are set equal to the Balaraman's example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "853a5fe1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of scenarios: 1000\n",
      "Length of time (in years): 30\n",
      "Number of steps: 360\n",
      "a: 0.1\n",
      "sigma: 0.1\n"
     ]
    }
   ],
   "source": [
    "print(\"Number of scenarios:\", HW.scen_size)\n",
    "print(\"Length of time (in years):\", HW.time_len)\n",
    "print(\"Number of steps:\", HW.step_size)\n",
    "print(\"a:\", HW.a)\n",
    "print(\"sigma:\", HW.sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9db74dc",
   "metadata": {},
   "source": [
    "Below is a list of cells defined in `HW`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5448ca15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{A_t_T,\n",
       " B_t_T,\n",
       " E_rt,\n",
       " E_rt_s,\n",
       " P_t_T,\n",
       " V_t_T,\n",
       " Var_rt,\n",
       " Var_rt_s,\n",
       " accum_short_rate,\n",
       " accum_short_rate2,\n",
       " alpha,\n",
       " disc_factor,\n",
       " disc_factor_paths,\n",
       " mean_disc_factor,\n",
       " mean_short_rate,\n",
       " mkt_fwd,\n",
       " mkt_zcb,\n",
       " short_rate,\n",
       " short_rate_paths,\n",
       " std_norm_rand,\n",
       " t_,\n",
       " var_short_rate}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.cells"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c76bea80",
   "metadata": {},
   "source": [
    "Time-dependent functions are paremeterized with integer indexes instead of times themselves, \n",
    "i.e. $f(t)$ where $t=t_i, i=1, 2, 3, \\ldots$ in math expression is translated as `f(i)`, `i=1, 2, 3...` in modelx formula.\n",
    "Mapping $i$ to $t_i$ is done by `t_(i)`. By defalut, $t_i$s are evenly spaced, but the model should work even if the intervals are set uneven."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "66cfc15a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "lambda i: i * time_len / step_size"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.t_.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f688053",
   "metadata": {},
   "source": [
    "By default, the instanteneous forward rates observed at time 0 ($f^M(0, t_i)$) are set to 0.05 in `mkt_fwd` to be consistent with the Balaraman's example. $P^M(0, t_i)$, the market prices of zero-coupon bonds by duration are calculated from $f^M(0, t_i)$ in `mkt_zcb`. These may be defined the other way around, i.e. $f^M(0, t_i)$ may be derived from $P^M(0, t_i)$ inputs. The forward rates don't have to be constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d50e2889",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def mkt_fwd(i):\n",
       "    \"\"\"The initial instantaneous forward rate for :attr:`t_(i)<t_>`.\n",
       "\n",
       "    By default, returns 0.05 for all ``i``.\n",
       "    \"\"\"\n",
       "    return 0.05"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.mkt_fwd.formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fb61ea42",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def mkt_zcb(i):\n",
       "    \"\"\"The initial price of zero coupon bond\n",
       "\n",
       "    The initial price of the unit zero coupon bond maturing at :attr:`t_(i)<t_>`.\n",
       "\n",
       "    If ``i=0`` returns 1. Otherwise, defined as::\n",
       "\n",
       "        mkt_zcb(i-1) * np.exp(-mkt_fwd(i-1)*dt)\n",
       "\n",
       "    where ``dt = t_(i) - t_(i-1)``.\n",
       "\n",
       "    .. seealso::\n",
       "        * :attr:`t_`\n",
       "        * :attr:`mkt_fwd`\n",
       "    \"\"\"\n",
       "    if i == 0:\n",
       "        return 1.0\n",
       "    else:\n",
       "        dt = t_(i) - t_(i-1)\n",
       "        return mkt_zcb(i-1) * np.exp(-mkt_fwd(i-1)*dt)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.mkt_zcb.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88ca3de3",
   "metadata": {},
   "source": [
    "`short_rate` corresponds to $r(t_{i})$, and recursively calculates stochastic paths of the instantaneous short rate at each time step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "f5d42e69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def short_rate(i):\n",
       "    r\"\"\"Stochastic short rates at :attr:`t_(i)<t_>`\n",
       "\n",
