{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "operating-tower",
   "metadata": {},
   "source": [
    "# Lucas Asset Pricing Model\n",
    "\n",
    "## A notebook by [Christopher D. Carroll](http://www.econ2.jhu.edu/people/ccarroll/) and [Mateo Velásquez-Giraldo](https://mv77.github.io/)\n",
    "### Inspired by its [Quantecon counterpart](https://julia.quantecon.org/multi_agent_models/lucas_model.html)\n",
    "\n",
    "This notebook presents simple computational tools to solve an instance of Lucas's asset-pricing model for which there is no analytical solution: The case when the logarithm of the asset's dividend follows an autoregressive process of order 1,\n",
    "\\begin{equation*}\n",
    "\\ln d_{t+1} = \\gamma + \\alpha \\ln d_t + \\varepsilon_{t+1}, \\qquad \\varepsilon \\sim \\mathcal{N}(-\\frac{\\sigma^2}{2}, \\sigma).\n",
    "\\end{equation*}\n",
    "\n",
    "A presentation of this model can be found in [Christopher D. Carroll's lecture notes](http://www.econ2.jhu.edu/people/ccarroll/public/lecturenotes/AssetPricing/LucasAssetPrice/).\n",
    "\n",
    "Those notes use [the Bellman equation](http://www.econ2.jhu.edu/people/ccarroll/public/lecturenotes/AssetPricing/LucasAssetPrice/#pofc) to derive a relationship between the price of the asset in the current period $t$ and the next period $t+1$:\n",
    "\n",
    "\\begin{equation*}\n",
    "P_{t} =\n",
    "\\overbrace{\\left(\\frac{1}{1+\\vartheta}\\right)}\n",
    "^{\\beta}\\mathbb{E}_{t}\\left[ \\frac{u^{\\prime}(d_{t+1})}{u^{\\prime}(d_t)} (P_{t+1} + d_{t+1}) \\right]\n",
    "\\end{equation*}\n",
    "\n",
    "The equilibrium pricing equation is a relationship between the price and the dividend (a \"pricing kernel\") $P^{*}(d)$ such that, if everyone _believes_ that to be the pricing kernel, everyone's Euler equation will be satisfied:\n",
    "\n",
    "\\begin{equation*}\n",
    "P^*(d_t) =   \\left(\\frac{1}{1+\\vartheta}\\right)\\mathbb{E}_{t}\\left[ \\frac{u^{\\prime}(d_{t+1})}{u^{\\prime}(d_t)} (P^*(d_{t+1}) + d_{t+1}) \\right]\n",
    "\\end{equation*}\n",
    "\n",
    "As noted in the handout, there are some special circumstances in which it is possible to solve for $P^{*}$ analytically:\n",
    "\n",
    "| Shock Process | Mean Restrictions  | CRRA | Solution for Pricing Kernel $P^*(d)$  |\n",
    "| --- | :-- | :--  | :---:  |\n",
    "| bounded, IID, $\\mathbb{E}[d]=\\bar{d}$  | $0 < d < \\infty$ | 1 (log) | $\\vartheta^{-1}d$  |\n",
    "| lognormal, mean 1 | $\\mu=-\\sigma^{2}/2$  | $\\rho$ | $\\vartheta^{-1}{d_t^\\rho}~e^{\\rho(\\rho-1)\\sigma^2/2}$  |\n",
    "| lognormal mean $e^{\\gamma}=\\mathbb{E}[d_{t+1}/d_{t}]$  | ${\\mu~=-\\sigma^{2}/2+\\gamma}$ |$\\rho$ |  $\\vartheta^{-1}d_t^{\\rho}e^{\\rho\\gamma+\\rho(\\rho-1)\\sigma^2/2}$  |\n",
    "\n",
    "However, under most circumstances, the only way to obtain the pricing function $P^{*}$ is by solving for it numerically, as outlined below."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bulgarian-bidder",
   "metadata": {},
   "source": [
    "# Finding the equilibrium pricing function.\n",
    "\n",
    "We know that the equilibrium pricing function must satisfy the equation above. Let's define an operator that allows us to evaluate whether any candidate pricing function satisfies this requirement.\n",
    "\n",
    "Let $T$ be an operator which takes as argument a function and returns another function (these are usually called [functionals or higher-order functions](https://en.wikipedia.org/wiki/Functional_(mathematics))). For some function $f$, denote with $T[f]$ the function that results from applying $T$ to $f$. Then, for any real number $x$, $T[f](x)$ will be the real number that one obtains when the function $T[f]$ is given $x$ as an input.\n",
    "\n",
    "We define our particular operator as follows. For any function $g:\\mathbb{R}\\rightarrow\\mathbb{R}$, $T[g]$ is obtained as\n",
    "\n",
    "\\begin{equation*}\n",
    "\\forall~d_t \\in \\mathbb{R},\\,\\,\\,\\, T[g](d_t) := \\beta~\\mathbb{E}_{t}\\left[ \\frac{u^{\\prime}(d_{t+1})}{u^{\\prime}(d_t)} (f(d_{t+1}) + d_{t+1}) \\right].\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "We can use $T$ to re-express our pricing equation. If $P^*(\\bullet)$ is our equilibrium pricing funtion, it must satisfy\n",
    "\n",
    "\\begin{equation*}\n",
    "\\forall~d_t,\\,\\,\\,\\,P^*(d_t) = \\beta\\mathbb{E}_{t}\\left[ \\frac{u^{\\prime}(d_{t+1})}{u^{\\prime}(d_t)} (P^*(d_{t+1}) + d_{t+1}) \\right] = T[P^*](d_t).\n",
    "\\end{equation*}\n",
    "or, expressed differently,\n",
    "\\begin{equation*}\n",
    "P^* = T[P^*].\n",
    "\\end{equation*}\n",
    "\n",
