{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", " \n", " \"QuantEcon\"\n", " \n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Asset Pricing I: Finite State Models\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Contents\n", "\n", "- [Asset Pricing I: Finite State Models](#Asset-Pricing-I:-Finite-State-Models) \n", " - [Overview](#Overview) \n", " - [Pricing Models](#Pricing-Models) \n", " - [Prices in the Risk Neutral Case](#Prices-in-the-Risk-Neutral-Case) \n", " - [Asset Prices under Risk Aversion](#Asset-Prices-under-Risk-Aversion) \n", " - [Exercises](#Exercises) \n", " - [Solutions](#Solutions) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> “A little knowledge of geometric series goes a long way” – Robert E. Lucas, Jr.\n", "\n", "\n", "> “Asset pricing is all about covariances” – Lars Peter Hansen" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overview\n", "\n", "\n", "\n", "An asset is a claim on one or more future payoffs.\n", "\n", "The spot price of an asset depends primarily on\n", "\n", "- the anticipated dynamics for the stream of income accruing to the owners \n", "- attitudes to risk \n", "- rates of time preference \n", "\n", "\n", "In this lecture we consider some standard pricing models and dividend stream specifications.\n", "\n", "We study how prices and dividend-price ratios respond in these different scenarios.\n", "\n", "We also look at creating and pricing *derivative* assets by repackaging income streams.\n", "\n", "Key tools for the lecture are\n", "\n", "- formulas for predicting future values of functions of a Markov state \n", "- a formula for predicting the discounted sum of future values of a Markov state " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Pricing Models\n", "\n", "\n", "\n", "In what follows let $ \\{d_t\\}_{t \\geq 0} $ be a stream of dividends.\n", "\n", "- A time-$ t $ **cum-dividend** asset is a claim to the stream $ d_t, d_{t+1}, \\ldots $. \n", "- A time-$ t $ **ex-dividend** asset is a claim to the stream $ d_{t+1}, d_{t+2}, \\ldots $. \n", "\n", "\n", "Let’s look at some equations that we expect to hold for prices of assets under ex-dividend contracts\n", "(we will consider cum-dividend pricing in the exercises)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Risk Neutral Pricing\n", "\n", "\n", "\n", "Our first scenario is risk-neutral pricing.\n", "\n", "Let $ \\beta = 1/(1+\\rho) $ be an intertemporal discount factor, where\n", "$ \\rho $ is the rate at which agents discount the future.\n", "\n", "The basic risk-neutral asset pricing equation for pricing one unit of an ex-dividend asset is.\n", "\n", "\n", "\n", "\n", "\n", "$$\n", "p_t = \\beta {\\mathbb E}_t [d_{t+1} + p_{t+1}] \\tag{1}\n", "$$\n", "\n", "This is a simple “cost equals expected benefit” relationship.\n", "\n", "Here $ {\\mathbb E}_t [y] $ denotes the best forecast of $ y $, conditioned on information available at time $ t $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pricing with Random Discount Factor\n", "\n", "\n", "\n", "What happens if for some reason traders discount payouts differently depending on the state of the world?\n", "\n", "Michael Harrison and David Kreps [[HK79]](../zreferences.html#harrisonkreps1979) and Lars Peter Hansen\n", "and Scott Richard [[HR87]](../zreferences.html#hansenrichard1987) showed that in quite general\n", "settings the price of an ex-dividend asset obeys\n", "\n", "\n", "\n", "$$\n", "p_t = {\\mathbb E}_t \\left[ m_{t+1} ( d_{t+1} + p_{t+1} ) \\right] \\tag{2}\n", "$$\n", "\n", "for some **stochastic discount factor** $ m_{t+1} $.\n", "\n", "The fixed discount factor $ \\beta $ in [(1)](#equation-rnapex) has been replaced by the random variable $ m_{t+1} $.\n", "\n", "The way anticipated future payoffs are evaluated can now depend on various random outcomes.\n", "\n", "One example of this idea is that assets that tend to have good payoffs in bad states of the world might be regarded as more valuable.\n", "\n", "This is because they pay well when the funds are more urgently needed.