{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### 18th Winter school on Mathematical Finance\n", "

\n", "\n", "### Lunteren, January 21-23, 2019\n", "\n", "

\n", "

\n", "\n", "### Rough volatility\n", "\n", "

\n", "#### Lecture 4: Affine models, the rough Heston model in particular\n", "\n", "\n", "\n", "Jim Gatheral \n", "Department of Mathematics \n", "\n", " \n", " \n", "

\n", "\n", "\n", "$$\n", "\\newcommand{\\BS}{\\text{BS}}\n", "\\newcommand{\\bea}{\\begin{eqnarray}}\n", "\\newcommand{\\eea}{\\end{eqnarray}}\n", "\\newcommand{\\beas}{\\begin{eqnarray*}}\n", "\\newcommand{\\eeas}{\\end{eqnarray*}}\n", "\\newcommand{\\supp}{\\mathrm{supp}}\n", "\\newcommand{\\E}{\\mathbb{E} }\n", "\\def\\Cov{{ \\mbox{Cov} }}\n", "\\def\\Var{{ \\mbox{Var} }}\n", "\\newcommand{\\1}{\\mathbf{1} }\n", "\\newcommand{\\cF}{\\mathcal{F} }\n", "\\newcommand{\\cO}{\\mathcal{O} }\n", "\\newcommand{\\PP}{\\mathbb{P} }\n", "\\newcommand{\\QQ}{\\mathbb{Q} }\n", "\\newcommand{\\RR}{\\mathbb{R} }\n", "\\newcommand{\\DD}{\\mathbb{D} }\n", "\\newcommand{\\HH}{\\mathbb{H} }\n", "\\newcommand{\\spn}{\\mathrm{span} }\n", "\\newcommand{\\cov}{\\mathrm{cov} }\n", "\\newcommand{\\HS}{\\mathcal{L}_{\\mathrm{HS}} }\n", "\\newcommand{\\trace}{\\mathrm{trace} }\n", "\\newcommand{\\LL}{\\mathcal{L} }\n", "\\newcommand{\\s}{\\mathcal{S} }\n", "\\newcommand{\\ee}{\\mathcal{E} }\n", "\\newcommand{\\ff}{\\mathcal{F} }\n", "\\newcommand{\\hh}{\\mathcal{H} }\n", "\\newcommand{\\bb}{\\mathcal{B} }\n", "\\newcommand{\\dd}{\\mathcal{D} }\n", "\\newcommand{\\g}{\\mathcal{G} }\n", "\\newcommand{\\half}{\\frac{1}{2} }\n", "\\newcommand{\\T}{\\mathcal{T} }\n", "\\newcommand{\\bi}{\\begin{itemize}}\n", "\\newcommand{\\ei}{\\end{itemize}}\n", "\\newcommand{\\beq}{\\begin{equation}}\n", "\\newcommand{\\eeq}{\\end{equation}}\n", "\\newcommand{\\ee}[1]{\\mathbb{E}\\left[{#1}\\right]}\n", "\\newcommand{\\eef}[1]{\\mathbb{E}\\left[\\left.{#1}\\right|\\cF_t\\right]}\n", "\\newcommand{\\Rplus}{\\mathbb{R}_{\\geqslant 0}}\n", "\\newcommand{\\Rpplus}{\\mathbb{R}_{> 0}}\n", "\\newcommand{\\Rminus}{\\mathbb{R}_{\\leqslant 0}}\n", "\\newcommand{\\p}{\\partial}\n", "\\newcommand{\\ui}{\\textrm{i}}\n", "\\newcommand{\\mP}{\\mathbb{P}}\n", "\\newcommand{\\mQ}{\\mathbb{Q}}\n", "\\newcommand{\\angl}[1]{\\langle{#1}\\rangle}\n", "\\newcommand{\\var}{{\\rm var}}\n", "\\newcommand{\\cov}{{\\rm cov}}\n", "\\newcommand{\\covf}[1]{\\cov\\left[\\left.{#1}\\right|\\cF_t\\right]}\n", "\\newcommand{\\varf}[1]{\\var\\left[\\left.{#1}\\right|\\cF_t\\right]}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Outline of lecture 4\n", "\n", "* Forward variance models\n", "* Affine forward variance models\n", "* The characteristic function of an affine forward variance model\n", " - The rough Heston characteristic function\n", "* Rational approximation of the rough Heston solution\n", "* Numerical experiments" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Forward variance models\n", "\n", "Following [Bergomi and Guyon][2], forward variance models may be written in the form \n", "\n", "$$\n", "\\beas\n", "dS_t &=& S_t \\, \\sqrt{v_t}\\, \\left(\\rho dW_t + \\sqrt{1 - \\rho^2} dW_t^\\bot\\right)\\\\\n", "d\\xi_t(u) &=& \\eta_t(u;\\omega) \\,dW_t,\n", "\\eeas\n", "$$\n", "\n", "where $W, W^\\bot$ are independent Brownian motions, the $\\Rplus$-valued stochastic process $\\eta_t(u;\\omega)$ is progressively measurable for all $u > 0$ and $\\xi$ is linked to the instantaneous variance $v$ by \n", "\n", "$$\n", "\\xi_t(T) = \\eef{v_T}.\n", "$$\n", "\n", "- Models of this form were also studied by Hans Bühler as *variance curve models*. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- If $v$ is continuous and uniformly integrable, we can recover $v_t$ from $\\xi_t(u)$ as $v_t = \\lim_{u \\downarrow t} \\xi_t(u)$. For our purposes, $v_t = \\xi_t(t)$.\n", "\n", "\n", "- The initial conditions of a forward variance model are the initial stock price $S_t$ and the initial forward variance curve $\\xi_t(u)_{u > t}$. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "#### Important remark\n", "\n", "As noted by [Bergomi and Guyon][3], all conventional finite-dimensional Markovian stochastic volatility models may be cast as forward variance models.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Example: The classical Heston model\n", "\n", "\n", "The classical Heston stochastic volatility model may be written as\n", "\n", "$$\n", "\\beas\n", "\\frac{dS_t}{S_t} &=& \\sqrt{v_t} \\,dZ_t\\\\\n", "dv_t &=& - \\lambda \\,(v_t - \\bar v)\\,dt + \\eta \\,\\sqrt {v_t} \\,dW_t\n", "\\eeas\n", "$$\n", "\n", "with $\n", "\\ee {dZ_t\\,dW_t} = \\rho \\, dt\n", "$ and where $\\lambda$ is the speed of reversion of $v_t$ to its long term\n", "mean $\\bar v$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Forward variance in the Heston model\n", "\n", "\n", "With $\\xi_t(u) = \\eef{v_u}$, take expectations of the SDE for $v_t$ to get\n", "\n", "$$\n", " d\\xi_t(u) = -\\lambda\\,(\\xi_t(u) -\\bar v)\\,du.\n", "$$\n", "\n", "This ODE has the solution\n", "\n", "$$\n", "\\xi_t(u) = (\\xi_t(t)-\\bar v)\\,e^{-\\lambda\\,(u-t)}+\\bar v = (v_t-\\bar v)\\,e^{-\\lambda\\,(u-t)}+\\bar v.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### The Heston model in forward variance form\n", "\n", "For each $u$, $\\xi_t(u)$ is a conditional expectation and so a martingale in $t$. It is then immediate from the last equation that\n", "\n", "$$\n", "d \\xi_t(u) = e^{-\\lambda\\,(u-t)}\\,\\widehat{d v_t} = \\eta\\,e^{-\\lambda\\,(u-t)}\\,\\sqrt{v_t}\\,dW_t\n", "$$\n", "\n", "where $\\widehat{d v_t}$ denotes the martingale part of $dv_t$.\n", "\n", "- It is easy to check explicitly that all drift (*i.e.* $dt$) terms cancel." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The rough Heston model\n", "\n", "By considering the limit of a simple Hawkes process-based model of order flow, [El Euch and Rosenbaum][4] derive a rough Heston model. The equation for variance in this model takes the form\n", "\n", "$$\n", "v_u = \\theta(u) - \\frac{1}{\\Gamma(H + 1/2)} \\int_{t}^u (u-s)^{H-1/2} \\lambda\\, v_s \\,ds +\\frac{1}{\\Gamma(H + 1/2)} \\int_{t}^u (u-s)^{H-1/2} \\eta \\sqrt{v_s} \\,dW_s.\n", "$$\n", "\n", "- $H \\in (0, 1/2]$ is the Hurst exponent of the volatility, $\\lambda>0$ is the mean reversion parameter, $\\eta>0$ is the volatility of volatility parameter.\n", "\n", "- The function $\\theta$ is assumed to be continuous and represents a time-dependent mean reversion level.\n", "\n", "- The rough Heston model is a natural fractional generalization of the classical Heston model which is recovered when $H=1/2$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Forward variance in the rough Heston model\n", "\n", "- We will consider only the special case $\\lambda=0$. In this case,\n", "$\\xi_t(u) = \\eef{v_u}= \\theta(u)$.\n", "\n", "\n", "- It follows that\n", "