    "Our equilibrium pricing function is therefore a *fixed point* of the operator $T$.\n",
    "\n",
    "It turns out that $T$ is a [contraction mapping](https://en.wikipedia.org/wiki/Contraction_mapping). This is useful because it implies, through [Banach's fixed-point theorem](https://en.wikipedia.org/wiki/Contraction_mapping), that:\n",
    "- $T$ has **exactly one** fixed point.\n",
    "- Starting from an arbitrary function $f$, the sequence $\\{T^n[f]\\}_{n=1}^{\\infty}$ converges to that fixed point.\n",
    "\n",
    "For our purposes, this translates to:\n",
    "- Our equilibrium pricing function not only exists, but is unique.\n",
    "- We can get arbitrarily close to the equilibrium pricing function by making some initial guess $f$ and applying the operator $T$ to it repeatedly.\n",
    "\n",
    "The code below creates a representation of our model and implements a solution routine to find $P^*$. The main components of this routine are:\n",
    "\n",
    "- `priceOnePeriod`: this is operator $T$ from above. It takes a function $f$, computes $\\beta~\\mathbb{E}_{t}\\left[ \\frac{u^{\\prime}(d_{t+1})}{u^{\\prime}(d_t)} (f(d_{t+1}) + d_{t+1}) \\right]$ for a grid of $d_t$ values, and uses the result to construct a piecewise linear interpolator that approximates $T[f]$.\n",
    "\n",
    "- `solve`: this is our iterative solution procedure. It generates an initial guess $f$ and applies `priceOnePeriod` to it iteratively. At each application, it constructs a measure of how much the candidate pricing function changed. Once changes between successive iterations are small enough, it declares that the solution has converged."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "relative-friendly",
   "metadata": {},
   "source": [
    "# A computational representation of the problem and its solution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "immediate-gilbert",
   "metadata": {},
   "source": [
    "`Uninteresting setup:`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "heated-hypothetical",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Setup\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from copy import copy\n",
    "\n",
    "from HARK.rewards import CRRAutilityP\n",
    "from HARK.distribution import Normal, calc_expectation\n",
    "from HARK.interpolation import LinearInterp, ConstantFunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "whole-livestock",
   "metadata": {},
   "outputs": [],
   "source": [
    "# A python class representing log-AR1 dividend processes.\n",
    "\n",
    "\n",
    "class DivProcess:\n",
    "    def __init__(self, α, σ, γ=0.0, nApprox=7):\n",
    "        self.α = α\n",
    "        self.σ = σ\n",
    "        self.γ = γ\n",
    "        self.nApprox = nApprox\n",
    "\n",
    "        # Create a discrete approximation to the random shock\n",
    "        self.ShkAppDstn = Normal(mu=-(σ**2) / 2, sigma=σ).discretize(N=nApprox)\n",
    "\n",
    "    def getLogdGrid(self, n=100):\n",
    "        \"\"\"\n",
    "        A method for creating a reasonable grid for log-dividends.\n",
    "        \"\"\"\n",
    "        μ = self.γ - (self.σ**2) / 2\n",
    "        uncond_sd = self.σ / np.sqrt(1 - self.α**2)\n",
    "        uncond_mean = μ / (1 - self.α)\n",
    "        logDGrid = np.linspace(-5 * uncond_sd, 5 * uncond_sd, n) + uncond_mean\n",
    "        return logDGrid\n",
    "\n",
    "\n",
    "# A class representing economies with Lucas trees.\n",
    "class LucasEconomy:\n",
    "    \"\"\"\n",
    "    A representation of an economy in which there are Lucas trees\n",
    "    whose dividends' logarithm follows an AR1 process.\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, CRRA, DiscFac, DivProcess):\n",
    "        self.CRRA = CRRA\n",
    "        self.DiscFac = DiscFac\n",
    "        self.DivProcess = DivProcess\n",
    "        self.uP = lambda c: CRRAutilityP(c, self.CRRA)\n",
    "\n",
    "    def priceOnePeriod(self, Pfunc_next, logDGrid):\n",
    "        # Create a function that, given current dividends\n",
    "        # and the value of next period's shock, returns\n",
    "        # the discounted value derived from the asset next period.\n",
    "        def discounted_value(shock, log_d_now):\n",
    "            # Find dividends\n",
    "            d_now = np.exp(log_d_now)\n",
    "            log_d_next = self.DivProcess.γ + self.DivProcess.α * log_d_now + shock\n",
    "            d_next = np.exp(log_d_next)\n",
    "\n",
    "            # Payoff and sdf\n",
    "            payoff_next = Pfunc_next(log_d_next) + d_next\n",
    "            SDF = self.DiscFac * self.uP(d_next / d_now)\n",
    "\n",
