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Plot the result of comparison of runtime
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‎lectures/markov_asset_numpy.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "143dede4",
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"metadata": {},
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"outputs": [],
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"source": [
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"import matplotlib.pyplot as plt\n",
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"import numpy as np\n",
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"import quantecon as qe\n",
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"from numpy.linalg import eigvals, solve"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "0c89899c",
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"metadata": {},
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"outputs": [],
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"source": [
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"class AssetPriceModel:\n",
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" \"\"\"\n",
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" A class that stores the primitives of the asset pricing model.\n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" β : scalar, float\n",
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" Discount factor\n",
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" mc : MarkovChain\n",
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" Contains the transition matrix and set of state values for the state\n",
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" process\n",
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" γ : scalar(float)\n",
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" Coefficient of risk aversion\n",
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" g : callable\n",
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" The function mapping states to growth rates\n",
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"\n",
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" \"\"\"\n",
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" def __init__(self, β=0.96, mc=None, γ=2.0, g=np.exp):\n",
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" self.β, self.γ = β, γ\n",
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" self.g = g\n",
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"\n",
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" # A default process for the Markov chain\n",
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" if mc is None:\n",
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" self.ρ = 0.9\n",
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" self.σ = 0.02\n",
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" self.mc = qe.tauchen(n, self.ρ, self.σ)\n",
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" else:\n",
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" self.mc = mc\n",
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"\n",
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" self.n = self.mc.P.shape[0]\n",
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"\n",
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" def test_stability(self, Q):\n",
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" \"\"\"\n",
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" Stability test for a given matrix Q.\n",
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" \"\"\"\n",
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" sr = np.max(np.abs(eigvals(Q)))\n",
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" if not sr < 1 / self.β:\n",
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" msg = f\"Spectral radius condition failed with radius = {sr}\"\n",
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" raise ValueError(msg)\n",
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"\n",
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"\n",
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"def tree_price(ap):\n",
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" \"\"\"\n",
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" Computes the price-dividend ratio of the Lucas tree.\n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" ap: AssetPriceModel\n",
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" An instance of AssetPriceModel containing primitives\n",
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"\n",
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" Returns\n",
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" -------\n",
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" v : array_like(float)\n",
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" Lucas tree price-dividend ratio\n",
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"\n",
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" \"\"\"\n",
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" # Simplify names, set up matrices\n",
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" β, γ, P, y = ap.β, ap.γ, ap.mc.P, ap.mc.state_values\n",
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" J = P * ap.g(y)**(1 - γ)\n",
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"\n",
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" # Make sure that a unique solution exists\n",
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" ap.test_stability(J)\n",
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"\n",
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" # Compute v\n",
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" I = np.identity(ap.n)\n",
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" Ones = np.ones(ap.n)\n",
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" v = solve(I - β * J, β * J @ Ones)\n",
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"\n",
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" return v"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "00ec6099",
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"metadata": {},
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"outputs": [],
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"source": [
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"def consol_price(ap, ζ):\n",
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" \"\"\"\n",
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" Computes price of a consol bond with payoff ζ\n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" ap: AssetPriceModel\n",
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" An instance of AssetPriceModel containing primitives\n",
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"\n",
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" ζ : scalar(float)\n",
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" Coupon of the console\n",
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"\n",
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" Returns\n",
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" -------\n",
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" p : array_like(float)\n",
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" Console bond prices\n",
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"\n",
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" \"\"\"\n",
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" # Simplify names, set up matrices\n",
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" β, γ, P, y = ap.β, ap.γ, ap.mc.P, ap.mc.state_values\n",
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" M = P * ap.g(y)**(- γ)\n",
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"\n",
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" # Make sure that a unique solution exists\n",
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" ap.test_stability(M)\n",
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"\n",
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" # Compute price\n",
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" I = np.identity(ap.n)\n",
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" Ones = np.ones(ap.n)\n",
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" p = solve(I - β * M, β * ζ * M @ Ones)\n",
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"\n",
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" return p"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "57f42de4",
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"metadata": {},
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"outputs": [],
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"source": [
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"def call_option(ap, ζ, p_s, ϵ=1e-7):\n",
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" \"\"\"\n",
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" Computes price of a call option on a consol bond.\n",
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"\n",
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" Parameters\n",
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" ----------\n",
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" ap: AssetPriceModel\n",
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" An instance of AssetPriceModel containing primitives\n",
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"\n",
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" ζ : scalar(float)\n",
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" Coupon of the console\n",
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"\n",
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" p_s : scalar(float)\n",
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" Strike price\n",
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"\n",
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" ϵ : scalar(float), optional(default=1e-8)\n",
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" Tolerance for infinite horizon problem\n",
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"\n",
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" Returns\n",
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" -------\n",
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" w : array_like(float)\n",
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" Infinite horizon call option prices\n",
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"\n",
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" \"\"\"\n",
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" # Simplify names, set up matrices\n",
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" β, γ, P, y = ap.β, ap.γ, ap.mc.P, ap.mc.state_values\n",
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" M = P * ap.g(y)**(- γ)\n",
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"\n",
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" # Make sure that a unique consol price exists\n",
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" ap.test_stability(M)\n",
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"\n",
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" # Compute option price\n",
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" p = consol_price(ap, ζ)\n",
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" w = np.zeros(ap.n)\n",
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" error = ϵ + 1\n",
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" while error > ϵ:\n",
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" # Maximize across columns\n",
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" w_new = np.maximum(β * M @ w, p - p_s)\n",
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" # Find maximal difference of each component and update\n",
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" error = np.amax(np.abs(w - w_new))\n",
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" w = w_new\n",
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"\n",
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" return w"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "6bc6db6f",
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"metadata": {},
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"outputs": [],
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"source": [
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"n = 25\n",
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"ap = AssetPriceModel(β=0.9)\n",
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"ζ = 1.0\n",
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"strike_price = 40\n",
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"\n",
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"x = ap.mc.state_values\n",
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"\n",
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"def timer_function():\n",
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" p = consol_price(ap, ζ)\n",
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" w = call_option(ap, ζ, strike_price)\n",
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"\n",
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"result = qe.timeit(\n",
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" timer_function, runs=1000, verbose=False, \n",
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" results=True, unit=\"milliseconds\"\n",
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" )"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "d4b6a2e3",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Results saved to timer_results_numpy.json\n"
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]
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}
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],
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"source": [
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"import json\n",
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"\n",
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"# result is already a dictionary, no need to call _asdict()\n",
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"result_dict = result\n",
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"\n",
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"# Define the filename\n",
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"filename = 'timer_results_numpy.json'\n",
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"\n",
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"# Save the dictionary to a JSON file\n",
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"with open(filename, 'w') as f:\n",
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" json.dump(result_dict, f, indent=4)\n",
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"\n",
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"print(f\"Results saved to {filename}\")"
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]
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}
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],
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"metadata": {
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"jupytext": {
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"default_lexer": "ipython"
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},
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"kernelspec": {
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"display_name": "quantecon",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.13.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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