\n", "$$\n", "v_u = \\xi_t(u) +\\frac{1}{\\Gamma(H + 1/2)} \\int_{t}^u (u-s)^{H-1/2} \\eta \\sqrt{v_s} \\,dW_s.\n", "$$\n", "\n", "- Also\n", "\n", "$$\n", "v_u = \\xi_{t+h}(u) +\\frac{1}{\\Gamma(H + 1/2)} \\int_{t+h}^u (u-s)^{H-1/2} \\eta \\sqrt{v_s} \\,dW_s.\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### The rough Heston model in forward variance form\n", "\n", "Subtracting these two equations gives\n", "\n", "$$\n", " \\xi_{t+h}(u) - \\xi_{t}(u) = \\frac{1}{\\Gamma(H + 1/2)} \\, \\int_t^{t+h} (u-s)^{H-1/2} \\eta \\sqrt{v_s} \\,dW_s.\n", "$$\n", "\n", "Taking the limit $h \\to 0$, we obtain \n", "\n", "$$\n", "d\\xi_{t}(u) = \\frac{\\eta}{{\\Gamma(H + 1/2)}}\\,(u-t)^{H-1/2}\\, \\sqrt{v_t} \\,dW_t,\n", "$$\n", "\n", "the rough Heston model in forward variance form.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Non-Markovianity of the rough Heston model\n", "\n", "- Note that the limit $u \\to t$ of the rough Heston model makes no sense.\n", " - This reflects the fact that the rough Heston model is not Markovian.\n", " - There is no SDE for $v_t$ and no corresponding PDE.\n", " - On the other hand, we can write an SDE for each $\\xi_t(u)$, $u>t$.\n", " - We can even apply Itô's Lemma!\n", " \n", " \n", "- The rough Heston model is Markovian in the infinite-dimensional forward variance curve $\\xi_t(u), \\, u>t$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Affine processes\n", "\n", "The following explanation is due to Martin Keller-Ressel:\n", "\n", ">An *affine process* can be described as a Markov process whose log-characteristic function is an affine \n", "function of its initial state vector.\n", "\n", "\n", "And here's a definition of the word *affine* from Wikipedia:\n", "\n", " \n", "\n", ">In geometry, an affine transformation or affine map or an affinity (from the Latin, *affinis*, \"connected with\") between two vector spaces (strictly speaking, two affine spaces) consists of a linear transformation followed by a translation:\n", "$$\n", "x \\mapsto A\\,x+b\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Affine CGF\n", "\n", "Let $X_t = \\log S_t$. According to Definition 2.2 of [Gatheral and Keller-Ressel][6], we say that a forward variance model has an *affine cumulant generating function* determined by $g(t;u)$, if its conditional cumulant generating function is of the form \n", "\n", "(1)\n", "$$\n", "\\log \\eef{e^{u(X_T - X_t)}} = \\int_t^T g(T-s;u)\\, \\xi_t(s)ds.\n", "$$\n", "\n", "for all $u \\in [0,1]$, $0 \\le t \\le T$ and $g(.;u)$ is $\\Rminus$-valued and continuous on $[0,T]$ for all $T > 0$ and $u \\in [0,1]$.\n", "\n", "- The restriction $u \\in [0,1]$ is for mathematical convenience. We will later allow complex $u$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### When is a forward variance model affine?\n", "\n", "Theorem 2.4 of [Gatheral and Keller-Ressel][6] states that a forward variance model has an affine CGF if and only if it takes the form\n", "\n", "$$\n", "\\beas\n", "\\frac{dS_t}{S_t} &=& \\sqrt{v_t}\\,dZ_t\\\\\n", "d\\xi_t(u) &=& \\sqrt{v_t}\\, \\kappa(u-t)\\,dW_t\n", "\\eeas\n", "$$\n", "\n", "for some deterministic, non-negative decreasing kernel $\\kappa$, which satisfies $\\int_0^T \\kappa(r) dr < \\infty$ for all $T > 0$.\n", "\n", "- Essentially, the only affine stochstic volatility model is the Heston model, up to a choice of kernel." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Moreover, $g(.,u): \\Rplus \\to \\Rminus$ in the definition [(1)](#eq:affineCGF) of the CGF is the unique global continuous solution of the convolution Riccati equation\n", "\n", "$$\n", "g(t,u) = R_V\\Big(u, \\int_0^t \\kappa(t-s) g(s,u) ds\\Big) = R_V\\Big(u,(\\kappa \\star g) (t,u)\\Big),\\quad t \\ge 0\n", "$$\n", "\n", "where\n", "\n", "$$\n", "R_V(u,w) = \\frac{1}{2}(u^2 - u) + \\rho\\, u\\, w + \\frac{1}{2}\\, w^2.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "Alternatively, $g(t,u)$ can be written as\n", "\n", "$$\n", "g(t,u) = R_V(u,f(t,u)),\n", "$$\n", "\n", "where $f(t,u)$ is the unique global solution of the non-linear Volterra equation\n", "\n", "$$\n", "f(t,u) = \\int_0^t \\kappa(t-s) R_V(u,f(t,s)) ds.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Derivation of the Riccati equation\n", "\n", "From the definition definition [(1)](#eq:affineCGF) of the CGF, \n", "\n", "$$\n", "M_t = \\eef{e^{u\\,X_T}} = \\exp\\left\\{u\\,X_t + \\int_t^T\\,\\xi_t(s)\\,g(T-s;u)\\,ds \\right\\} =: \\exp\\left\\{u\\,X_t + G_t \\right\\}\n", "$$\n", "\n", "is a conditional expectation and thus a martingale in $t$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Applying Itô's Lemma to $M$ gives\n", "\n", "$$\n", "\\frac{d M_t}{M_t} = u\\,dX_t + dG_t + \\frac{u^2}2\\,d\\angl{X}_t + \\frac12\\,d\\angl{G}_t +u\\,d\\angl{X,G}_t.\n", "$$\n", "\n", "Now\n", "\n", "$$\n", "\\beas\n", "dX_t &=& -\\frac 12 \\,v_t\\,dt + \\sqrt{v_t}\\,dZ_t\\\\\n", "dG_t &=& -\\xi_t(t)\\,g(T-t;u)\\,dt + \\int_t^T\\,d\\xi_t(s)\\,g(T-s;u)\\,ds\\\\\n", " &=& -v_t\\,g(T-t;u)\\,dt + \\int_t^T\\,\\kappa(s-t)\\,\\sqrt{v_t}\\,dW_t\\,g(T-s;u)\\,ds.\n", "\\eeas\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "We compute\n", "\n", "$$\n", "\\beas\n", "d\\angl{X}_t &=& v_t\\,dt\\\\\n", "d\\angl{G}_t &=& v_t\\,dt\\, \\left( \\int_t^T\\,\\kappa(s-t)\\,g(T-s;u)\\,ds \\right)^2\\\\\n", "d\\angl{X,G}_t &=& \\rho\\,v_t\\, dt\\,\\int_t^T\\,\\kappa(s-t)\\,g(T-s;u)\\,ds.\n", "\\eeas\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Imposing $\\ee{dM_t}=0$ and letting $\\tau = T-t$ gives\n", "\n", "$$\n", "0 = v_t\\,dt\\,\\left\\{-\\frac 12\\,u +\\frac12\\,u^2 -g(\\tau;u)\n", "+\\rho\\,u\\,(\\kappa \\star g) (\\tau,u) + \\frac12\\,(\\kappa \\star g) (\\tau,u)^2\n", "\\right\\}\n", "$$\n", "\n", "where the convolution integral is given by\n", "\n", "$$\n", "(\\kappa \\star g) (\\tau,u) = \\int_0^\\tau\\,\\kappa(\\tau - s)\\,g(s;u)\\,ds.\n", "$$\n", "\n", "- It is almost obvious why the CGF is affine if an only if the forward variance process is of the form $d\\xi_t(u) = \\sqrt{v_t}\\, \\kappa(u-t)\\,dW_t$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### The convolution Riccati equation\n", "\n", "Rearranging gives \n", "\n", "$$\n", "g(\\tau;u) = \\frac 12\\,u(u-1) + \\rho \\,u\\, (\\kappa \\star g) (\\tau;u) + \\frac 12\\, (\\kappa \\star g) (\\tau;u)^2 = R_V(u,(\\kappa \\star g)),\n", "$$\n", "\n", "as required." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Example: The classical Heston model\n", "\n", "In this case, \n", "$\n", "\\kappa(\\tau) =\\eta\\,e^{-\\lambda\\,\\tau}$.\n", "\n", "Then\n", "\n", "$$\n", "\\eta\\,h(\\tau;u):=(\\kappa \\star g)(\\tau;u) = \\eta\\, \\int_0^\\tau\\,e^{-\\lambda\\,(\\tau-s)}\\,g(s;u)\\,ds .\n", "$$\n", "\n", "Also, \n", "$\n", "\\p_\\tau h(\\tau;u) = -\\lambda\\,h(\\tau;u) + g(\\tau;u).\n", "$\n", "The convolution Riccati equation then becomes\n", "\n", "(2)\n", "$$\n", "\\p_\\tau h(\\tau;u) = \\frac 12\\,u\\,(u-1) - (\\lambda - \\rho\\,\\eta\\,u)\\, h (\\tau;u) + \\frac 12\\,\\eta^2\\, h(\\tau;u)^2\n", "$$\n", "\n", "consistent with the classical derivation in (for example) Chapter 2 of [The Volatility Surface][5]." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### The Heston characteristic function\n", "\n", "- The classical Heston Riccati ODE [(2)](#eq:HestonRiccati) may be solved in closed form as in as in equation (2.12) of [The Volatility Surface][5].\n", "\n", "\n", "- The characteristic function is then given by \n", "