    "            return SDF * payoff_next\n",
    "\n",
    "        # The price at a given d_t is the expectation of the discounted value.\n",
    "        # Compute it at every d in our grid. The expectation is taken over next\n",
    "        # period's shocks\n",
    "        prices_now = calc_expectation(\n",
    "            self.DivProcess.ShkAppDstn, discounted_value, logDGrid\n",
    "        )\n",
    "\n",
    "        # Create new interpolating price function\n",
    "        Pfunc_now = LinearInterp(logDGrid, prices_now, lower_extrap=True)\n",
    "\n",
    "        return Pfunc_now\n",
    "\n",
    "    def solve(self, Pfunc_0=None, logDGrid=None, tol=1e-5, maxIter=500, disp=False):\n",
    "        # Initialize the norm\n",
    "        norm = tol + 1\n",
    "\n",
    "        # Initialize Pfunc if initial guess is not provided\n",
    "        if Pfunc_0 is None:\n",
    "            Pfunc_0 = ConstantFunction(0.0)\n",
    "\n",
    "        # Create a grid for log-dividends if one is not provided\n",
    "        if logDGrid is None:\n",
    "            logDGrid = self.DivProcess.getLogdGrid()\n",
    "\n",
    "        # Initialize function and compute prices on the grid\n",
    "        Pf_0 = copy(Pfunc_0)\n",
    "        P_0 = Pf_0(logDGrid)\n",
    "\n",
    "        it = 0\n",
    "        while norm > tol and it < maxIter:\n",
    "            # Apply the pricing equation\n",
    "            Pf_next = self.priceOnePeriod(Pf_0, logDGrid)\n",
    "            # Find new prices on the grid\n",
    "            P_next = Pf_next(logDGrid)\n",
    "            # Measure the change between price vectors\n",
    "            norm = np.linalg.norm(P_0 - P_next)\n",
    "            # Update price function and vector\n",
    "            Pf_0 = Pf_next\n",
    "            P_0 = P_next\n",
    "            it = it + 1\n",
    "            # Print iteration information\n",
    "            if disp:\n",
    "                print(\"Iter:\" + str(it) + \"   Norm = \" + str(norm))\n",
    "\n",
    "        if disp:\n",
    "            if norm <= tol:\n",
    "                print(\"Price function converged!\")\n",
    "            else:\n",
    "                print(\"Maximum iterations exceeded!\")\n",
    "\n",
    "        self.EqlogPfun = Pf_0\n",
    "        self.EqPfun = lambda d: self.EqlogPfun(np.log(d))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "arranged-rider",
   "metadata": {},
   "source": [
    "# Creating and solving an example economy with AR1 dividends\n",
    "\n",
    "An economy is fully specified by:\n",
    "- **The dividend process for the assets (trees)**: we assume that $\\ln d_{t+1} = \\alpha \\ln d_t + \\varepsilon_{t+1}$, $\\varepsilon_{t+1}\\sim\\mathcal{N}(-\\sigma^2/2,\\sigma)$. We must create a dividend process specifying $\\alpha$ and $\\sigma_{\\varepsilon}$.\n",
    "- **The coefficient of relative risk aversion (CRRA).**\n",
    "- **The time-discount factor ($\\beta$).**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "three-binary",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a log-AR1 process for dividends\n",
    "DivProc = DivProcess(α=0.90, σ=0.1)\n",
    "\n",
    "# Create an example economy\n",
    "economy = LucasEconomy(CRRA=2, DiscFac=0.95, DivProcess=DivProc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "becoming-gnome",
   "metadata": {},
   "source": [
    "Once created, the economy can be 'solved', which means finding the equilibrium price kernel. The distribution of dividends at period $t+1$ depends on the value of dividends at $t$, which also determines the resources agents have available to buy trees. Thus, $d_t$ is a state variable for the economy. The pricing function gives the price of trees that equates their demand and supply at every level of current dividends $d_t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1585d161-7d1a-4239-a6e9-14be795460f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__bool__',\n",
       " '__class__',\n",
       " '__delattr__',\n",
       " '__dir__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__le__',\n",
       " '__lt__',\n",
       " '__ne__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__setattr__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(economy.solve())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "divine-perry",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iter:1   Norm = 14.343105940863438\n",
      "Iter:2   Norm = 14.614867281705969\n",
      "Iter:3   Norm = 14.814622331196347\n",
      "Iter:4   Norm = 14.939364249843893\n",
      "Iter:5   Norm = 14.989619417063066\n",
      "Iter:6   Norm = 14.968432855040833\n",