       "    Returns, in a numpy array, simulated stochastic short rates at :attr:`t_(i)<t_>`\n",
       "    for all scenarios.\n",
       "\n",
       "    For ``i=0``, defined as :meth:`mkt_fwd(0)<mkt_fwd>`.\n",
       "\n",
       "    For ``i>0``, defined as\n",
       "    :math:`r(t_i) = E\\{r(t_i) | \\mathcal{F}_{i-1}\\} + \\sqrt{Var\\{ r(t_i) | \\mathcal{F}_{i-1} \\}} * Z`,\n",
       "\n",
       "    where :math:`E\\{r(t_i) | \\mathcal{F}_{i-1}\\}`, the expected value of\n",
       "    :math:`r(t_i)` conditional on :math:`\\mathcal{F}_{i-1}` is calculated by :meth:`E_rt_s(i-1, i)<E_rt_s>`,\n",
       "    :math:`Var\\{ r(t_i) | \\mathcal{F}_{i-1} \\}` the variance of :math:`r(t_i)` conditional on :math:`\\mathcal{F}_{i-1}`\n",
       "    is calculated by :meth:`Var_rt_s(i-1, i)<Var_rt_s>`,\n",
       "    and :math:`Z`, a random number drawn from :math:`\\mathcal{N}(0, 1)`\n",
       "    a standard normal distribution calculated by :meth:`std_norm_rand`.\n",
       "\n",
       "    .. seealso::\n",
       "        * :attr:`scen_size`\n",
       "        * :meth:`mkt_fwd`\n",
       "        * :meth:`E_rt_s`\n",
       "        * :meth:`Var_rt_s`\n",
       "        * :meth:`std_norm_rand`\n",
       "        * :attr:`seed1`\n",
       "    \"\"\"\n",
       "    if i == 0:\n",
       "        return np.full(scen_size, mkt_fwd(0))\n",
       "    else:\n",
       "        return E_rt_s(i-1, i) + Var_rt_s(i-1, i)**0.5 * std_norm_rand(seed1)[:, i-1]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.short_rate.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b28f6f7",
   "metadata": {},
   "source": [
    "Note that the initial stochastic differential equation, $dr(t) = (\\theta(t) - a r(t))dt + \\sigma dW$ is not used in this model.\n",
    "Rather, the model uses the fact that the Hull-White model is a Gaussian process, \n",
    "and $r(t^i)$ conditional on $\\mathcal{F}_{t_{i-1}} $ is normally distributed. `short_rate(i)` corresponds to the following expression\n",
    "\n",
    "$$r(t_i) = E\\{r(t_i) | \\mathcal{F}_{t_{i-1}}\\} + \\sqrt{Var\\{ r(t_i) | \\mathcal{F}_{t_{i-1}} \\}} * Z$$\n",
    "\n",
    "where $Z$ represents random samples drawn from $\\mathcal{N}(0, 1)$, the strandard normal distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8651ebec",
   "metadata": {},
   "source": [
    "$E\\{r(t_j) | \\mathcal{F}_i\\}$, the mean of $r(t_j)$ conditional on $\\mathcal{F}_{t_i} $ is modeled as `E_rt_s(i, j)`. By replacing $t_{i}$ with $s$ and $t_{j}$ with $t$, the mean is expressed as:\n",
    "\n",
    "\n",
    "$$ E\\{r(t) | \\mathcal{F}_{s}\\} = r(s)e^{-a(t-s)}  + \\alpha(t) - \\alpha(s)e^{-a(t-s)} $$\n",
    "   where \n",
    "   $$ \\alpha(t) = f^M(0, t) + \\frac{\\sigma^2} {2a^2}(1-e^{-at})^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "60fcf2f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def E_rt_s(i, j):\n",
       "    r\"\"\"Conditional expected values of :math:`r(t_j)`\n",
       "\n",
       "    Returns, in a numpy array,\n",
       "    :math:`E\\{r(t_j) | \\mathcal{F}_{i}\\}`,\n",
       "    the expected values of :math:`r(t_j)` conditional on :math:`\\mathcal{F}_{i}`\n",
       "    for all scenarios.\n",
       "    :math:`E\\{r(t) | \\mathcal{F}_{s}\\}` is calculated as:\n",
       "\n",
       "    .. math::\n",
       "\n",
       "        r(s)e^{-a(t-s)}  + \\alpha(t) - \\alpha(s)e^{-a(t-s)}\n",
       "\n",
       "    where :math:`\\alpha(t)` is calculated by :meth:`alpha`.\n",
       "\n",
       "    .. seealso:\n",
       "        * :meth:`short_rate`\n",
       "        * :meth:`alpha`\n",
       "    \"\"\"\n",
       "    s, t = t_(i), t_(j)\n",
       "    r_s = short_rate(i)\n",
       "    return r_s * np.exp(-a * (t-s)) + alpha(j) - alpha(i) * np.exp(-a * (t-s))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.E_rt_s.formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b26d1172",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def E_rt():\n",
       "    \"\"\"The expected values of :math:`r(t_i)` at time 0 for all :math:`t_i`.\n",
       "\n",
       "    Returns, in a numpy array, the expected values of\n",
       "    :math:`r(t_i)` for all :math:`t_i`.\n",
       "    Calculated as :math:`E\\{r(t_i) | \\mathcal{F}_{0}\\}`.\n",
       "\n",
       "    .. seealso::\n",
       "\n",
       "       * :meth:`E_rt_s`\n",