\n", "$$\n", "\\beas\n", "\\varphi_t^T(a) = \\eef{e^{\\ui a X_T}} = \\exp\\left\\{\\ui a X_t + \\int_t^T\\,\\xi_t(s)\\,g(T-s;\\ui a)\\,ds\\right\\}\n", "\\eeas\n", "$$\n", "

\n", "where\n", "$$\n", "g(\\tau;u)=\\p_\\tau h(\\tau;u) +\\lambda\\,h(\\tau;u).\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Example: The rough Heston model (with $\\lambda=0$)\n", "\n", "In this case, with $\\alpha=H+\\frac12$,\n", "$\n", "\\kappa(\\tau) =\\frac{\\eta}{\\Gamma(\\alpha)} \\,\\tau^{\\alpha-1}\n", "$\n", "and\n", "\n", "$$\n", "\\eta\\,h(\\tau;u):=(\\kappa \\star g)(\\tau;u) = \\frac{\\eta}{\\Gamma(\\alpha)} \\int_0^\\tau\\,(\\tau-s)^{\\alpha-1}\\,g(s;u)\\,ds = \\eta\\,I^\\alpha g(\\tau;u).\n", "$$\n", "where $D^\\alpha$ and $I^\\alpha$ represent fractional differential and integral operators respectively.\n", "\n", "Inverting this gives\n", "$\n", "g(\\tau;u) =D^\\alpha h(\\tau; u).\n", "$\n", "\n", "The convolution integral Riccati equation then reads\n", "\n", "(3)\n", "$$\n", "D^\\alpha h(\\tau;u) = \\frac 12\\,u\\,(u-1) + \\rho\\,\\eta\\, u\\, h (\\tau;u) + \\frac 12\\,\\eta^2\\, h(\\tau;u)^2,\n", "$$\n", "\n", "consistent with [El Euch and Rosenbaum][6]." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### An aside: Fractional calculus\n", "\n", "Define the fractional integral and differential operators:\n", "\n", "$$\n", "I^{\\alpha} f(t) = \\frac{1}{\\Gamma(\\alpha)}\\,\\int_0^t\\,(t-s)^{\\alpha-1}\\,f(s)\\,ds;\\quad D^\\alpha f(t) = \\frac{d}{dt}\\,I^{1-\\alpha} f(t).\n", "$$\n", "\n", "The fractional integral is a natural generalization of the ordinary integral using the Cauchy formula for repeated integration:\n", "\n", "$$\n", "\\beas\n", "I^{n} f(t) &:=& \\int_0^t dt_1\\int_0^{t_1}...dt_{n-1}\\int_0^{t_{n-1}}f(t_n)\\,dt_n\\\\\n", "&=&\\frac{1}{(n-1)!}\\,\\int_0^t\\, (t-s)^{n-1}\\,f(s)\\,ds.\n", "\\eeas\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The proof follows easily by induction when you notice that\n", "\n", "$$\n", "D\\,I^{n} f(t) = \\frac{1}{(n-1)!}\\,\\int_0^t\\, (n-1)\\,(t-s)^{n-2}\\,f(s)\\,ds = I^{n-1}f(t)\n", "$$\n", "\n", "and of course that $D\\,I\\, f(t) = f(t)$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### A microstructural foundation of the rough Heston model\n", "\n", "- The rough Heston model emerges as the continuous time limit of a Hawkes process-based model of order flow.\n", " - Buys(sells) make the price go up(down)\n", " - Buys(sells) induce more buys(sells). That is, the processes are self-exciting.\n", " - Excitations decay as a power law.\n", "\n", "\n", "- We explain the relationship between the class of Affine Forward Intensity (AFI) models of order flow and their limiting Affine Forward Variance (AFV) models in Lecture 5. \n", "\n", " \n", "- This gives us a clue as to why rough volatility appears to be universal.\n", "\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The rough Heston characteristic function\n", "\n", "- There exist a number of standard numerical techniques, such as the Adams scheme, for solving fractional differential equations such as the rough Heston fractional Riccati equation.\n", " - These techniques are all slow!\n", " \n", " \n", "- Recently, [Gatheral and Radoičić][7] showed how to approximate the solution of the rough Heston fractional Riccati equation by a rational function.\n", " - This approximation solution is just as fast as the classical Heston solution and appears to be more accurate than the Adams scheme for any reasonable number of time steps!" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "slideshow": { "slide_type": "slide" } }, "source": [ "### Rational approximation to the rough Heston solution\n", "\n", "\n", "Wlog, set $\\nu=1$ and $x=t$. Then the rough Heston fractional Riccati ODE reads\n", "\n", "$$\n", "\\beas\n", "D^\\alpha h(a,x) &=& -\\frac12\\,a(a+\\ui) + \\ui\\,\\rho\\,a\\,h(a,x) + \\frac{1}{2}\\,h(a,x)^2\\\\\n", "&=&\\frac12\\,\\left(h(a,x)-r_-\\right)\\,\\left(h(a,x)-r_+\\right)\n", "\\eeas\n", "$$\n", "with\n", "$$\n", "A= \\sqrt{a\\,(a+i) -\\rho^2\\,a^2 };\\quad r_\\pm = \\left\\{ -\\ui\\,\\rho\\,a \\pm A \\right\\}.\n", "$$\n", "\n", "The idea is to paste together short- and long-time expansions of the solution using a rational (Padé approximation)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Short-time expansion\n", "\n", "From the exponentiation theorem of [Alòs, Gatheral and Radoičić][1], $h(a,x)$ can be written as\n", "

\n", "$$\n", "h(a,x) = \\sum_{j=0}^\\infty\\,\\frac{\\Gamma(1+j\\,\\alpha)}{\\Gamma(1+(j+1)\\,\\alpha)}\\beta_j(a)\\,x^{(j+1)\\,\\alpha}\n", "$$\n", "with\n", "$$\n", "\\beas\n", "\\beta_0(a) &=& -\\frac{1}{2}\\,a(a+\\ui)\\nonumber\\\\\n", "\\beta_k(a) &=& \\frac12\\,\\sum_{i,j=0}^{k-2}\\,\\mathbb{1}_{i+j = k-2}\\,\\beta_i(a)\\,\\beta_j(a) \\frac{\\Gamma(1+i\\,\\alpha)}{\\Gamma(1+(i+1)\\,\\alpha)}\\,\n", "\\frac{\\Gamma(1+j\\,\\alpha)}{\\Gamma(1+(j+1)\\,\\alpha)}\\nonumber\\\\\n", "&&\\qquad + \\ui\\,\\rho\\,a\\,\\frac{\\Gamma(1+(k-1)\\,\\alpha)}{\\Gamma(1+k\\,\\alpha)}\\beta_{k-1}(a).\n", "\\eeas\n", "$$\n", "\n", "- We will explain the exponentiation theorem in Lecture 5." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Solving the rough Heston Riccati equation for long times\n", "\n", "\n", "- In analogy with the classical Heston solution, we expect that for a suitable range of $a$, \n", "