\n", "\n", "We give examples of how the stochastic discount factor has been modeled below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Asset Pricing and Covariances\n", "\n", "Recall that, from the definition of a conditional covariance $ {\\rm cov}_t (x_{t+1}, y_{t+1}) $, we have\n", "\n", "\n", "\n", "$$\n", "{\\mathbb E}_t (x_{t+1} y_{t+1}) = {\\rm cov}_t (x_{t+1}, y_{t+1}) + {\\mathbb E}_t x_{t+1} {\\mathbb E}_t y_{t+1} \\tag{3}\n", "$$\n", "\n", "If we apply this definition to the asset pricing equation [(2)](#equation-lteeqs0) we obtain\n", "\n", "\n", "\n", "$$\n", "p_t = {\\mathbb E}_t m_{t+1} {\\mathbb E}_t (d_{t+1} + p_{t+1}) + {\\rm cov}_t (m_{t+1}, d_{t+1}+ p_{t+1}) \\tag{4}\n", "$$\n", "\n", "It is useful to regard equation [(4)](#equation-lteeqs102) as a generalization of equation [(1)](#equation-rnapex).\n", "\n", "- In equation [(1)](#equation-rnapex), the stochastic discount factor $ m_{t+1} = \\beta $, a constant. \n", "- In equation [(1)](#equation-rnapex), the covariance term $ {\\rm cov}_t (m_{t+1}, d_{t+1}+ p_{t+1}) $ is zero because $ m_{t+1} = \\beta $. \n", "\n", "\n", "Equation [(4)](#equation-lteeqs102) asserts that the covariance of the stochastic discount factor with the one period payout $ d_{t+1} + p_{t+1} $ is an important determinant of the price $ p_t $.\n", "\n", "We give examples of some models of stochastic discount factors that have been proposed later in this lecture and also in a [later lecture](lucas_model.html)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Price-Dividend Ratio\n", "\n", "Aside from prices, another quantity of interest is the **price-dividend ratio** $ v_t := p_t / d_t $.\n", "\n", "Let’s write down an expression that this ratio should satisfy.\n", "\n", "We can divide both sides of [(2)](#equation-lteeqs0) by $ d_t $ to get\n", "\n", "\n", "\n", "$$\n", "v_t = {\\mathbb E}_t \\left[ m_{t+1} \\frac{d_{t+1}}{d_t} (1 + v_{t+1}) \\right] \\tag{5}\n", "$$\n", "\n", "Below we’ll discuss the implication of this equation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prices in the Risk Neutral Case\n", "\n", "What can we say about price dynamics on the basis of the models described above?\n", "\n", "The answer to this question depends on\n", "\n", "1. the process we specify for dividends \n", "1. the stochastic discount factor and how it correlates with dividends \n", "\n", "\n", "For now let’s focus on the risk neutral case, where the stochastic discount factor is constant, and study how prices depend on the dividend process." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 1: Constant dividends\n", "\n", "The simplest case is risk neutral pricing in the face of a constant, non-random dividend stream $ d_t = d > 0 $.\n", "\n", "Removing the expectation from [(1)](#equation-rnapex) and iterating forward gives\n", "\n", "$$\n", "\\begin{aligned}\n", " p_t & = \\beta (d + p_{t+1})\n", " \\\\\n", " & = \\beta (d + \\beta(d + p_{t+2}))\n", " \\\\\n", " & \\quad \\vdots\n", " \\\\\n", " & = \\beta (d + \\beta d + \\beta^2 d + \\cdots + \\beta^{k-2} d + \\beta^{k-1} p_{t+k})\n", "\\end{aligned}\n", "$$\n", "\n", "Unless prices explode in the future, this sequence converges to\n", "\n", "\n", "\n", "$$\n", "\\bar p := \\frac{\\beta d}{1-\\beta} \\tag{6}\n", "$$\n", "\n", "This price is the equilibrium price in the constant dividend case.\n", "\n", "Indeed, simple algebra shows that setting $ p_t = \\bar p $ for all $ t $\n", "satisfies the equilibrium condition $ p_t = \\beta (d + p_{t+1}) $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 2: Dividends with deterministic growth paths\n", "\n", "Consider a growing, non-random dividend process $ d_{t+1} = g d_t $\n", "where $ 0 < g \\beta < 1 $.\n", "\n", "While prices are not usually constant when dividends grow over time, the price\n", "dividend-ratio might be.\n", "\n", "If we guess this, substituting $ v_t = v $ into [(5)](#equation-pdex) as well as our\n", "other assumptions, we get $ v = \\beta g (1 + v) $.\n", "\n", "Since $ \\beta g < 1 $, we have a unique positive solution:\n", "\n", "$$\n", "v = \\frac{\\beta g}{1 - \\beta g }\n", "$$\n", "\n", "The price is then\n", "\n", "$$\n", "p_t = \\frac{\\beta g}{1 - \\beta g } d_t\n", "$$\n", "\n", "If, in this example, we take $ g = 1+\\kappa $ and let\n", "$ \\rho := 1/\\beta - 1 $, then the price becomes\n", "\n", "$$\n", "p_t = \\frac{1 + \\kappa}{ \\rho - \\kappa} d_t\n", "$$\n", "\n", "This is called the *Gordon formula*.