      "Iter:7   Norm = 14.880572667620445\n",
      "Iter:8   Norm = 14.73192747401416\n",
      "Iter:9   Norm = 14.529020475581598\n",
      "Iter:10   Norm = 14.278638854628213\n",
      "Iter:11   Norm = 13.98755544879696\n",
      "Iter:12   Norm = 13.662325970904492\n",
      "Iter:13   Norm = 13.30914799799349\n",
      "Iter:14   Norm = 12.933769279361973\n",
      "Iter:15   Norm = 12.541434778119806\n",
      "Iter:16   Norm = 12.136863389363524\n",
      "Iter:17   Norm = 11.72424679151222\n",
      "Iter:18   Norm = 11.3072642486562\n",
      "Iter:19   Norm = 10.889108394490156\n",
      "Iter:20   Norm = 10.472518082357029\n",
      "Iter:21   Norm = 10.059815280329316\n",
      "Iter:22   Norm = 9.652943734511783\n",
      "Iter:23   Norm = 9.25350773099282\n",
      "Iter:24   Norm = 8.862809773368156\n",
      "Iter:25   Norm = 8.481886375492982\n",
      "Iter:26   Norm = 8.111541464653387\n",
      "Iter:27   Norm = 7.7523771140274755\n",
      "Iter:28   Norm = 7.404821488811609\n",
      "Iter:29   Norm = 7.069154009563305\n",
      "Iter:30   Norm = 6.745527819188141\n",
      "Iter:31   Norm = 6.433989694880894\n",
      "Iter:32   Norm = 6.134497580005323\n",
      "Iter:33   Norm = 5.846935928796918\n",
      "Iter:34   Norm = 5.571129063207804\n",
      "Iter:35   Norm = 5.3068527395357386\n",
      "Iter:36   Norm = 5.0538441152756475\n",
      "Iter:37   Norm = 4.811810295859226\n",
      "Iter:38   Norm = 4.580435628061414\n",
      "Iter:39   Norm = 4.35938789292628\n",
      "Iter:40   Norm = 4.148323536854981\n",
      "Iter:41   Norm = 3.9468920655415816\n",
      "Iter:42   Norm = 3.75473971208845\n",
      "Iter:43   Norm = 3.571512478103787\n",
      "Iter:44   Norm = 3.3968586350059375\n",
      "Iter:45   Norm = 3.2304307621839126\n",
      "Iter:46   Norm = 3.071887389099922\n",
      "Iter:47   Norm = 2.9208942998374487\n",
      "Iter:48   Norm = 2.777125550947049\n",
      "Iter:49   Norm = 2.640264246662137\n",
      "Iter:50   Norm = 2.5100031095739093\n",
      "Iter:51   Norm = 2.3860448796004987\n",
      "Iter:52   Norm = 2.2681025694850123\n",
      "Iter:53   Norm = 2.155899601045682\n",
      "Iter:54   Norm = 2.0491698429087717\n",
      "Iter:55   Norm = 1.9476575674272234\n",
      "Iter:56   Norm = 1.8511173418644895\n",
      "Iter:57   Norm = 1.7593138666580268\n",
      "Iter:58   Norm = 1.672021771624403\n",
      "Iter:59   Norm = 1.5890253792862707\n",
      "Iter:60   Norm = 1.5101184430586014\n",
      "Iter:61   Norm = 1.435103866792883\n",
      "Iter:62   Norm = 1.363793411118631\n",
      "Iter:63   Norm = 1.2960073911145966\n",
      "Iter:64   Norm = 1.2315743690705405\n",
      "Iter:65   Norm = 1.1703308454399979\n",
      "Iter:66   Norm = 1.1121209505264504\n",
      "Iter:67   Norm = 1.0567961389685385\n",
      "Iter:68   Norm = 1.0042148886880011\n",
      "Iter:69   Norm = 0.9542424056244497\n",
      "Iter:70   Norm = 0.9067503352924983\n",
      "Iter:71   Norm = 0.8616164819572145\n",
      "Iter:72   Norm = 0.8187245360206581\n",
      "Iter:73   Norm = 0.777963810043276\n",
      "Iter:74   Norm = 0.7392289836834668\n",
      "Iter:75   Norm = 0.7024198577214341\n",
      "Iter:76   Norm = 0.6674411172382658\n",
      "Iter:77   Norm = 0.6342021039411869\n",
      "Iter:78   Norm = 0.6026165975626968\n",
      "Iter:79   Norm = 0.5726026062095592\n",
      "Iter:80   Norm = 0.5440821654963962\n",
      "Iter:81   Norm = 0.5169811462657237\n",
      "Iter:82   Norm = 0.49122907067354443\n",
      "Iter:83   Norm = 0.46675893639789856\n",
      "Iter:84   Norm = 0.4435070487169933\n",
      "Iter:85   Norm = 0.42141286019367263\n",
      "Iter:86   Norm = 0.400418817696813\n",
      "Iter:87   Norm = 0.3804702164882442\n",
      "Iter:88   Norm = 0.3615150611045506\n",
      "Iter:89   Norm = 0.3435039327629058\n",
      "Iter:90   Norm = 0.3263898630258408\n",
      "Iter:91   Norm = 0.3101282134631076\n",
      "Iter:92   Norm = 0.29467656105468776\n",
      "Iter:93   Norm = 0.2799945890862761\n",
      "Iter:94   Norm = 0.2660439832949582\n",
      "Iter:95   Norm = 0.25278833303012815\n",
      "Iter:96   Norm = 0.24019303720337937\n",
      "Iter:97   Norm = 0.22822521480791005\n",
      "Iter:98   Norm = 0.21685361979728984\n",
      "Iter:99   Norm = 0.20604856012012812\n",
      "Iter:100   Norm = 0.19578182071639585\n",
      "Iter:101   Norm = 0.18602659028841215\n",
      "Iter:102   Norm = 0.1767573916671875\n",
      "Iter:103   Norm = 0.1679500156034705\n",
      "Iter:104   Norm = 0.15958145781813754\n",
      "Iter:105   Norm = 0.1516298591567539\n",
      "Iter:106   Norm = 0.1440744486970465\n",