\n", "$$\n", "\\lim_{x \\to \\infty} h(a,x) = r_-.\n", "$$\n", "\n", "\n", "- In that case, for large $x$, we could linearize the fractional Riccati equation as follows.\n", "$$\n", "\\beas\n", "D^\\alpha h(a,x) &=& \\frac12\\,\\left(h(a,x)-r_-\\right)\\,\\left(h(a,x)-r_+\\right)\\nonumber\\\\\n", "& \\approx & -\\frac12\\,\\left(r_+ - r_-\\right)\\left(h(a,x)-r_-\\right)\\nonumber\\\\\n", "&=& - A\\,\\left(h(a,x)-r_-\\right).\n", "\\eeas\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "slideshow": { "slide_type": "subslide" } }, "source": [ "- The above linear fractional differential equation has the exact solution\n", "

\n", "

\n", "$$\n", "h_\\infty(a,x) = r_-\\,\\left[1-E_\\alpha(-A\\,x^\\alpha)\\right],\n", "$$\n", "where $E_{\\alpha}(\\cdot)$ is the Mittag-Leffler function.\n", "\n", "\n", "\n", "- As $x \\to \\infty$,\n", "$$\n", "E_\\alpha(-A\\,x^\\alpha) = -\\frac{1}{A}\\,\\frac{x^{-\\alpha}}{\\Gamma(1-\\alpha)} + \\cO\\left(|A\\,x^\\alpha|^{-2} \\right).\n", "$$\n", "\n", "\n", "- Thus, as $x \\to \\infty$,\n", "

\n", "$$\n", "h_\\infty (a,x) - r_- = \\frac{r_-}{A}\\,\\frac{x^{-\\alpha}}{\\Gamma(1-\\alpha)} + \\cO\\left(|A\\,x^\\alpha|^{-2} \\right).\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Large $x$ expansion\n", "\n", "- The form of the asymptotic solution motivates the following expansion of $h$ for large $x$:\n", "

\n", "$$\n", "h(a,x) = r_-\\,\\sum_{k=0}^\\infty\\,\\gamma_k\\,\\frac{x^{-k \\alpha}}{A^k\\,\\Gamma(1-k \\alpha)}.\n", "$$\n", "\n", "- The coefficients $\\gamma_k$ satisfy the recursion\n", "\n", "$$\n", "\\beas\n", "\\gamma_1 &=&-\\gamma_0 = -1\\\\\n", "\\gamma_{k} &=& - \\gamma_{k-1} + \\frac{r_-}{2 A}\n", "\\sum_{i,j=1}^\\infty\\,\\mathbb{1}_{i+j=k} \\,\\gamma_i\\,\\gamma_j\\,\\frac{\\Gamma(1-k \\alpha)}{\\Gamma(1-i \\alpha)\\,\\Gamma(1-j \\alpha)}.\n", "\\eeas\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Rational approximation\n", "\n", "\n", "- Now we have small- and large-$x$ expansions we can compute global rational approximations to $h(a,x)$ of the form\n", "

\n", "$$\n", "h^{(m,n)}(a,x)=\\frac{\\sum_{i=1}^m\\,p_m y^m}{\\sum_{j=0}^n\\,q_n y^n}\n", "$$\n", "

\n", "with $y = x^\\alpha$ that match these expansions up to order $m$ and $n$ respectively.\n", "\n", "\n", "- Only the diagonal approximants $h^{(n,n)}$ are admissible approximations of $h$. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### $h^{(3,3)}$ is the best\n", "\n", "- From various numerical experiments, the particular approximation $h^{(3,3)}$ seems to be amazingly close to the true solution for reasonable choices of model parameters. \n", "\n", "\n", "- Though the excellent quality of the global approximation $h^{(3,3)}$ might at first seem very surprising, it is consistent with many Padé approximation stories from the literature.\n", " \n", " \n", "- In our case, $h^{(3,3)}$ is clearly better than either $h^{(2,2)}$ or $h^{(4,4)}$.\n", " - $h^{(5,5)}$ is another very good approximation, but still not as good as $h^{(3,3)}$. $h^{(5,5)}$ is obviously also slower to compute.\n", " - Higher order approximations may turn out to beat $h^{(3,3)}$. However, $h^{(3,3)}$ may still be best in practice if speed of computation is taken into account.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Computing $h^{(3,3)}$\n", "\n", "\n", "- We have the series expansion of $h$ for small $y$: \n", "$$\n", " h_s(y) = b_1\\,y+b_2 \\,y^2 +b_3 \\,y^3+ \\cO(y^4). \n", "$$\n", "\n", "\n", "- We have the series expansion of $h$ for large $y$: \n", "$$\n", "h_\\ell(y) = g_0 + \\frac{g_1 }y+\\frac{g_2 }{y^2}+\\cO\\left(\\frac{1}{y^3}\\right).\n", "$$\n", "\n", "- Matching the coefficients of the rational approximation\n", "$$\n", "h^{(3,3)}(y) = \\frac{p_1 \\,y + p_2\\,y^2+p_3\\,y^3}{1 + q_1 \\,y+q_2\\,y^2+q_3\\,y^3 }\n", "$$\n", "

\n", "to $h_s(y)$ and $h_\\ell(y)$ respectively gives a linear system of six equations with six unknowns." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Some R-code" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "setwd(\"./LRV\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "source(\"BlackScholes.R\")\n", "source(\"Lewis.R\")\n", "source(\"roughHestonPade.R\")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "library(repr)\n", "options(repr.plot.height=5)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### R implementation of the rational approximation\n", "\n", "The code below shows how the solution is implemented." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "

function (params) \n",
       "function(a, x) {\n",
       "    H <- params$H\n",
       "    rho <- params$rho\n",
       "    eta <- params$eta\n",
       "    al <- H + 0.5\n",
       "    aa <- sqrt(a * (a + (0 + (0+1i))) - rho^2 * a^2)\n",
       "    rm <- -(0 + (0+1i)) * rho * a - aa\n",
       "    rp <- -(0 + (0+1i)) * rho * a + aa\n",
       "    b1 <- -a * (a + (0+1i))/(2 * gamma(1 + al))\n",
       "    b2 <- (1 - a * (0+1i)) * a^2 * rho/(2 * gamma(1 + 2 * al))\n",
       "    g0 <- rm\n",
       "    g1 <- -rm/(aa * gamma(1 - al))\n",
       "    den <- g0^2 + b1 * g1\n",
       "    p1 <- b1\n",
       "    p2 <- (b1^2 * g0 + b2 * g0^2)/den\n",
       "    q1 <- (b1 * g0 - b2 * g1)/den\n",
       "    q2 <- (b1^2 + b2 * g0)/den\n",
       "    y <- x^al\n",
       "    h.pade <- (p1 * y + p2 * y^2)/(1 + q1 * y + q2 * y^2)\n",
       "    res <- 1/2 * (h.pade - rm) * (h.pade - rp)\n",
       "    return(res)\n",
       "}
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (params) \n", "function(a, x) \\{\n", " H <- params\\$H\n", " rho <- params\\$rho\n", " eta <- params\\$eta\n", " al <- H + 0.5\n", " aa <- sqrt(a * (a + (0 + (0+1i))) - rho\\textasciicircum{}2 * a\\textasciicircum{}2)\n", " rm <- -(0 + (0+1i)) * rho * a - aa\n", " rp <- -(0 + (0+1i)) * rho * a + aa\n", " b1 <- -a * (a + (0+1i))/(2 * gamma(1 + al))\n", " b2 <- (1 - a * (0+1i)) * a\\textasciicircum{}2 * rho/(2 * gamma(1 + 2 * al))\n", " g0 <- rm\n", " g1 <- -rm/(aa * gamma(1 - al))\n", " den <- g0\\textasciicircum{}2 + b1 * g1\n", " p1 <- b1\n", " p2 <- (b1\\textasciicircum{}2 * g0 + b2 * g0\\textasciicircum{}2)/den\n", " q1 <- (b1 * g0 - b2 * g1)/den\n", " q2 <- (b1\\textasciicircum{}2 + b2 * g0)/den\n", " y <- x\\textasciicircum{}al\n", " h.pade <- (p1 * y + p2 * y\\textasciicircum{}2)/(1 + q1 * y + q2 * y\\textasciicircum{}2)\n", " res <- 1/2 * (h.pade - rm) * (h.pade - rp)\n", " return(res)\n", "\\}\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (params) \n", "function(a, x) {\n", " H <- params$H\n", " rho <- params$rho\n", " eta <- params$eta\n", " al <- H + 0.5\n", " aa <- sqrt(a * (a + (0 + (0+1i))) - rho^2 * a^2)\n", " rm <- -(0 + (0+1i)) * rho * a - aa\n", " rp <- -(0 + (0+1i)) * rho * a + aa\n", " b1 <- -a * (a + (0+1i))/(2 * gamma(1 + al))\n", " b2 <- (1 - a * (0+1i)) * a^2 * rho/(2 * gamma(1 + 2 * al))\n", " g0 <- rm\n", " g1 <- -rm/(aa * gamma(1 - al))\n", " den <- g0^2 + b1 * g1\n", " p1 <- b1\n", " p2 <- (b1^2 * g0 + b2 * g0^2)/den\n", " q1 <- (b1 * g0 - b2 * g1)/den\n", " q2 <- (b1^2 + b2 * g0)/den\n", " y <- x^al\n", " h.pade <- (p1 * y + p2 * y^2)/(1 + q1 * y + q2 * y^2)\n", " res <- 1/2 * (h.pade - rm) * (h.pade - rp)\n", " return(res)\n", "}\n", "```" ], "text/plain": [ "function (params) \n", "function(a, x) {\n", " H <- params$H\n", " rho <- params$rho\n", " eta <- params$eta\n", " al <- H + 0.5\n", " aa <- sqrt(a * (a + (0 + (0+1i))) - rho^2 * a^2)\n", " rm <- -(0 + (0+1i)) * rho * a - aa\n", " rp <- -(0 + (0+1i)) * rho * a + aa\n", " b1 <- -a * (a + (0+1i))/(2 * gamma(1 + al))\n", " b2 <- (1 - a * (0+1i)) * a^2 * rho/(2 * gamma(1 + 2 * al))\n", " g0 <- rm\n", " g1 <- -rm/(aa * gamma(1 - al))\n", " den <- g0^2 + b1 * g1\n", " p1 <- b1\n", " p2 <- (b1^2 * g0 + b2 * g0^2)/den\n", " q1 <- (b1 * g0 - b2 * g1)/den\n", " q2 <- (b1^2 + b2 * g0)/den\n", " y <- x^al\n", " h.pade <- (p1 * y + p2 * y^2)/(1 + q1 * y + q2 * y^2)\n", " res <- 1/2 * (h.pade - rm) * (h.pade - rp)\n", " return(res)\n", "}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d.h.Pade22" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Computing option prices from the characteristic function\n", "\n", "It turns out (see [Carr and Madan][3] and [Lewis][8]) that it is quite\n", "straightforward to get option prices by inverting the characteristic\n", "function of a given stochastic process (if it is known in closed-form).\n", "\n", "\n", "Formula (5.6) of [The Volatility Surface][5] is a special case of formula (2.10) of Lewis (as\n", "usual we assume zero interest rates and dividends):\n", "\n", "