\n", "\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Example 3: Markov growth, risk neutral pricing\n", "\n", "Next we consider a dividend process\n", "\n", "\n", "\n", "$$\n", "d_{t+1} = g_{t+1} d_t \\tag{7}\n", "$$\n", "\n", "The stochastic growth factor $ \\{g_t\\} $ is given by\n", "\n", "$$\n", "g_t = g(X_t), \\quad t = 1, 2, \\ldots\n", "$$\n", "\n", "where\n", "\n", "1. $ \\{X_t\\} $ is a finite Markov chain with state space $ S $ and\n", " transition probabilities \n", "\n", "\n", "$$\n", "P(x, y) := \\mathbb P \\{ X_{t+1} = y \\,|\\, X_t = x \\}\n", "\\qquad (x, y \\in S)\n", "$$\n", "\n", "1. $ g $ is a given function on $ S $ taking positive values \n", "\n", "\n", "You can think of\n", "\n", "- $ S $ as $ n $ possible “states of the world” and $ X_t $ as the\n", " current state \n", "- $ g $ as a function that maps a given state $ X_t $ into a growth\n", " factor $ g_t = g(X_t) $ for the endowment \n", "- $ \\ln g_t = \\ln (d_{t+1} / d_t) $ is the growth rate of dividends \n", "\n", "\n", "(For a refresher on notation and theory for finite Markov chains see [this lecture](../tools_and_techniques/finite_markov.html))\n", "\n", "The next figure shows a simulation, where\n", "\n", "- $ \\{X_t\\} $ evolves as a discretized AR1 process produced using [Tauchen’s method](../tools_and_techniques/finite_markov.html#mc-ex3) \n", "- $ g_t = \\exp(X_t) $, so that $ \\ln g_t = X_t $ is the growth rate " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Setup" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "hide-output": true }, "outputs": [], "source": [ "using InstantiateFromURL\n", "# optionally add arguments to force installation: instantiate = true, precompile = true\n", "github_project(\"QuantEcon/quantecon-notebooks-julia\", version = \"0.8.0\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "hide-output": false }, "outputs": [], "source": [ "using LinearAlgebra, Statistics\n", "using Parameters, Plots, QuantEcon\n", "gr(fmt = :png);" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 25\n", "mc = tauchen(n, 0.96, 0.25)\n", "sim_length = 80\n", "\n", "x_series = simulate(mc, sim_length; init = round(Int, n / 2))\n", "g_series = exp.(x_series)\n", "d_series = cumprod(g_series) # assumes d_0 = 1\n", "\n", "series = [x_series g_series d_series log.(d_series)]\n", "labels = [\"X_t\" \"g_t\" \"d_t\" \"ln(d_t)\"]\n", "plot(series, layout = 4, labels = labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Pricing\n", "\n", "To obtain asset prices in this setting, let’s adapt our analysis from the case of deterministic growth.\n", "\n", "In that case we found that $ v $ is constant.\n", "\n", "This encourages us to guess that, in the current case, $ v_t $ is constant given the state $ X_t $.\n", "\n", "In other words, we are looking for a fixed function $ v $ such that the price-dividend ratio satisfies $ v_t = v(X_t) $.\n", "\n", "We can substitute this guess into [(5)](#equation-pdex) to get\n", "\n", "$$\n", "v(X_t) = \\beta {\\mathbb E}_t [ g(X_{t+1}) (1 + v(X_{t+1})) ]\n", "$$\n", "\n", "If we condition on $ X_t = x $, this becomes\n", "\n", "$$\n", "v(x) = \\beta \\sum_{y \\in S} g(y) (1 + v(y)) P(x, y)\n", "$$\n", "\n", "or\n", "\n", "\n", "\n", "$$\n", "v(x) = \\beta \\sum_{y \\in S} K(x, y) (1 + v(y))\n", "\\quad \\text{where} \\quad\n", "K(x, y) := g(y) P(x, y) \\tag{8}\n", "$$\n", "\n", "Suppose that there are $ n $ possible states $ x_1, \\ldots, x_n $.\n", "\n", "We can then think of [(8)](#equation-pstack) as $ n $ stacked equations, one for each state, and write it in matrix form as\n", "\n", "\n", "\n", "$$\n", "v = \\beta K (\\mathbb 1 + v) \\tag{9}\n", "$$\n", "\n", "Here\n", "\n", "- $ v $ is understood to be the column vector $ (v(x_1), \\ldots, v(x_n))' $ \n", "- $ K $ is the matrix $ (K(x_i, x_j))_{1 \\leq i, j \\leq n} $ \n", "- $ {\\mathbb 1} $ is a column vector of ones \n", "\n", "\n", "When does [(9)](#equation-vcumrn) have a unique solution?\n", "\n", "From the [Neumann series lemma](../tools_and_techniques/linear_algebra.html#la-neumann) and Gelfand’s formula, this will be the case if $ \\beta K $ has spectral radius strictly less than one.\n", "\n", "In other words, we require that the eigenvalues of $ K $ be strictly less than $ \\beta^{-1} $ in modulus.