      "Iter:107   Norm = 0.13689548966716145\n",
      "Iter:108   Norm = 0.1300742280379501\n",
      "Iter:109   Norm = 0.12359284365898583\n",
      "Iter:110   Norm = 0.11743440381385287\n",
      "Iter:111   Norm = 0.11158281907722682\n",
      "Iter:112   Norm = 0.10602280136008793\n",
      "Iter:113   Norm = 0.10073982403586114\n",
      "Iter:114   Norm = 0.09572008404578435\n",
      "Iter:115   Norm = 0.09095046588485789\n",
      "Iter:116   Norm = 0.0864185073769838\n",
      "Iter:117   Norm = 0.08211236714997107\n",
      "Iter:118   Norm = 0.07802079372733338\n",
      "Iter:119   Norm = 0.07413309615584324\n",
      "Iter:120   Norm = 0.07043911609432163\n",
      "Iter:121   Norm = 0.06692920128960897\n",
      "Iter:122   Norm = 0.06359418037266723\n",
      "Iter:123   Norm = 0.06042533890809721\n",
      "Iter:124   Norm = 0.05741439663543477\n",
      "Iter:125   Norm = 0.0545534858432239\n",
      "Iter:126   Norm = 0.05183513081940738\n",
      "Iter:127   Norm = 0.04925222832435246\n",
      "Iter:128   Norm = 0.04679802903643069\n",
      "Iter:129   Norm = 0.044466119920942716\n",
      "Iter:130   Norm = 0.042250407477211725\n",
      "Iter:131   Norm = 0.04014510181974677\n",
      "Iter:132   Norm = 0.03814470155214248\n",
      "Iter:133   Norm = 0.03624397939440211\n",
      "Iter:134   Norm = 0.03443796852605711\n",
      "Iter:135   Norm = 0.03272194960919093\n",
      "Iter:136   Norm = 0.031091438458342748\n",
      "Iter:137   Norm = 0.029542174324351838\n",
      "Iter:138   Norm = 0.02807010876144615\n",
      "Iter:139   Norm = 0.026671395049848924\n",
      "Iter:140   Norm = 0.02534237814417421\n",
      "Iter:141   Norm = 0.024079585123427883\n",
      "Iter:142   Norm = 0.022879716116433774\n",
      "Iter:143   Norm = 0.021739635679333895\n",
      "Iter:144   Norm = 0.02065636460273195\n",
      "Iter:145   Norm = 0.019627072127074915\n",
      "Iter:146   Norm = 0.018649068545738362\n",
      "Iter:147   Norm = 0.017719798176789193\n",
      "Iter:148   Norm = 0.01683683268482979\n",
      "Iter:149   Norm = 0.015997864735639244\n",
      "Iter:150   Norm = 0.01520070196686856\n",
      "Iter:151   Norm = 0.014443261259225083\n",
      "Iter:152   Norm = 0.01372356329318788\n",
      "Iter:153   Norm = 0.01303972737681467\n",
      "Iter:154   Norm = 0.01238996653112736\n",
      "Iter:155   Norm = 0.01177258282077334\n",
      "Iter:156   Norm = 0.011185962916940791\n",
      "Iter:157   Norm = 0.010628573881535102\n",
      "Iter:158   Norm = 0.010098959161585905\n",
      "Iter:159   Norm = 0.009595734782818086\n",
      "Iter:160   Norm = 0.009117585733336243\n",
      "Iter:161   Norm = 0.008663262527128218\n",
      "Iter:162   Norm = 0.00823157793924956\n",
      "Iter:163   Norm = 0.007821403903161793\n",
      "Iter:164   Norm = 0.007431668562943248\n",
      "Iter:165   Norm = 0.007061353472601577\n",
      "Iter:166   Norm = 0.0067094909344451005\n",
      "Iter:167   Norm = 0.006375161470483464\n",
      "Iter:168   Norm = 0.006057491419617507\n",
      "Iter:169   Norm = 0.0057556506546531105\n",
      "Iter:170   Norm = 0.005468850413060355\n",
      "Iter:171   Norm = 0.005196341235746825\n",
      "Iter:172   Norm = 0.0049374110086715705\n",
      "Iter:173   Norm = 0.004691383101924792\n",
      "Iter:174   Norm = 0.004457614601628931\n",
      "Iter:175   Norm = 0.00423549462978277\n",
      "Iter:176   Norm = 0.004024442748050179\n",
      "Iter:177   Norm = 0.0038239074409148017\n",
      "Iter:178   Norm = 0.003633364674561328\n",
      "Iter:179   Norm = 0.0034523165273896567\n",
      "Iter:180   Norm = 0.003280289888824077\n",
      "Iter:181   Norm = 0.003116835223200215\n",
      "Iter:182   Norm = 0.0029615253947873586\n",
      "Iter:183   Norm = 0.0028139545518069764\n",
      "Iter:184   Norm = 0.002673737065811069\n",
      "Iter:185   Norm = 0.002540506523863044\n",
      "Iter:186   Norm = 0.002413914771256878\n",
      "Iter:187   Norm = 0.0022936310015267115\n",
      "Iter:188   Norm = 0.00217934089206645\n",
      "Iter:189   Norm = 0.002070745782833111\n",
      "Iter:190   Norm = 0.0019675618956844555\n",
      "Iter:191   Norm = 0.0018695195931025907\n",
      "Iter:192   Norm = 0.0017763626732679354\n",
      "Iter:193   Norm = 0.0016878477009184716\n",
      "Iter:194   Norm = 0.0016037433708348346\n",
      "Iter:195   Norm = 0.0015238299036204764\n",
      "Iter:196   Norm = 0.0014478984713628656\n",
      "Iter:197   Norm = 0.0013757506520023714\n",
      "Iter:198   Norm = 0.0013071979105124451\n",
      "Iter:199   Norm = 0.001242061106642273\n",
      "Iter:200   Norm = 0.001180170026421574\n",