       "\n",
       "    \"\"\"\n",
       "    return np.array([E_rt_s(0, i)[0] for i in range(step_size + 1)])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.E_rt.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e048eb28",
   "metadata": {},
   "source": [
    "In the same way, $Var\\{r(t_{j}) | \\mathcal{F}_{t_i}\\}$, the variance of $r(t_j)$ conditional on $\\mathcal{F}_{t_i}$ is modeled as `Var_rt_s(i, j)`. With the same definitions for $s$, $t$, $\\alpha(t)$ as above, the variance is expressed as:\n",
    "\n",
    "$$ Var\\{ r(t) | \\mathcal{F}_s \\} = \\frac{\\sigma^2}{2a} (1 - e^{-2a(t-s)})$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "080f961d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def Var_rt_s(i, j):\n",
       "    r\"\"\"The variance of :math:`r(t_j)` conditional on :math:`\\mathcal{F}_{t_i}`\n",
       "\n",
       "    :math:`Var\\{r(t_{j}) | \\mathcal{F}_{t_i}\\}`,\n",
       "    the variance of :math:`r(t_j)` conditional on :math:`\\mathcal{F}_{t_i}`,\n",
       "    calculated as:\n",
       "\n",
       "    .. math::\n",
       "\n",
       "        Var\\{ r(t) | \\mathcal{F}_s \\} = \\frac{\\sigma^2}{2a} (1 - e^{-2a(t-s)})\n",
       "\n",
       "    .. seealso::\n",
       "        * :attr:`a`\n",
       "        * :attr:`sigma`\n",
       "\n",
       "    \"\"\"\n",
       "    s, t = t_(i), t_(j)\n",
       "    return sigma**2 / (2*a) * (1 - np.exp(-2 * a * (t-s)))"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.Var_rt_s.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1bc419f2",
   "metadata": {},
   "source": [
    "Note that for each `i`, `short_rate(i)` returns a 1-dimensional numpy array having `scen_size` elements,\n",
    "and for each pair of `i` and `j`, both `E_rt_s(i, j)` and `Var_rt_s(i, j)` also return an array with `scen_size` elements. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dca46262",
   "metadata": {},
   "source": [
    "$\\alpha(t_{i})$ is modeled as `alpha(i)`. `alpha(i)` doesn't vary by scenario, so it returns a single value for each `i`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "80339d01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def alpha(i):\n",
       "    r\"\"\":math:`\\alpha(t_i)`\n",
       "\n",
       "    Returns, in a numpy array, :math:`\\alpha(t_i)` for all scenarios.\n",
       "    :math:`\\alpha` appears in the expression of\n",
       "    :math:`E\\{r(t) | \\mathcal{F}_{s}\\}` and is defined as:\n",
       "\n",
       "    .. math::\n",
       "\n",
       "        \\alpha(t) = f^M(0, t) + \\frac{\\sigma^2} {2a^2}(1-e^{-at})^2\n",
       "\n",
       "    .. seealso::\n",
       "        * :meth:`E_rt_s`\n",
       "\n",
       "    \"\"\"\n",
       "    t = t_(i)\n",
       "    return mkt_fwd(i) + 0.5 * sigma**2 / a**2 * (1 - np.exp(-a*t))**2"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.alpha.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a5a37b8",
   "metadata": {},
   "source": [
    "## Simulating $r(t_i)$\n",
    "\n",
    "The chart below shows the first 10 paths of $r(t_i)$.\n",
    "`short_rate_paths()` is defined to return $r(t_i)$ for all the scenarios and all the tim steps in a 2-dimensional array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8a28a393",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def short_rate_paths():\n",
       "    \"\"\"Short rate paths.\n",
       "\n",
       "    Returns, as a 2D numpy array, the simulated short rate paths\n",
       "    for all scenarios.\n",
       "\n",
       "    .. seealso::\n",
       "        * :meth:`short_rate`\n",
       "    \"\"\"\n",
       "    return np.array([short_rate(i) for i in range(step_size + 1)]).transpose()"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.short_rate_paths.formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "824f6ee1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    plt.plot(range(HW.step_size+1), HW.short_rate_paths()[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75a7a999",
   "metadata": {},
   "source": [
    "For each $t_i$, the mean of $r(t_i)$ should converge to $E\\{r(t_i) | \\mathcal{F}_{0}\\}$. For convenience, `mean_short_rate` and `E_rt` are defined to represent the mean of $r(t_i)$ and $E\\{r(t_i) | \\mathcal{F}_{0}\\}$ respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "50153c02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def mean_short_rate():\n",