\n", "\n", "The solution is then\n", "\n", "\n", "\n", "$$\n", "v = (I - \\beta K)^{-1} \\beta K{\\mathbb 1} \\tag{10}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code\n", "\n", "Let’s calculate and plot the price-dividend ratio at a set of parameters.\n", "\n", "As before, we’ll generate $ \\{X_t\\} $ as a [discretized AR1 process](../tools_and_techniques/finite_markov.html#mc-ex3) and set $ g_t = \\exp(X_t) $.\n", "\n", "Here’s the code, including a test of the spectral radius condition" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "hide-output": false }, "outputs": [ { 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" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 25 # size of state space\n", "β = 0.9\n", "mc = tauchen(n, 0.96, 0.02)\n", "\n", "K = mc.p .* exp.(mc.state_values)'\n", "\n", "v = (I - β * K) \\ (β * K * ones(n, 1))\n", "\n", "plot(mc.state_values,\n", " v,\n", " lw = 2,\n", " ylabel = \"price-dividend ratio\",\n", " xlabel = \"state\",\n", " alpha = 0.7,\n", " label = \"v\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Why does the price-dividend ratio increase with the state?\n", "\n", "The reason is that this Markov process is positively correlated, so high\n", "current states suggest high future states.\n", "\n", "Moreover, dividend growth is increasing in the state.\n", "\n", "Anticipation of high future dividend growth leads to a high price-dividend ratio." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Asset Prices under Risk Aversion\n", "\n", "Now let’s turn to the case where agents are risk averse.\n", "\n", "We’ll price several distinct assets, including\n", "\n", "- The price of an endowment stream. \n", "- A consol (a variety of bond issued by the UK government in the 19th century). \n", "- Call options on a consol. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pricing a Lucas tree\n", "\n", "\n", "\n", "Let’s start with a version of the celebrated asset pricing model of Robert E. Lucas, Jr. [[Luc78]](../zreferences.html#lucas1978).\n", "\n", "As in [[Luc78]](../zreferences.html#lucas1978), suppose that the stochastic discount factor takes the form\n", "\n", "\n", "\n", "$$\n", "m_{t+1} = \\beta \\frac{u'(c_{t+1})}{u'(c_t)} \\tag{11}\n", "$$\n", "\n", "where $ u $ is a concave utility function and $ c_t $ is time $ t $ consumption of a representative consumer.\n", "\n", "(A derivation of this expression is given in a [later lecture](lucas_model.html))\n", "\n", "Assume the existence of an endowment that follows [(7)](#equation-mass-fmce).\n", "\n", "The asset being priced is a claim on the endowment process.\n", "\n", "Following [[Luc78]](../zreferences.html#lucas1978), suppose further that in equilibrium, consumption\n", "is equal to the endowment, so that $ d_t = c_t $ for all $ t $.\n", "\n", "For utility, we’ll assume the **constant relative risk aversion** (CRRA)\n", "specification\n", "\n", "\n", "\n", "$$\n", "u(c) = \\frac{c^{1-\\gamma}}{1 - \\gamma} \\ {\\rm with} \\ \\gamma > 0 \\tag{12}\n", "$$\n", "\n", "When $ \\gamma =1 $ we let $ u(c) = \\ln c $.\n", "\n", "Inserting the CRRA specification into [(11)](#equation-lucsdf) and using $ c_t = d_t $ gives\n", "\n", "\n", "\n", "$$\n", "m_{t+1}\n", "= \\beta \\left(\\frac{c_{t+1}}{c_t}\\right)^{-\\gamma}\n", "= \\beta g_{t+1}^{-\\gamma} \\tag{13}\n", "$$\n", "\n", "Substituting this into [(5)](#equation-pdex) gives the price-dividend ratio\n", "formula\n", "\n", "$$\n", "v(X_t)\n", "= \\beta {\\mathbb E}_t\n", "\\left[\n", " g(X_{t+1})^{1-\\gamma} (1 + v(X_{t+1}) )\n", "\\right]\n", "$$\n", "\n", "Conditioning on $ X_t = x $, we can write this as\n", "\n", "$$\n", "v(x)\n", "= \\beta \\sum_{y \\in S} g(y)^{1-\\gamma} (1 + v(y) ) P(x, y)\n", "$$\n", "\n", "If we let\n", "\n", "$$\n", "J(x, y) := g(y)^{1-\\gamma} P(x, y)\n", "$$\n", "\n", "then we can rewrite in vector form as\n", "\n", "$$\n", "v = \\beta J ({\\mathbb 1} + v )\n", "$$\n", "\n", "Assuming that the spectral radius of $ J $ is strictly less than $ \\beta^{-1} $, this equation has the unique solution\n", "\n", "\n", "\n", "$$\n", "v = (I - \\beta J)^{-1} \\beta J {\\mathbb 1} \\tag{14}\n", "$$\n", "\n", "We will define a function tree_price to solve for \\$v\\$ given parameters stored in\n", "the AssetPriceModel objects" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "tree_price (generic function with 1 method)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# A default Markov chain for the state process\n", "ρ = 0.9\n", "σ = 0.02\n", "n = 25\n", "default_mc = tauchen(n, ρ, σ)\n", "\n", "AssetPriceModel = @with_kw (β = 0.96,\n", " γ = 2.0,\n", " mc = default_mc,\n", " n = size(mc.p)[1],\n", " g = exp)\n", "\n", "# test stability of matrix Q\n", "function test_stability(ap, Q)\n", " sr = maximum(abs, eigvals(Q))\n", " if sr ≥ 1 / ap.