\n", "Formula (2.10) of Lewis

\n", "
\n", "
\n", "
\n", "(7)\n", "$$\n", "C(S,K,t,T)=S-\\sqrt{SK}\\frac{1}{\\pi}\\int_0^\\infty\\frac{du}{u^2+\\frac{1}{4}}\n", "\\,\\mathrm{Re}\\left[e^{-iuk}\\varphi_t^T\\left(u-i/2\\right)\\right]\n", "$$\n", "
\n", "
\n", "\n", "
\n", "\n", "
\n", "\n", "\n", "with $k=\\log\\left(\\frac{K}{S}\\right)$. \n", "\n", " - An anologous formula holds for puts." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### R implementation of the Lewis formula" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "
function (phi, k, t) \n",
       "{\n",
       "    integrand <- function(u) {\n",
       "        Re(exp(-(0+1i) * u * k) * phi(u - (0+1i)/2, t)/(u^2 + \n",
       "            1/4))\n",
       "    }\n",
       "    k.minus <- (k < 0) * k\n",
       "    res <- exp(k.minus) - exp(k/2)/pi * integrate(integrand, \n",
       "        lower = 0, upper = Inf, rel.tol = 1e-08)$value\n",
       "    return(res)\n",
       "}
" ], "text/latex": [ "\\begin{minted}{r}\n", "function (phi, k, t) \n", "\\{\n", " integrand <- function(u) \\{\n", " Re(exp(-(0+1i) * u * k) * phi(u - (0+1i)/2, t)/(u\\textasciicircum{}2 + \n", " 1/4))\n", " \\}\n", " k.minus <- (k < 0) * k\n", " res <- exp(k.minus) - exp(k/2)/pi * integrate(integrand, \n", " lower = 0, upper = Inf, rel.tol = 1e-08)\\$value\n", " return(res)\n", "\\}\n", "\\end{minted}" ], "text/markdown": [ "```r\n", "function (phi, k, t) \n", "{\n", " integrand <- function(u) {\n", " Re(exp(-(0+1i) * u * k) * phi(u - (0+1i)/2, t)/(u^2 + \n", " 1/4))\n", " }\n", " k.minus <- (k < 0) * k\n", " res <- exp(k.minus) - exp(k/2)/pi * integrate(integrand, \n", " lower = 0, upper = Inf, rel.tol = 1e-08)$value\n", " return(res)\n", "}\n", "```" ], "text/plain": [ "function (phi, k, t) \n", "{\n", " integrand <- function(u) {\n", " Re(exp(-(0+1i) * u * k) * phi(u - (0+1i)/2, t)/(u^2 + \n", " 1/4))\n", " }\n", " k.minus <- (k < 0) * k\n", " res <- exp(k.minus) - exp(k/2)/pi * integrate(integrand, \n", " lower = 0, upper = Inf, rel.tol = 1e-08)$value\n", " return(res)\n", "}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "option.OTM.raw" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Some notable features of R\n", "\n", "\n", "\n", "* Complex arithmetic with $\\text{1i}$.\n", "\n", "* Functional programming:\n", " * This is what allows us to code a function which is called as: \n", " \n", " impvol.phi(phiHeston(paramsBCC))(0,1)\n", " \n", " * We can define a function that returns a function (and so on indefinitely).\n", " \n", " * We could even conveniently define a new function: \n", " \n", " impvolBCC <-\n", " impvol.phi(phiHeston(paramsBCC)) " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "* We can conceptually separate parameters and variables rather than having to carry all the parameters around with each function call." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The rough Heston smile" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "params.rHeston <- list(H=0.05,nu=0.4,rho=-.65,eta=0.4)\n", "xiCurve <- function(t){.16^2+0*t}" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "phi <- phiRoughHestonDhApprox(params.rHeston, xiCurve, dh.approx= d.h.Pade33, n=20)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ " user system elapsed \n", " 0.976 0.034 1.009 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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QRaKsAsdi3lbf/GNbPdmYo+TQP+yfa3hhYggAACCCCAAAKBCiRqFrtAZdjYsAVI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\ncv9WQvtljvoFgMsm0ixAghTD0d9Db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T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\nAAECBAi0IfAPHnvwoYxJbh4AAAAASUVORK5CYII=", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vol <- function(k){\n", " sapply(k,function(x){impvol.phi(phi)(x,1)})}\n", "system.time(curve(vol(x),from=-.4,to=.4,col=\"red\"))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Figure 1: The 1-year rough Heston smile using the approximation $h^{(3,3)}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### How does $h^{(3,3)}$ compare with $h^{(2,2)}$ and $h^{(4,4)}$ ?