       "    \"\"\"The means of generated short rates\n",
       "\n",
       "    Returns, as a numpy array, the means of short rates of all scenarios\n",
       "    for all :math:`t_i`.\n",
       "    This should converge to the theoretical variances\n",
       "    calculated by :meth:`E_rt`.\n",
       "\n",
       "    .. seealso::\n",
       "        * :meth:`short_rate`\n",
       "        * :meth:`E_rt`\n",
       "    \"\"\"\n",
       "    return np.array([np.mean(short_rate(i)) for i in range(step_size + 1)])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.mean_short_rate.formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1beaed66",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def E_rt():\n",
       "    \"\"\"The expected values of :math:`r(t_i)` at time 0 for all :math:`t_i`.\n",
       "\n",
       "    Returns, in a numpy array, the expected values of\n",
       "    :math:`r(t_i)` for all :math:`t_i`.\n",
       "    Calculated as :math:`E\\{r(t_i) | \\mathcal{F}_{0}\\}`.\n",
       "\n",
       "    .. seealso::\n",
       "\n",
       "       * :meth:`E_rt_s`\n",
       "\n",
       "    \"\"\"\n",
       "    return np.array([E_rt_s(0, i)[0] for i in range(step_size + 1)])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.E_rt.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbde5f1c",
   "metadata": {},
   "source": [
    "The chart below compares the mean of $r(t_i)$ against $E\\{r(t_i) | \\mathcal{F}_{0}\\}$ with 1000 scenarios. The chart looks similar to Balaraman's analysis. The mean converges pretty well during the first 20 years (240 steps), but diverges from the expectation around the 300th step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "bab42dc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24faa550b20>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "HW.scen_size = 1000\n",
    "plt.plot(range(HW.step_size + 1), HW.E_rt(), \"b-\")\n",
    "plt.plot(range(HW.step_size + 1), HW.mean_short_rate(), \"r--\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50adfb01",
   "metadata": {},
   "source": [
    "The chart below is with 10,000 scenarios. The divergence dissapears and the mean fits the expectation much better."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "871056b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24faa3f3ac0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "HW.scen_size = 10000\n",
    "HW.a = 0.1\n",
    "HW.sigma = 0.1\n",
    "plt.plot(range(HW.step_size + 1), HW.E_rt(), \"b-\")\n",
    "plt.plot(range(HW.step_size + 1), HW.mean_short_rate(), \"r--\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c975725",
   "metadata": {},
   "source": [
    "In the same manner as the mean, for each $t_i$, the variance of $r(t_i)$ should converge to $Var\\{r(t_i) | \\mathcal{F}_{0}\\}$. For convenience, `var_short_rate` and `Var_rt` are defined to represent the variance of $r(t_i)$ and $Var\\{r(t_i) | \\mathcal{F}_{0}\\}$ respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7aebb20c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def var_short_rate():\n",
       "    \"\"\"Variance of generated short rates\n",
       "\n",
       "    Returns, as a vector in a numpy array, the variances of\n",
       "    the generated short rates for all :math:`t_i`.\n",
       "    This should converge to the theoretical variances\n",
       "    calculated by :meth:`Var_rt`.\n",
       "\n",
       "    .. seealso::\n",
       "        * :meth:`short_rate`\n",
       "        * :meth:`Var_rt`\n",
       "\n",
       "    \"\"\"\n",
       "    return np.array([np.var(short_rate(i)) for i in range(step_size + 1)])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.var_short_rate.formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "975d0644",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def Var_rt():\n",
       "    r\"\"\"The variance of :math:`r(t_i)` at time 0 for all :math:`t_i`.\n",
       "\n",
       "    Returns, in a numpy array, the variance of\n",
       "    :math:`r(t_i)` for all :math:`t_i`.\n",
       "    Calculated as :math:`Var\\{r(t_i) | \\mathcal{F}_{0}\\}`.\n",
       "\n",
       "    .. seealso::\n",
       "        * :meth:`Var_rt_s`\n",
       "    \"\"\"\n",