β\n", " msg = \"Spectral radius condition failed with radius = $sr\"\n", " throw(ArgumentError(msg))\n", " end\n", "end\n", "\n", "# price/dividend ratio of the Lucas tree\n", "function tree_price(ap; γ = ap.γ)\n", " # Simplify names, set up matrices\n", " @unpack β, mc = ap\n", " P, y = mc.p, mc.state_values\n", " y = reshape(y, 1, ap.n)\n", " J = P .* ap.g.(y).^(1 - γ)\n", "\n", " # Make sure that a unique solution exists\n", " test_stability(ap, J)\n", "\n", " # Compute v\n", " v = (I - β * J) \\ sum(β * J, dims = 2)\n", "\n", " return v\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here’s a plot of $ v $ as a function of the state for several values of $ \\gamma $,\n", "with a positively correlated Markov process and $ g(x) = \\exp(x) $" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "γs = [1.2, 1.4, 1.6, 1.8, 2.0]\n", "ap = AssetPriceModel()\n", "states = ap.mc.state_values\n", "\n", "lines = []\n", "labels = []\n", "\n", "for γ in γs\n", " v = tree_price(ap, γ = γ)\n", " label = \"gamma = $γ\"\n", " push!(labels, label)\n", " push!(lines, v)\n", "end\n", "\n", "plot(lines,\n", " labels = reshape(labels, 1, length(labels)),\n", " title = \"Price-dividend ratio as a function of the state\",\n", " ylabel = \"price-dividend ratio\",\n", " xlabel = \"state\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that $ v $ is decreasing in each case.\n", "\n", "This is because, with a positively correlated state process, higher states suggest higher future consumption growth.\n", "\n", "In the stochastic discount factor [(13)](#equation-lucsdf2), higher growth decreases the\n", "discount factor, lowering the weight placed on future returns." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Special cases\n", "\n", "In the special case $ \\gamma =1 $, we have $ J = P $.\n", "\n", "Recalling that $ P^i {\\mathbb 1} = {\\mathbb 1} $ for all $ i $ and applying [Neumann’s geometric series lemma](../tools_and_techniques/linear_algebra.html#la-neumann), we are led to\n", "\n", "$$\n", "v = \\beta(I-\\beta P)^{-1} {\\mathbb 1}\n", "= \\beta \\sum_{i=0}^{\\infty} \\beta^i P^i {\\mathbb 1}\n", "= \\beta \\frac{1}{1 - \\beta} {\\mathbb 1}\n", "$$\n", "\n", "Thus, with log preferences, the price-dividend ratio for a Lucas tree is constant.\n", "\n", "Alternatively, if $ \\gamma = 0 $, then $ J = K $ and we recover the\n", "risk neutral solution [(10)](#equation-rned).\n", "\n", "This is as expected, since $ \\gamma = 0 $ implies $ u(c) = c $ (and hence agents are risk neutral)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### A Risk-Free Consol\n", "\n", "Consider the same pure exchange representative agent economy.\n", "\n", "A risk-free consol promises to pay a constant amount $ \\zeta> 0 $ each period.\n", "\n", "Recycling notation, let $ p_t $ now be the price of an ex-coupon claim to the consol.\n", "\n", "An ex-coupon claim to the consol entitles the owner at the end of period $ t $ to\n", "\n", "- $ \\zeta $ in period $ t+1 $, plus \n", "- the right to sell the claim for $ p_{t+1} $ next period \n", "\n", "\n", "The price satisfies [(2)](#equation-lteeqs0) with $ d_t = \\zeta $, or\n", "\n", "$$\n", "p_t = {\\mathbb E}_t \\left[ m_{t+1} ( \\zeta + p_{t+1} ) \\right]\n", "$$\n", "\n", "We maintain the stochastic discount factor [(13)](#equation-lucsdf2), so this becomes\n", "\n", "\n", "\n", "$$\n", "p_t\n", "= {\\mathbb E}_t \\left[ \\beta g_{t+1}^{-\\gamma} ( \\zeta + p_{t+1} ) \\right] \\tag{15}\n", "$$\n", "\n", "Guessing a solution of the form $ p_t = p(X_t) $ and conditioning on\n", "$ X_t = x $, we get\n", "\n", "$$\n", "p(x)\n", "= \\beta \\sum_{y \\in