      "Iter:201   Norm = 0.0011213629375867195\n",
      "Iter:202   Norm = 0.00106548616699432\n",
      "Iter:203   Norm = 0.0010123936987897616\n",
      "Iter:204   Norm = 0.000961946792948954\n",
      "Iter:205   Norm = 0.0009140136229792023\n",
      "Iter:206   Norm = 0.0008684689310162018\n",
      "Iter:207   Norm = 0.000825193700814404\n",
      "Iter:208   Norm = 0.0007840748466052515\n",
      "Iter:209   Norm = 0.0007450049175907054\n",
      "Iter:210   Norm = 0.0007078818171714935\n",
      "Iter:211   Norm = 0.0006726085362399303\n",
      "Iter:212   Norm = 0.0006390928994438927\n",
      "Iter:213   Norm = 0.0006072473245845859\n",
      "Iter:214   Norm = 0.0005769885936142892\n",
      "Iter:215   Norm = 0.0005482376350670938\n",
      "Iter:216   Norm = 0.0005209193176860744\n",
      "Iter:217   Norm = 0.0004949622539935965\n",
      "Iter:218   Norm = 0.0004702986134931324\n",
      "Iter:219   Norm = 0.0004468639458287134\n",
      "Iter:220   Norm = 0.00042459701210610814\n",
      "Iter:221   Norm = 0.0004034396248758427\n",
      "Iter:222   Norm = 0.00038333649622088043\n",
      "Iter:223   Norm = 0.0003642350931570935\n",
      "Iter:224   Norm = 0.00034608550027206037\n",
      "Iter:225   Norm = 0.00032884028958557384\n",
      "Iter:226   Norm = 0.0003124543962632851\n",
      "Iter:227   Norm = 0.00029688500116376195\n",
      "Iter:228   Norm = 0.00028209141865459883\n",
      "Iter:229   Norm = 0.0002680349905641573\n",
      "Iter:230   Norm = 0.0002546789849526282\n",
      "Iter:231   Norm = 0.00024198850022569054\n",
      "Iter:232   Norm = 0.00022993037390888185\n",
      "Iter:233   Norm = 0.00021847309604123574\n",
      "Iter:234   Norm = 0.00020758672669099641\n",
      "Iter:235   Norm = 0.00019724281794847865\n",
      "Iter:236   Norm = 0.00018741433927534293\n",
      "Iter:237   Norm = 0.00017807560719459208\n",
      "Iter:238   Norm = 0.00016920221788795464\n",
      "Iter:239   Norm = 0.00016077098371868116\n",
      "Iter:240   Norm = 0.00015275987235209654\n",
      "Iter:241   Norm = 0.00014514794933393412\n",
      "Iter:242   Norm = 0.00013791532336898804\n",
      "Iter:243   Norm = 0.00013104309441994732\n",
      "Iter:244   Norm = 0.00012451330402438656\n",
      "Iter:245   Norm = 0.00011830888870680162\n",
      "Iter:246   Norm = 0.00011241363534546826\n",
      "Iter:247   Norm = 0.00010681213854175862\n",
      "Iter:248   Norm = 0.00010148976060541114\n",
      "Iter:249   Norm = 9.643259320452332e-05\n",
      "Iter:250   Norm = 9.162742109229409e-05\n",
      "Iter:251   Norm = 8.70616875479753e-05\n",
      "Iter:252   Norm = 8.272346146074222e-05\n",
      "Iter:253   Norm = 7.860140627708161e-05\n",
      "Iter:254   Norm = 7.468475039850256e-05\n",
      "Iter:255   Norm = 7.0963258890926e-05\n",
      "Iter:256   Norm = 6.742720680376837e-05\n",
      "Iter:257   Norm = 6.4067353890438e-05\n",
      "Iter:258   Norm = 6.087492014295212e-05\n",
      "Iter:259   Norm = 5.784156328112338e-05\n",
      "Iter:260   Norm = 5.495935660648073e-05\n",
      "Iter:261   Norm = 5.2220768368362004e-05\n",
      "Iter:262   Norm = 4.9618642119478945e-05\n",
      "Iter:263   Norm = 4.7146178145679874e-05\n",
      "Iter:264   Norm = 4.479691539580191e-05\n",
      "Iter:265   Norm = 4.256471481217405e-05\n",
      "Iter:266   Norm = 4.044374335830097e-05\n",
      "Iter:267   Norm = 3.842845849333558e-05\n",
      "Iter:268   Norm = 3.65135938982983e-05\n",
      "Iter:269   Norm = 3.469414573857619e-05\n",
      "Iter:270   Norm = 3.296535951104323e-05\n",
      "Iter:271   Norm = 3.132271754394994e-05\n",
      "Iter:272   Norm = 2.9761927337833437e-05\n",
      "Iter:273   Norm = 2.8278910250457216e-05\n",
      "Iter:274   Norm = 2.68697908851335e-05\n",
      "Iter:275   Norm = 2.5530887090597235e-05\n",
      "Iter:276   Norm = 2.4258699914108744e-05\n",
      "Iter:277   Norm = 2.304990501459641e-05\n",
      "Iter:278   Norm = 2.1901343551848983e-05\n",
      "Iter:279   Norm = 2.081001414924194e-05\n",
      "Iter:280   Norm = 1.9773064941147656e-05\n",
      "Iter:281   Norm = 1.878778626580937e-05\n",
      "Iter:282   Norm = 1.7851603348882715e-05\n",
      "Iter:283   Norm = 1.696206982122841e-05\n",
      "Iter:284   Norm = 1.6116861097587833e-05\n",
      "Iter:285   Norm = 1.53137686383757e-05\n",
      "Iter:286   Norm = 1.4550693709896469e-05\n",
      "Iter:287   Norm = 1.3825642311385432e-05\n",
      "Iter:288   Norm = 1.31367197206651e-05\n",
      "Iter:289   Norm = 1.2482125700600421e-05\n",
      "Iter:290   Norm = 1.1860149674182694e-05\n",
      "Iter:291   Norm = 1.126916626144979e-05\n",