       "    return np.array([Var_rt_s(0, i) for i in range(step_size + 1)])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.Var_rt.formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "423dcd7a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24fa877da30>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "HW.scen_size = 1000\n",
    "plt.plot(range(HW.step_size + 1), HW.Var_rt(), \"b-\")\n",
    "plt.plot(range(HW.step_size + 1), HW.var_short_rate(), \"r--\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "0ff67c94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24fa8416910>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "HW.scen_size = 10000\n",
    "plt.plot(range(HW.step_size + 1), HW.Var_rt(), \"b-\")\n",
    "plt.plot(range(HW.step_size + 1), HW.var_short_rate(), \"r--\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4f88b73",
   "metadata": {},
   "source": [
    "## Simulating the discount factor"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "950401f4",
   "metadata": {},
   "source": [
    "Along with $r(t_{i})$, the discount factor needs to be simulated. The discount factor is defined as $e^{-Y(t_i)}$ where\n",
    "\n",
    "$$Y(t_i)=\\int_0^{t_i}r(t)dt$$\n",
    "\n",
    "For simplicity, we model $Y(t_i)$ as a descrete approximation to the integral:\n",
    "\n",
    "$$\\sum_{j=1}^{i}r(t_{j-1})(t_j-t_{j-1})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "63c8f842",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def accum_short_rate(i):\n",
       "    r\"\"\"Accumulated short rates.\n",
       "\n",
       "    a descrete approximation to the integral :math:`\\int_0^{t_i}r(t)dt`,\n",
       "    calculated as :math:`\\sum_{j=1}^{i}r(t_{j-1})(t_j-t_{j-1})`\n",
       "\n",
       "    .. seealso::\n",
       "        * :meth:`disc_factor`\n",
       "    \"\"\"\n",
       "    if i == 0:\n",
       "        return np.full(scen_size, 0.0)\n",
       "    else:\n",
       "        dt = t_(i) - t_(i-1)\n",
       "        return accum_short_rate(i-1) + short_rate(i-1) * dt"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.accum_short_rate.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c79984f0",
   "metadata": {},
   "source": [
    "There is an alternative approach to simulate $Y(t_i)$ by using the fact that $Y(t_i)$ follows a normal distribution, and by simulating the joint distribution of $(r(t_i), Y(t_i))$ as suggested in [Monte Carlo Methods in Financial Engineering](https://link.springer.com/book/10.1007/978-0-387-21617-1). `accum_short_rate2` implements this alternative approach, althogh it does not have material impact on the discussion below.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "132cdae9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def accum_short_rate2(i):\n",
       "    r\"\"\"Alternative implementation of accumulated short rates.\n",
       "\n",
       "    An alternative approach to simulate :math:`Y(t_i)=\\int_0^{t_i}r(t)dt`\n",
       "    by using the fact that :math:`Y(t_i)` follows a normal distribution,\n",
       "    and by simulating the joint distribution of :math:`(r(t_i), Y(t_i))`,\n",
       "    as suggested in Glasserman (2003).\n",
       "\n",
       "    .. seealso::\n",
       "        * :meth:`accum_short_rate`\n",
       "        * :attr:`seed2`\n",
       "        * Paul Glasserman (2003). Monte Carlo Methods in Financial Engineering\n",
       "    \"\"\"\n",
       "    if i == 0:\n",
       "        return np.full(scen_size, 0.0)\n",
       "    else:\n",
       "        t, T = t_(i-1), t_(i)\n",
       "        dt = T - t\n",
       "        cov = sigma**2/(2*a**2)*(1 + np.exp(-2*a*dt) -2 * np.exp(-a*dt))\n",
       "        z1 = std_norm_rand(seed1)[:, i-1]\n",
       "        z2 = std_norm_rand(seed2)[:, i-1]\n",
       "\n",
       "        rho = cov / (Var_rt_s(i-1, i)**0.5 * V_t_T(i-1, i)**0.5)\n",
       "\n",
       "        mean = B_t_T(i-1, i) * (short_rate(i-1) - alpha(i-1)) + np.log(mkt_zcb(i-1)/mkt_zcb(i)) + 0.5*(V_t_T(0, i)-V_t_T(0, i-1))\n",
       "        return accum_short_rate2(i-1) + mean + V_t_T(i-1, i)**0.5 * (rho*z1 + (1-rho**2)**0.5*z2)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.accum_short_rate2.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85d20beb",
   "metadata": {},
   "source": [