S} g(y)^{-\\gamma} (\\zeta + p(y)) P(x, y)\n", "$$\n", "\n", "Letting $ M(x, y) = P(x, y) g(y)^{-\\gamma} $ and rewriting in vector notation\n", "yields the solution\n", "\n", "\n", "\n", "$$\n", "p = (I - \\beta M)^{-1} \\beta M \\zeta {\\mathbb 1} \\tag{16}\n", "$$\n", "\n", "The above is implemented in the function consol_price" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "consol_price (generic function with 1 method)" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function consol_price(ap, ζ)\n", " # Simplify names, set up matrices\n", " @unpack β, γ, mc, g, n = ap\n", " P, y = mc.p, mc.state_values\n", " y = reshape(y, 1, n)\n", " M = P .* g.(y).^(-γ)\n", "\n", " # Make sure that a unique solution exists\n", " test_stability(ap, M)\n", "\n", " # Compute price\n", " return (I - β * M) \\ sum(β * ζ * M, dims = 2)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Pricing an Option to Purchase the Consol\n", "\n", "Let’s now price options of varying maturity that give the right to purchase a consol at a price $ p_S $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### An infinite horizon call option\n", "\n", "We want to price an infinite horizon option to purchase a consol at a price $ p_S $.\n", "\n", "The option entitles the owner at the beginning of a period either to\n", "\n", "1. purchase the bond at price $ p_S $ now, or \n", "1. Not to exercise the option now but to retain the right to exercise it later \n", "\n", "\n", "Thus, the owner either *exercises* the option now, or chooses *not to exercise* and wait until next period.\n", "\n", "This is termed an infinite-horizon *call option* with *strike price* $ p_S $.\n", "\n", "The owner of the option is entitled to purchase the consol at the price $ p_S $ at the beginning of any period, after the coupon has been paid to the previous owner of the bond.\n", "\n", "The fundamentals of the economy are identical with the one above, including the stochastic discount factor and the process for consumption.\n", "\n", "Let $ w(X_t, p_S) $ be the value of the option when the time $ t $ growth state is known to be $ X_t $ but *before* the owner has decided whether or not to exercise the option\n", "at time $ t $ (i.e., today).\n", "\n", "Recalling that $ p(X_t) $ is the value of the consol when the initial growth state is $ X_t $, the value of the option satisfies\n", "\n", "$$\n", "w(X_t, p_S)\n", "= \\max \\left\\{\n", " \\beta \\, {\\mathbb E}_t \\frac{u'(c_{t+1})}{u'(c_t)} w(X_{t+1}, p_S), \\;\n", " p(X_t) - p_S\n", "\\right\\}\n", "$$\n", "\n", "The first term on the right is the value of waiting, while the second is the value of exercising now.\n", "\n", "We can also write this as\n", "\n", "\n", "\n", "$$\n", "w(x, p_S)\n", "= \\max \\left\\{\n", " \\beta \\sum_{y \\in S} P(x, y) g(y)^{-\\gamma}\n", " w (y, p_S), \\;\n", " p(x) - p_S\n", "\\right\\} \\tag{17}\n", "$$\n", "\n", "With $ M(x, y) = P(x, y) g(y)^{-\\gamma} $ and $ w $ as the vector of\n", "values $ (w(x_i), p_S)_{i = 1}^n $, we can express [(17)](#equation-feoption0) as the nonlinear vector equation\n", "\n", "\n", "\n", "$$\n", "w = \\max \\{ \\beta M w, \\; p - p_S {\\mathbb 1} \\} \\tag{18}\n", "$$\n", "\n", "To solve [(18)](#equation-feoption), form the operator $ T $ mapping vector $ w $\n", "into vector $ Tw $ via\n", "\n", "$$\n", "T w\n", "= \\max \\{ \\beta M w,\\; p - p_S {\\mathbb 1} \\}\n", "$$\n", "\n", "Start at some initial $ w $ and iterate to convergence with $ T $.\n", "\n", "We can find the solution with the following function call_option" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "call_option (generic function with 2 methods)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# price of perpetual call on consol bond\n", "function call_option(ap, ζ, p_s, ϵ = 1e-7)\n", "\n", " # Simplify names, set up matrices\n", " @unpack β, γ, mc, g, n = ap\n", " P, y = mc.p, mc.state_values\n", " y = reshape(y, 1, n)\n", " M = P .* g.(y).^(-γ)\n", "\n", " # Make sure that a unique console price exists\n", " test_stability(ap, M)\n", "\n", " # Compute option price\n", " p = consol_price(ap, ζ)\n", " w = zeros(ap.n, 1)\n", " error = ϵ + 1\n", " while (error > ϵ)\n", " # Maximize across columns\n", " w_new = max.(β * M * w, p .