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "phi2 <- phiRoughHestonDhApprox(params.rHeston, xiCurve, dh.approx= d.h.Pade22, n=20)\n", "phi4 <- phiRoughHestonDhApprox(params.rHeston, xiCurve, dh.approx= d.h.Pade44, n=20)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "vol2 <- function(k){sapply(k,function(x){impvol.phi(phi2)(x,1)})}\n", "vol4 <- function(k){sapply(k,function(x){impvol.phi(phi4)(x,1)})}" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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Yp3CCCAAAIIIIAAAh0CkUqQaGLH3zUCTuB4qx450dZzsyuYzXvCmvbayF67daqt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BBBAIScDPbekdwtUyX8O3zlD3RFN/VQ/p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\ngAACCCC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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "curve(vol(x),from=-.4,to=.4,col=\"red\")\n", "curve(vol2(x),from=-.4,to=.4,col=\"blue\",add=T,lty=2)\n", "curve(vol4(x),from=-.4,to=.4,col=\"green4\",add=T,lty=3)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Figure 2: The 1-year rough Heston smile in red with approximation $h^{(3,3)}$. The blue dashed line is $h^{(2,2)}$, and the green dotted line $h^{(4,4)}$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Sensitivity of the rough Heston smile to $\\eta$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "First, a function to compute the 1-year smile:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "vol <- function(params)function(k){ # A function to compute the 1-year smile\n", " phi <- phiRoughHestonDhApprox(params, xiCurve, dh.approx= d.h.Pade33, n=20)\n", " sapply(k,function(x){impvol.phi(phi)(x,1)})}\n", " \n", "myCol <- rainbow(6)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sub.eta <- function(eta.in){\n", " tmp <- params.rHeston\n", " tmp$eta <- eta.in\n", " return(tmp)\n", "}" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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GmfsZXz+i2OfFJeF90qpNqk3/gvqE1qS43pCCCAAAIIIIBAjxYgQerRuy83N75b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KYimDlEe38QHyat3n0u1aYk9daQV2o1A2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\nBERABERABERABERABERABERABERABERABERABERABERABERABERABERABER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Y5BBNCSNJ/CT6CN2FrIUoKH9QvtHEXYOSBetG2Fj4jgS7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\nQmCC", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "yrange <- c(0.05,.35)\n", "curve(vol(params.rHeston)(x),from=-.5,to=.5,col=myCol[1],ylim=yrange,lwd=2,ylab=\"Implied vol.\",xlab=\"Log-strike k\")\n", "eta.vec <- params.rHeston$eta + c(0.1,0.2,0.3,0.4,0.5)\n", "for (j in 1:5)\n", " {\n", " \n", " curve(vol(sub.eta(eta.vec[j]))(x),from=-.5,to=.5,col=myCol[j+1],lty=2,add=T)\n", " }" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Figure 3: The dotted lines are smiles with $\\eta \\mapsto =\\eta+\\{0.1,0.2,0.3,0.4,0.5\\}$. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Sensitivity of the rough Heston smile to $\\rho$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "sub.rho <- function(rho.in){\n", " tmp <- params.rHeston\n", " tmp$rho <- rho.in\n", " return(tmp)\n", "}" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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6pd4f7R+dSr9AvVH85eMerdyQ1BaZ6GCr/EDxkenW/Vo2mAC9Ppi6axH+yxyhVB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3eS6XhSuDVNIfQ2VOBESguAjYQPfQpzbgvSJcYQxXWIdPDoXeZuHO/h1d5ZVUYI/m\nnsdZF+JPU0I1dEcyo9RhAOc8BmlKovyOohveLq5ie+Z42BuTsQ/GYUfut0pFwsA7JvNH+svG\nrZ9EhXlSO9cwGfM0qbNz3/EQlzIPNs6nB0anvavo1+Da9cP80CjS0A+zxrwCbgPSgKcJ8cpW\nAzMEuk8awjObudF1rua9SDpbfbClG+jkxdiXzoeQVau8m8Fcj/0ZbF9xruFRWD/W0rNtPb8e\n72rnqvYLuYb+E0N1f2/r8+ncjwnflc/Y63CeyPOPw/pxdt5yoRAtOUEF346YbKmTQ9GBCAMf\neomtgggESUAGKUiaWY7rI+JPZ+DkSJ67KMtpi41eBimWhvZFQAREIMcEpjLGor8LLafybVNH\n25IQD6ERVJqrqV1ezf7P0Y3ccMHMUGgpXau24/hStDeV2l98G6r9F/sJA5V8/EcnWgeWPRYK\nuVW/zlPL79TdVewacu124R3WCoWSt8isfoFNrewWYbQWkmYUWojhWkhFm4knnFWuSVY4rNqy\n04HTa/rGaZjXxADxA6Jfk3Ocb0vwK3nPeJ4YS5yf0KLySZ2r+6SLc9+3JZZU7qV17gbS91Pu\nHUVaUf0rodBKa20LJLAW0VZwwzSEDiJC++WbIWLukQmh2uGBvCAaiff4IMolFAJdTPC+PTOG\nrD89FPo65mwAu94M7X7ITNHByD7X1uJpLVI3kV8+MwoiECgBGaRAcWY3MmsyfhQNRU+gu1Aq\nwf7zDew/4BReKIOUAiTdIgIiIALZIsAMd7RIuMXznTu+p3M27uMRxBAbdxSVya8YD7IfNdvb\nODZncgpdn8K/wK/vK3b2rm7qhJCbwrWEgTExW/HYM1zkb1LoDWv5YP9xWj9ovGkacDc9K13F\nkPau3da8z37gG4yRGcjWKrg5DH4J75/OuyfSmmSV9/G0DH1NXr/+m3NTRpKJTBODcazEI24J\nG/5GtxtMD/PfYSCbtJxwT9jgcb6pscjw5RjckyiLS4m8D+8f1+BCz5LPZ+kC+CZvpGEw82CT\nKWB8D2rv3GHEtj/ALqAVEnOS7RCewOHLyFvsc2qm6Gnyay18CiKQLQIySNkim6V4bdah19DW\naEdkrUqFFmSQCq1ElB4REIGyIsCCshtTmbWK5HJq6Id2bGxJuIfjPdBZVC5v7+F9l07OXUal\n+ldUdg9vy/gQKvrUkzswQ1j7I6iQo3BXsffZPowxuBYDUMt7Wgw0zXTu5qoG4BcG0s3Otr3x\nDNb6Q0uQLVkRbhliazO1hciKBd7aGKLbFVxbFGlpwvyFaHHyi7iZMS/+OwwQhqjd9CWuZvra\njeYw8ngwG1KzFr35aNVoR3cv617ohpAG+levMAAAMjJJREFUWq/8N+xTkV92BhwCMSetpXiQ\nr9iVd2+80tW+MCPkmhnV1p5v6TrrE2Fo3eHITBHl7eDtnmX75ET7oZbmr5aeDfZ8mO/H5JEy\nVxCBnBCQQcoJ5mBfsjnRjUH8MQr/hxVs7M1j44+AG4nsw5JK2JSb9kD0UAhm0CfxKIiACIiA\nCLSBwELnu2OArOXI/mYcXulCjEX1v2b/CvQcGkaFcxHjRrbARE2YwQwBnEsYmPrZxilt3OAa\nrpoUqnst/ia6jm3DuR+jPdCRRGVjiko60JJ2LRk8EabvsR3dqGWjMUVzgsz4YG9jpir3pfVr\nX8pgyDJXs+33ITc7yHckiqsvhcof/dkYohlcf5J3PzXJOVqkQgGaPm8/+u6JzIBZ97n/8Jk8\nh62CCOSbgAxSvksgzffbfyD8x+yOR5+mGUeqj1lXiGtQqgZpEPduh2SQgKAgAiIgAvkiMMrR\nZ44xGlRyT6SVaHi1C91HhX4L0mPd6y6kMkpLR+thPV+1OYNOLuJZWovcGCrrV33rah5JtfsW\n01Qfzbuse9+HxMHfrIbPQqEVk1t/c+7uoEWIv3FVG9AqRpfEdhuTTuuayA9+NlPf0s3iu8Vx\nP1i5GnB3uV7ede7MGlS8fy9itzFhAzAnk3nNS4yPemZSqP7xIKnQStSNZqBKxqLNio93oPdr\nTQqFFsSfz+zYr83zhyAzRfshq1uMQk+ih8jzXLYKIpBvAva5tBbSnRA/LimIQOYErIsd/5+7\nzplHpRhEQAREQAQyJcBaSWcyLqmO9ZIwKSkE79tROT6fcScYhtWBSR4G2/TQjHlZwro5M9Df\nUlk3hzV8fkCDxO3oA7SM1hcWPe28kP230I2YDetOl9XAO3hp4r9LpOEOVBeTrvcwdfdw7gJm\n89stqwmLi9zWIoLxHNg+wj7rVbmN4m7J+NBaDSnf89BrjEerZXt/xpGmHIEfTxWBVjb/L/QT\nZD+mKohAoREwg2R12aGFlrB00hP+NSedB/VMoAQ0BilQnIpMBERABDIngEnavpYZ7Tq70IxW\nY2M2soGMNeGP6h7cexutT5cxIH9VtzmbQrq9qzyO68NoSHl+YqjmT63GGbkBk9LOOVv/p90P\naC2w1iz2l51NS0yTlgMMCmNeQvReCC2hnkL3v9BStsi6btu2/v5QqGZs7HuJuz0TJVzPufVQ\nN57pzhZ527cKzygm7aNlpmnAGP2Q+NYiTV9lu3sghoe0VTFmyG9T42ovmRbKzfpQrE80FPA/\no8Z3MOU2gO0X6Bn2n5kUfNc5GhzDY8malGkjdd+D7TzKg56dCiJQsATs/4uSaUHie65QAARk\nkAqgEJQEERABEWgbAd+L+49Bt1J5tYqBo2XBBuhfTEXa1g+6eblzf/s+FEpt/It1WQu5Gosn\nnYDZoSLd8QTS0hXRI8F3Ih7rmWBiP3QDZuf52LgbDVLnKxrPeSrhbj7PsW2HPPvLxmPEAu4y\nFpuCuH3c4wBXuTXGZCj8mMghxDTobgBpmcul18Az4tuQa9a1LS6WQA4pyyeIqMpMEdtnMLwT\nA4l4VSQ2yUZ4XaJDI9sJ5HfbVZe1IwLFRaCkDFJxoS/d1KqLXemWrXImAiJQsgSsO52nlch/\ngRi6FAneh6hcH4O+oDvWYrYjo5da2tI1bFu6idWwfRmdaV3zWrq3lM+T95OY4MKjb9i/D51m\n47nouINPCjas4/0alM9hlM+JwcacLDbfm8/Kb9DLiAZKj/n0jCPyxyNa5BREoGgJmEHi94TS\n6GJXtKWQpYSPIN5P0GlZir+laGWQWiKj8yIgAiJQQAQYl7Q7Xe+utoVlG5NlXdH8XYjuT56u\najHjQ+h2RwX851TAH3PeV7aWDdZU2ouFS69jLM2ERpNQ+ZkdD/JVR1PtsC5YxRswODY2iHz9\n1MZhsX1ioLd1oeIC+WSMlk1KEHxgnBhjibal69wFlImNJaphuwzdHfzLWorR38Fn5Ft0Ldob\ntfq5aCkmnReBAiMgg1RgBRJkckYSmbnfC4OMNIW4ZJBSgKRbREAERCDfBGy9JAzSZPQxEzhs\nujo9fl/+fExEk9Dhq8+nt4eB2GKwr/g9ZuJZWpZms29r6hRVGOgrd7RWINI/hu1SM31s56L/\nka/LevjwzK05yRMm6DcYotnIo08wSVcwG90+zoenzQ44DdYS5HcPOFJFJwKFTqCkDFLgTdaF\nXnqtpM/6k5tmRtTK7YFdNoNkU8jazDQMpFUQAREQAREoVAKLnF+b5iNajZyts3MWA4cYg2TB\n21ifi9AZ6GzGk9zINnGgYj6I6cQbmNhhcuMCorRAtS00mqZ29/Pe8Tz5JWn5gqmtv6p3ddOJ\nbGY2JjOg1WctxgfhbSr6kL+BvI9T7bpMdDXn0wmuSR4G+/YHMZbpSO5hcgNT/acTQ47sZjHQ\nasc84k3SYW8zM8RsFH1g9BLTcH8ffArCZvlg4jWZmWX8lq3HFFrIVkEEyoFASY1BCpVDiRVB\nHmWQiqCQlEQREAERiCVAK9Lp/BH9O+deYDKG4V1XrUfjB3JuAZVj1ELwvmKQc9dRYT+JO2ax\nvafOufumh0Jft/BEs9Pretex0lViQEKbkY5NiGNTzAgz3IXC3fEanB8+MVR7Z5MHvatc31X+\nFWNWyX02scTKkGvg1e2qMVodiONjnrmnyTMcWEsQ7zgmGjeGp4H3fsd2Euc//9bVno5BIp7c\nBlqGrJve7lGRlnUnYuAwSWlPdpF6DvwA7j0HmSmyMWNWdk9H9CasGGOkIAJlQ0AGqciLmv7i\n4fUj+GPgmAo1PDtPvlttZJCK/EOl5IuACJQnAbrZbU6l/N+oO/Mzb9I7PLV26iz6er8Of4yG\n8cQJaEv0Hubl3snWqyCdSj7Tdg9ybp2Qq+pZ42q+oRUJ7xYTvKse7CpvovLOVN7OTFEVaa9k\niFDYLLEg7asTQnVXxzwR3rUuf9419G5woTl1rnb2NEwdhigvBoDWoG1I86m0ZJkx2sjzd5zj\nN+D2Gnphaij0WXz6s3Psf0S8I9BziJnuQt9k5z2KVQSKgkBJGaSiIB5AIrcmjjuQTQ3K/6XN\n9C3nrItED5SPYAbJ0mXdMxREQAREQASKiMB456ttQdmRzlNnTxb8RfxX/zNEb6/mgUVmt7Sx\nMbSKTGC7U/M7dMYIwOc09Cj6DZy2dky+kB0yNoGC3wNdjPpm5x2KVQRKhkBJjUEqmVJJkpE/\ncy1qiiaz/zayJvAHkf3qMxp9h+yeOeg4lOsgg5Rr4nqfCIiACOScgD+PPzX0XPBfIv7WtK1i\nb61NmIIdMQQJDVbOsxPkC5nlD7MzhAkUTiGPt6Ix7M/ENDLcK5fBus35U9FjaBGilcy/hgbn\nMhV6lwgUIQEZpCIqtKNIqxkfM0JDkqSb1nm3G3of2f25/uVOBgnoCiIgAiJQSgRGYoA+aDaN\ns6engmdhVr8UfYGORSm1gGAaTkL1aC7m4RH0W7RbLx+eHKIo0ZH+E9D7aAVixgc/ie0jbH+P\nYcrh32K/CeXwOaIO4OlB6Bm75alDFOfaRPOcX5MZFwczTm775c7vST6sntMkLHa+h42jQ6dy\n74G0gm4ykXFoTW7SgQikTkAGKXVWeb/zflJg3efoZ51SsPFJ/GLkbknp7uBukkEKjqViEgER\nEIGCIMCaSb+n8jmRyud+zRPke1JpvRJFjdLA5vc0P2OtSBiH4zERt6OxGIk6E/sfYJSIszBC\nD++7RLoMHkHafksaz02UMvJyELJ1ifa3vCW6JzfnwutZ/R/lsUVu3hfsW/icnYze4TM3HdUg\nmr5WaeEy59eNfyPXd+GZsehL9pdF7m9gO41zb7DdI/4ZHYtAEgIlZZDCM90kyWyxX7IBr+8g\nG3yaSrBpOceifqncrHtEQAREQAREoCUCTNpwQ3emlqY/3HNUOO9dztTfa7rQvMb7QzYm9ndU\nyG0WvBMRXe9aDzNCIesKbj/+mZy1HtEHbVuaPTaZ2Ti1tJ1eFTAeu9N08CuuT0BT2Z/LRAZz\nbUvfsTnEN2XVzcl26AI3kHGydYg/qAtnh0LN0su7LiOKPYl7ENtekegW8V77ofK9yHGTzeRQ\n6FlOmLIY/AZEvifaB+2NmHku9C+2MSFkf/9vjDmR9935tF51