    "`discount_factor` and `mean_disc_factor` are defined as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d3a94e25",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def disc_factor(i):\n",
       "    \"\"\"Discount factors\n",
       "\n",
       "    Returns, in a numpy array, the discount factors for\n",
       "    cashflows at :math:`t_i` for all scenarios.\n",
       "    Defined as::\n",
       "\n",
       "        np.exp(-accum_short_rate(i))\n",
       "\n",
       "    .. seealso::\n",
       "        * accum_short_rate\n",
       "\n",
       "    \"\"\"\n",
       "    return np.exp(-accum_short_rate(i))"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.disc_factor.formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "511e1583",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "def mean_disc_factor():\n",
       "    \"\"\"Discount factor means\n",
       "\n",
       "    Returns, as a numpy array, the mean of discount factors of all scenarios\n",
       "    for each :math:`t_i`.\n",
       "\n",
       "    .. seealso::\n",
       "        * :meth:`disc_factor`\n",
       "    \"\"\"\n",
       "    return np.array([np.mean(disc_factor(i)) for i in range(step_size + 1)])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HW.mean_disc_factor.formula"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54082cfa",
   "metadata": {},
   "source": [
    "The chart below compares the mean of the simulated discount factors against $P^M(0, t_i)$ with 1000 scenarios. The mean diverges from the expectation significantly after the 150th step."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "a5430a48",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24fa85de9d0>]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "HW.scen_size = 1000\n",
    "plt.plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], \"b-\")\n",
    "plt.plot(range(HW.step_size+1), HW.mean_disc_factor(), \"r--\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "797cddbb",
   "metadata": {},
   "source": [
    "The chart shows the case of 10,000 scenarios. The stochastic mean does not converge well. Even with 100,000 scenarios, the convergence is still poor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "527baff8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24fa8643460>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "HW.scen_size = 10000\n",
    "plt.plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], \"b-\")\n",
    "plt.plot(range(HW.step_size+1), HW.mean_disc_factor(), \"r--\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19df009a",
   "metadata": {},
   "source": [
    "The charts below examine the convergence of the discount factor for various combinations of $\\sigma$ and $a$, first by changing $\\sigma$ and secondly by changing $a$.\n",
    "As Balaraman's study shows, the convergence gets worse as $\\sigma/a$ gets larger than 1, and gets better as $\\sigma/a$ gets smaller than 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8e446619",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "HW.scen_size = 1000\n",
    "\n",
    "fig, axs = plt.subplots(2, 2, sharex=True, sharey=True)\n",
    "fig.suptitle(r\"$a=$\" + str(HW.a))\n",
    "for sigma, (h, v) in zip([0.05, 0.075, 0.1, 0.125], [(0, 0), (0, 1), (1, 0), (1, 1)]):\n",
    "    HW.sigma = sigma\n",
    "    axs[h, v].set_title(r\"$\\sigma=$\" + str(sigma) +  r\", $\\sigma/a=$\" + \"%.2f\" % (sigma/HW.a))\n",
    "    axs[h, v].plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], \"b-\")\n",
    "    axs[h, v].plot(range(HW.step_size+1), HW.mean_disc_factor(), \"r--\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "71a47989",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "HW.scen_size = 1000\n",
    "HW.sigma = 0.1\n",
    "\n",
    "fig, axs = plt.subplots(2, 2, sharex=True, sharey=True)\n",
    "fig.suptitle(r\"$\\sigma=$\" + str(HW.sigma))\n",
    "for a, (h, v) in zip([0.05, 0.1, 0.15, 0.2], [(0, 0), (0, 1), (1, 0), (1, 1)]):\n",
    "    HW.a = a\n",
    "    axs[h, v].set_title(r\"$a=$\" + str(a) +  r\", $\\sigma/a=$\" + \"%.2f\" % (HW.sigma/HW.a))\n",
    "    axs[h, v].plot(range(HW.step_size+1), [HW.mkt_zcb(i) for i in range(HW.step_size+1)], \"b-\")\n",
    "    axs[h, v].plot(range(HW.step_size+1), HW.mean_disc_factor(), \"r--\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}