      "Iter:292   Norm = 1.0707631197088599e-05\n",
      "Iter:293   Norm = 1.0174077048776084e-05\n",
      "Iter:294   Norm = 9.66710954583558e-06\n",
      "Price function converged!\n",
      "P(1) = 20.1571\n"
     ]
    }
   ],
   "source": [
    "# Solve the economy, displaying the error term for each iteration\n",
    "economy.solve(disp=True)\n",
    "\n",
    "# After the economy is solved, we can use its Equilibrium price function\n",
    "# to tell us the price if the dividend is 1\n",
    "dvdnd = 1\n",
    "print(\"P({}) = {:.6}\".format(dvdnd, economy.EqPfun(dvdnd)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "moderate-network",
   "metadata": {},
   "source": [
    "## The effect of risk aversion.\n",
    "\n",
    "[The notes](https://llorracc.github.io/LucasAssetPrice/#a-surprise) discuss the surprising implication that an increase in the coefficient of relative risk aversion $\\rho$ leads to higher prices for the risky trees! This is demonstrated below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "qualified-layout",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$P_t$')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create two economies with different risk aversion\n",
    "Disc = 0.95\n",
    "LowCRRAEcon = LucasEconomy(CRRA=2, DiscFac=Disc, DivProcess=DivProc)\n",
    "HighCRRAEcon = LucasEconomy(CRRA=4, DiscFac=Disc, DivProcess=DivProc)\n",
    "\n",
    "# Solve both\n",
    "LowCRRAEcon.solve()\n",
    "HighCRRAEcon.solve()\n",
    "\n",
    "# Plot the pricing functions for both\n",
    "dGrid = np.linspace(0.5, 2.5, 30)\n",
    "plt.figure()\n",
    "plt.plot(dGrid, LowCRRAEcon.EqPfun(dGrid), label=\"Low CRRA\")\n",
    "plt.plot(dGrid, HighCRRAEcon.EqPfun(dGrid), label=\"High CRRA\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"$d_t$\")\n",
    "plt.ylabel(\"$P_t$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "postal-agenda",
   "metadata": {},
   "source": [
    "# Testing our analytical solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aboriginal-vault",
   "metadata": {},
   "source": [
    "## Case 1: Log Utility\n",
    "\n",
    "The lecture notes show that with logarithmic utility (a CRRA of $1$), the pricing kernel has a closed form expression: $$P^*(d_t) = \\frac{d_t}{\\vartheta}$$.\n",
    "\n",
    "We now compare our numerical solution with this analytical expression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "silent-ownership",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, '$P^*(d_t)$')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create an economy with log utility and the same dividend process from before\n",
    "logUtilEcon = LucasEconomy(CRRA=1, DiscFac=Disc, DivProcess=DivProc)\n",
    "# Solve it\n",
    "logUtilEcon.solve()\n",
    "\n",
    "# Generate a function with our analytical solution\n",
    "theta = 1 / Disc - 1\n",
    "\n",
    "\n",
    "def aSol(d):\n",
    "    return d / theta\n",
    "\n",
    "\n",
    "# Get a grid for d over which to compare them\n",
    "dGrid = np.exp(DivProc.getLogdGrid())\n",
    "\n",
    "# Plot both\n",
    "plt.figure()\n",
    "plt.plot(dGrid, aSol(dGrid), \"*\", label=\"Analytical solution\")\n",
    "plt.plot(dGrid, logUtilEcon.EqPfun(dGrid), label=\"Numerical solution\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"$d_t$\")\n",
    "plt.ylabel(\"$P^*(d_t)$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "presidential-electron",
   "metadata": {},
   "source": [
    " ## Case 2: I.I.D dividends\n",
    "\n",
    " The [notes also show](https://llorracc.github.io/LucasAssetPrice/#when-dividends-are-IID) that, if $\\ln d_{t+n}\\sim \\mathcal{N}(-\\sigma^2/2, \\sigma^2)$ for all $n$, the pricing kernel is exactly\n",
    " \\begin{equation*}\n",
    " P^*(d_t) = d_t^\\rho\\times e^{\\rho(\\rho-1)\\sigma^2/2}\\overbrace{\\frac{\\beta}{1-\\beta}}^{=\\vartheta}\n",
    " \\end{equation*}\n",
    "\n",
    " We now our numerical solution for this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "measured-password",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create an i.i.d. dividend process\n",
    "σ = 0.1\n",
    "iidDivs = DivProcess(α=0.0, σ=σ)\n",
    "\n",
    "# And an economy that embeds it\n",
    "CRRA = 2\n",
    "Disc = 0.9\n",
    "\n",
    "iidEcon = LucasEconomy(CRRA=CRRA, DiscFac=Disc, DivProcess=iidDivs)\n",
    "iidEcon.solve()\n",
    "\n",
    "# Generate a function with our analytical solution\n",
    "dTil = np.exp((σ**2) / 2 * CRRA * (CRRA - 1))\n",
    "\n",
    "\n",
    "def aSolIID(d):\n",
    "    return d**CRRA * dTil * Disc / (1 - Disc)\n",
    "\n",
    "\n",
    "# Get a grid for d over which to compare them\n",