- p_s)\n", " # Find maximal difference of each component and update\n", " error = maximum(abs, w - w_new)\n", " w = w_new\n", " end\n", "\n", " return w\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here’s a plot of $ w $ compared to the consol price when $ P_S = 40 $" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ap = AssetPriceModel(β=0.9)\n", "ζ = 1.0\n", "strike_price = 40.0\n", "\n", "x = ap.mc.state_values\n", "p = consol_price(ap, ζ)\n", "w = call_option(ap, ζ, strike_price)\n", "\n", "plot(x, p, color = \"blue\", lw = 2, xlabel = \"state\", label = \"consol price\")\n", "plot!(x, w, color = \"green\", lw = 2, label = \"value of call option\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In large states the value of the option is close to zero.\n", "\n", "This is despite the fact the Markov chain is irreducible and low states —\n", "where the consol prices is high — will eventually be visited.\n", "\n", "The reason is that $ \\beta=0.9 $, so the future is discounted relatively rapidly" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Risk Free Rates\n", "\n", "Let’s look at risk free interest rates over different periods." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The one-period risk-free interest rate\n", "\n", "As before, the stochastic discount factor is $ m_{t+1} = \\beta g_{t+1}^{-\\gamma} $.\n", "\n", "It follows that the reciprocal $ R_t^{-1} $ of the gross risk-free interest rate $ R_t $ in state $ x $ is\n", "\n", "$$\n", "{\\mathbb E}_t m_{t+1} = \\beta \\sum_{y \\in S} P(x, y) g(y)^{-\\gamma}\n", "$$\n", "\n", "We can write this as\n", "\n", "$$\n", "m_1 = \\beta M {\\mathbb 1}\n", "$$\n", "\n", "where the $ i $-th element of $ m_1 $ is the reciprocal of the one-period gross risk-free interest rate in state $ x_i $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Other terms\n", "\n", "Let $ m_j $ be an $ n \\times 1 $ vector whose $ i $ th component is the reciprocal of the $ j $ -period gross risk-free interest rate in state $ x_i $.\n", "\n", "Then $ m_1 = \\beta M $, and $ m_{j+1} = M m_j $ for $ j \\geq 1 $." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercises" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 1\n", "\n", "In the lecture, we considered **ex-dividend assets**.\n", "\n", "A **cum-dividend** asset is a claim to the stream $ d_t, d_{t+1}, \\ldots $.\n", "\n", "Following [(1)](#equation-rnapex), find the risk-neutral asset pricing equation for\n", "one unit of a cum-dividend asset.\n", "\n", "With a constant, non-random dividend stream $ d_t = d > 0 $, what is the equilibrium\n", "price of a cum-dividend asset?\n", "\n", "With a growing, non-random dividend process $ d_t = g d_t $ where $ 0 < g \\beta < 1 $,\n", "what is the equilibrium price of a cum-dividend asset?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2\n", "\n", "Consider the following primitives" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "1.0" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 5\n", "P = fill(0.0125, n, n) + (0.95 - 0.0125)I\n", "s = [1.05, 1.025, 1.0, 0.975, 0.95]\n", "γ = 2.0\n", "β = 0.94\n", "ζ = 1.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $ g $ be defined by $ g(x) = x $ (that is, $ g $ is the identity map).\n", "\n", "Compute the price of the Lucas tree.\n", "\n", "Do the same for\n", "\n", "- the price of the risk-free consol when $ \\zeta = 1 $ \n", "- the call option on the consol when $ \\zeta = 1 $ and $ p_S = 150.0 $ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Let’s consider finite horizon call options, which are more common than the\n", "infinite horizon variety.\n", "\n", "Finite horizon options obey functional equations closely related to [(17)](#equation-feoption0).\n", "\n", "A $ k $ period option expires after $ k $ periods.\n", "\n", "If we view today as date zero, a $ k $ period option gives the owner the right to exercise the option to purchase the risk-free consol at the strike price $ p_S $ at dates $ 0, 1, \\ldots , k-1 $.\n", "\n", "The option expires at time $ k $.\n", "\n", "Thus, for $ k=1, 2, \\ldots $, let $ w(x, k) $ be the value of a $ k $-period option.\n", "\n", "It obeys\n", "\n", "$$\n", "w(x, k)\n", "= \\max \\left\\{\n", " \\beta \\sum_{y \\in S} P(x, y) g(y)^{-\\gamma}\n", " w (y, k-1), \\;\n", " p(x) - p_S\n", "\\right\\}\n", "$$\n", "\n", "where $ w(x, 0) = 0 $ for all $ x $.\n", "\n", "We can express the preceding as the sequence of nonlinear vector equations\n", "\n", "$$\n", "w_k = \\max \\{ \\beta M w_{k-1}, \\; p - p_S {\\mathbb 1} \\}\n", " \\quad k =1, 2, \\ldots\n", " \\quad \\text{with } w_0 = 0\n", "$$\n", "\n", "Write a function that computes $ w_k $ for any given $ k $.\n", "\n", "Compute the value of the option with `k = 5` and `k = 25` using parameter values as in Exercise 1.\n", "\n", "Is one higher than the other? Can you give intuition?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solutions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "150.0" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 5\n", "P = fill(0.0125, n, n) + (0.95 - 0.0125)I\n", "s = [0.95, 0.975, 1.0, 1.025, 1.05] # state values\n", "mc = MarkovChain(P, s)\n", "\n", "γ = 2.0\n", "β = 0.94\n", "ζ = 1.0\n", "p_s = 150.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we’ll create an instance of AssetPriceModel to feed into the functions." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "(β = 0.94, γ = 2.0, mc = Discrete Markov Chain\n", "stochastic matrix of type Array{Float64,2}:\n", "[0.95 0.0125 … 0.0125 0.0125; 0.0125 0.95 … 0.0125 0.0125; … ; 0.0125 0.0125 … 0.95 0.0125; 0.0125 0.0125 … 0.0125 0.95], n = 5, g = var\"#5#6\"())" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ap = AssetPriceModel(β = β, mc = mc, γ = γ, g = x -> x)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Lucas Tree Prices: [29.474015777145; 21.935706611219704; 17.571422357262904; 14.725150017725884; 12.722217630644252]\n", "\n" ] } ], "source": [ "v = tree_price(ap)\n", "println(\"Lucas Tree Prices: $v\\n\")" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "hide-output": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Consol Bond Prices: [753.8710047641987; 242.55144081989457; 148.67554548466478; 109.25108965024712; 87.56860138531121]\n", "\n" ] } ], "source": [ "v_consol = consol_price(ap, 1.0)\n", "println(\"Consol Bond Prices: $(v_consol)\\n\")" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "5×1 Array{Float64,2}:\n", " 603.8710047641987\n", " 176.839334301913\n", " 108.67734499337003\n", " 80.05179254233045\n", " 64.30843748377002" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w = call_option(ap, ζ, p_s)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 3\n", "\n", "Here’s a suitable function:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "hide-output": false }, "outputs": [ { "data": { "text/plain": [ "finite_horizon_call_option (generic function with 1 method)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function finite_horizon_call_option(ap, ζ, p_s, k)\n", "\n", " # Simplify names, set up matrices\n", " @unpack β, γ, mc = ap\n", " P, y = mc.p, mc.state_values\n", " y = y'\n", " M = P .* ap.g.(y).^(- γ)\n", "\n", " # Make sure that a unique console price exists\n", " test_stability(ap, M)\n", "\n", " # Compute option price\n", " p = consol_price(ap, ζ)\n", " w = zeros(ap.n, 1)\n", " for i in 1:k\n", " # Maximize across columns\n", " w = max.(β * M * w, p .- p_s)\n", " end\n", "\n", " return w\n", "end" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "hide-output": false }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lines = []\n", "labels = []\n", "for k in [5, 25]\n", " w = finite_horizon_call_option(ap, ζ, p_s, k)\n", " push!(lines, w)\n", " push!(labels, \"k = $k\")\n", "end\n", "plot(lines, labels = reshape(labels, 1, length(labels)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Not surprisingly, the option has greater value with larger $ k $.\n", "This is because the owner has a longer time horizon over which he or she\n", "may exercise the option." ] } ], "metadata": { "date": 1591310625.5790236, "download_nb": 1, "download_nb_path": "https://julia.quantecon.org/", "filename": "markov_asset.rst", "filename_with_path": "multi_agent_models/markov_asset", "kernelspec": { "display_name": "Julia 1.4.2", "language": "julia", "name": "julia-1.4" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.4.2" }, "title": "Asset Pricing I: Finite State Models" }, "nbformat": 4, "nbformat_minor": 2 }