    "dGrid = np.exp(iidDivs.getLogdGrid())\n",
    "\n",
    "# Plot both\n",
    "plt.figure()\n",
    "plt.plot(dGrid, aSolIID(dGrid), \"*\", label=\"Analytical solution\")\n",
    "plt.plot(dGrid, iidEcon.EqPfun(dGrid), label=\"Numerical solution\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"$d_t$\")\n",
    "plt.ylabel(\"$P^*(d_t)$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db9d2d68",
   "metadata": {},
   "source": [
    "## Case 3: Dividends that are a geometric random walk with drift\n",
    "\n",
    "The notes also show that if the dividend process is\n",
    "\\begin{equation*}\n",
    "\\ln d_{t+1} = \\gamma + \\ln d_t + \\varepsilon_{t+1}, \\qquad \\varepsilon \\sim \\mathcal{N}(-\\frac{\\sigma^2}{2}, \\sigma).\n",
    "\\end{equation*}\n",
    "so that $E_t[d_{t+1}/d_t] = e^\\gamma$, then we have\n",
    "\\begin{equation*}\n",
    " P^*(d_t) = d_t^\\rho\\times e^{(\\rho-1)\\left(\\rho\\sigma^2/2 - \\gamma\\right)}\\overbrace{\\frac{\\beta}{1-\\beta}}^{\\vartheta}\n",
    "\\end{equation*}\n",
    "which, when $\\rho=1$, reduces (as it should) to\n",
    "\\begin{equation*}\n",
    " \\frac{P^*(d_t)}{d_t} = \\vartheta\n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3cb3d0e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CRRA = 2\n",
    "Disc = 0.9\n",
    "σ = 0.1\n",
    "γ = 0.3\n",
    "\n",
    "# Create a random walk dividend process\n",
    "# (it turns out that the whole model can be normalized by d_t, and\n",
    "# in normalized, terms the dividend proces becomes iid again)\n",
    "rw_divs = DivProcess(γ=γ, α=0, σ=σ)\n",
    "\n",
    "# And an economy that embeds it\n",
    "rw_econ = LucasEconomy(CRRA=CRRA, DiscFac=Disc, DivProcess=rw_divs)\n",
    "rw_econ.solve()\n",
    "\n",
    "# Generate a function with our analytical solution\n",
    "a_sol_factor = np.exp((CRRA - 1) * (CRRA * σ**2 / 2 - γ))\n",
    "\n",
    "\n",
    "def a_sol_rw(d):\n",
    "    return d**CRRA * a_sol_factor * Disc / (1 - Disc)\n",
    "\n",
    "\n",
    "# Get a grid for d over which to compare them\n",
    "dGrid = np.exp(rw_divs.getLogdGrid())\n",
    "\n",
    "# Plot both\n",
    "plt.figure()\n",
    "plt.plot(dGrid, a_sol_rw(dGrid), \"*\", label=\"Analytical solution\")\n",
    "plt.plot(dGrid, rw_econ.EqPfun(dGrid), label=\"Numerical solution\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"$d_t$\")\n",
    "plt.ylabel(\"$P^*(d_t)$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pacific-cliff",
   "metadata": {},
   "source": [
    "# Testing our approximation of the dividend process\n",
    "\n",
    "Hidden in the solution method implemented above is the fact that, in order to make expectations easy to compute, we discretize the random shock $\\varepsilon_t$, which is to say, we create a discrete variable $\\tilde{\\varepsilon}$ that approximates the behavior of $\\varepsilon_t$. This is done using a [Gauss-Hermite quadrature](https://en.wikipedia.org/wiki/Gauss%E2%80%93Hermite_quadrature).\n",
    "\n",
    "A parameter for the numerical solution is the number of different values that we allow our discrete approximation $\\tilde{\\varepsilon}$ to take, $n^{\\#}$. We would expect a higher $n^#$ to improve our solution, as the discrete approximation of $\\varepsilon_t$ improves. We test this below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "interstate-globe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Increase CRRA to make the effect of uncertainty more evident.\n",
    "CRRA = 10\n",
    "Disc = 0.9\n",
    "σ = 0.1\n",
    "ns = [1, 2, 10]\n",
    "\n",
    "dTil = np.exp((σ**2) / 2 * CRRA * (CRRA - 1.0))\n",
    "\n",
    "\n",
    "def aSolIID(d):\n",
    "    return d**CRRA * dTil * Disc / (1 - Disc)\n",
    "\n",
    "\n",
    "dGrid = np.exp(iidDivs.getLogdGrid())\n",
    "\n",
    "plt.figure()\n",
    "for n in ns:\n",
    "    iidDivs = DivProcess(α=0.0, σ=σ, nApprox=n)\n",
    "    iidEcon = LucasEconomy(CRRA=CRRA, DiscFac=Disc, DivProcess=iidDivs)\n",
    "    iidEcon.solve()\n",
    "    plt.plot(dGrid, iidEcon.EqPfun(dGrid), label=\"Num.Sol. $n^\\#$ = {}\".format(n))\n",
    "\n",
    "# Plot both\n",
    "plt.plot(dGrid, aSolIID(dGrid), \"*\", label=\"Analytical solution\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"$d_t$\")\n",
    "plt.ylabel(\"$P^*(d_t)$\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "jupytext": {
   "cell_metadata_json": true,
   "encoding": "# -*- coding: utf-8 -*-",
   "formats": "ipynb,py:percent",
   "notebook_metadata_filter": "all,-widgets,-varInspector"
  },
  "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": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}