YWZCK1u0Kc2MtHK5FZUudHR8\n4ijTaXzOnmY7mXtncu+cesqYTM3p60LL4u+3Y+J5k43Vkwg+hFPvTQ2X9XzdYCtD4prdeE3/\nioAIlBqBF8kQXRhsOtOUQrQFiV/1chrUgpRT3HqZCIiACOSOAL/ED8UgjWM7l+3/jXK+IrW3\nW3en5l2jUnu28S5mfNsM43IzrTgvsh3H9ntUg2zBVM/1I+Pj6+l9L65NRd/zzHy2q+63Zzj3\nQPwzdkxL0C/QBVw/ltaj7fPXImRdFv3xCBPkMYCrus3Z8Qkox+OaEtFq+RyfkavQZD4v1grU\nENl/ge11dIP7cctPZv/KeCYkad5tNPvv1RuKgkBJtSAVBfEMEsl/kOExRU+y3SFJPPxY4nZF\noxE/kLmdUS6DDFIuaetdIiACIpBjAlappIJ7FhXe+Ww/t/EhrSfBP8WfsKmIVia/Tev3p35H\nd++7YnYGUAfHTMQF70MYp0MxOsdgeI5gf1+2O3H/VhifDXI/cUJc+lo99P3gNR49hGzChY1a\nfSRHN0Q+Bz/kM/BLzM4RiV7L+Z/adbTt942LDye6LS/nSNP1fIankkarXymIQCwBGaRYGgW+\nb8bnLETLcdgoTWP7LnoG2S9gtrUueDMQrcrhNR3OZJvrIIOUa+J6nwiIgAjkgcAi59ehcnlJ\nigZpHf40/Rq9hejx5L9GF6NN85D0AnlleOrtbWFwBvoPymuLSmtQmCBhIKZiGLoZvYe5WIGs\nZchMBmVZXGG282uQj7vQV8WVcqU2BwRkkHIAOehX2C91ZoimIzNCsTLzxC9N4dXQ+7PNR5BB\nygd1vVMEREAEioZAePrp8/jz9THib5i/vmiSnlFCrYuh/wm6Br2NViDLPxX08ExzP8go+iw/\njJH4BjM0Az2O/oAxPoDZ43pm+bVZjR5jdzR5sTF0CiIQS0AGKZZGEe53Jc1mhDZEaxZI+mWQ\nCqQglAwREAERyBcBKp7HMttYCj/UWQuSTUudKPg+XEtxjFOi5/N1rqW1ncL5mUSenkMj0YFo\n7XylMvre8YzFwfzsiH6DHsIwXBi9FrstxfE6Nisj+a2Jzaf2RQACMkj6GAROQAYpcKSKUARE\nQASKiwAV7beoeK5ke6t1zWp76j0VlPDipsvZjkY3o+FoCLLKSwEEW7PJb42OQX9G96MxyFqG\nGC9UuAFjsA9lYxMo2HTaK5FNoPA5uovy2qtwUx5sysjvduTdF9r4qGBzqdjSICCDlAY0PZKc\ngAxScj66KgIiIAJlQYBK+KFUQG2sSi3bO2lV2qxtGQ8vRHsQZuOP6FE0GVmXNGbn9pcnjstX\ncy0AA+WZldrW2wkboHbN32ULv/p6ZOlhCunw2Kq72J6LDkABpKH5W4M6Q3m8Tbm8SJmMpJz2\nt2m4g4q7mOIh7xuaQaK1s18xpVtpzToBGaSsIy6/F8gglV+ZK8ciIAIi0CIBKqEHUCF/0yqi\n6JXMxq1YlzRbrNZvmfiF/jOumWlhvRz/HfoSWQsUS2X4O1p4ZhjXPkITEEs+eWaADcdh8TSg\n7Zo/Z13/vE2w0L35tfydYeKMteF9MMbnUliPgvtV+UtN4b95rvNd4TR7qbPujwoisIpASRmk\nIuynvKogtCMCIiACIiACJUmggws9T8aep7L+QxzHTxGmI90QwsA4zE6LYX+uDEA2LjdeLS0W\nymQR7h60EC2IbKP7mCxbdzQ+hDBR7oP4s/k4xgwdzewPjGdyQ9luzHY5jD8A8tscP5SPNBXL\nO9d2oUWktUexpFfpFAERKF4CakEq3rJTykVABEQgLwSsVcl+zc/Ly4v8pbSAPIv5fBCdibYv\nxckUiryIlPziI1BSLUjFh780UyyDVJrlqlyJgAiIQNYIULG32dNsXZ3HaRE5ztaoydrLiiDi\nqc53hMVQuNjMcg+gCaiFLoJFkCElUQSKi4AMUnGVV1GkVgapKIpJiRQBERCBwiEwjkkNbOwM\nJuBujMECtBw9xvGpjA/pWzgpzWZKfIj8XofGkvc6ZDPLfYHuRiNSmzY9m+lT3CJQNgRkkMqm\nqHOXURmk3LHWm0RABESg5AhEzNIhmIK70BSMgo1hKonAFNrrYQQPoZVs00QZ4vxl5PcctIe6\nHCYipHMikBMCJWWQNElDTj4zeokIiIAIiIAIZI/A5o6GFOeejsj9xyVeeBUTcaGlgskIPjZ1\ndCGmAS+U4EMshnRIe+c2Z8IEmzhhIyZM2JytTRzBDHvuYvQFahKqXeiCJid0kHUCZlgpo6V8\nfkZl/WV6gQjkgYAMUh6g65UiIAIiIAIikE0CR7sQ6w0lDPVUbA9kkaLfoi4YpgUcf8qdk9Dr\nVS4U+JgdGxvF6rBrUeHoxbv6Y3r6Yc6eZaa+CbEpXOzcOpijm7mHWfDc19z3AvddbeljAadv\nRroQhwqFQIDPztGkw2YlHFUI6VEaRCBoAjJIQRNVfCIgAiIgAiJQoAQqXegSkobCrTUbYEJ+\nyPHmbAdgRAYnSjZd9q7j/KEID+MWc69taexx1JNdDQfDu7uQTfG9KtDCcABm5z5O2GKq7DYG\nnl3Ie6Zx9A1qYpDWcCGbUrx/4536t8AJLKAs1y3wNCp5IpA2gYq0n9SDIiACIiACIiACRUog\n5Ds4N57Emx5OlgkMze1Uhm3dozXYrkEzTle21Rw3cG0Zzmhl/PPLnXu3k3OncO9C3NECtvNZ\nPGdWTxdaEn+vjouPAOU+n8/AD4ov5UqxCKRGQAYpNU66SwREQAREQATKkgBjfD4j46aUQzcX\nssVjH035Ad1YVAQwR/MxSdY6qCACJUnAmscVREAEREAEREAEREAERCBVAmaAu6V6s+4TgWIj\nIINUbCWm9IqACIiACIiACIhAHgnQemRjkNSClMcy0KuzS0AGKbt8FbsIiIAIiIAIiIAIlBQB\nKo9zyVCXksqUMiMCMQRkkGJgaFcEREAEREAEREAERCA5gcece5tWpJ2T36WrIlC8BDRJQ/GW\nnVIuAiIgAiIgAiIgAjknEFlna3TOX6wXikCOCKgFKUeg9RoREAEREAEREAEREAEREIHCJyCD\nVPhlpBSKgAiIgAiIgAiIgAiIgAjkiEC5d7EbAOeN0Sz0FWJtOwUREAEREAEREAEREAEREIFy\nJVDqLUinUrD/Rh3jCthWf34fTUIvoI/Qd+g8xKLfCiIgAiIgAiIgAiIgAi0RWOH8RrOc10x2\nLQHSeREoYAJ3kTYmWnFrxqSxP/u2wJmdN5N0CzITNQ3ZuatRrsPJvNDe3TnXL9b7REAEREAE\nREAERKCtBGqcfxed1dbndH/JEqgiZ1aXHVoKOSzHLnaXU3BmmH6NbowpxE7s347sy/4s+h9S\nEAEREAEREAEREAERiCPAQrFLGpxbO+60DkWgJAiUehe7RIW0EyffQ7HmyO5bhoYjW/xsL6Qg\nAiIgAiIgAiIgAiKQmMACTNJaiS/prAgUN4FyNEhdKbJPWyg2m6ThS7RFC9d1WgREQAREQARE\nQATKngB9qeYDQQap7D8JpQmgHA3ShxSlTdKQKFhT8XbIJmxQEAEREAEREAEREAERSEAAg2Qt\nSN0SXNIpESh6AuVikKxL3f3obPQ22hYdhmLDehxYtzsbZPZa7AXti4AIiIAIiIAIiIAIrCZA\nBXIBJkktSKuRaE8EiobAkaT0UTQB2cwasZrCcTQczE4tsutvIX4UyWnQLHY5xa2XiYAIiIAI\niIAIZEKAGexOR+MyiUPPlhQBzWJXRMX5CGk1WbCZ634Yo1gTZGsf2fijB5DNYmdGSUEEREAE\nREAEREAERCABAWawe5lWJKsUK4iACJQoAVtItjKPeVMLUh7h69UiIAIiIAIiIAIiIAIZEVAL\nUkb48v+wDSi01qRqtAQtQEuRggiIgAiIgAiIgAiIgAiIQJkTKJdJGramnO9As9A8NBHZdN7T\nkJmkb9GtqAdSEAEREAEREAEREAEREAERKFMCFWWQ7z+Tx4si+bSJGd5BZpLMGFlLUndkM9id\ngn6CzkD/RgoiIAIiIAIiIAIiIAIiIAIiUFIEjiI3NuHCc2hIkpzZhA27ofeR3b8TymXQGKRc\n0ta7REAEREAEREAEREAEgiRQUmOQggRTiHHdT6Ks+5yNN0ol2PikReiWVG4O8B4ZpABhKioR\nEAEREAEREIHsE2Ca70/R9tl/k95QBARKyiCV+hikLflAWZe6lSl+sOZz31jUL8X7dZsIiIAI\niIAIiIAIlCUBut+sQ7eb9csy88p0SRMo9TFI31F626BKZAvBthasBclMlU3YkGlYgwhS5dsp\n05fpeREQAREQAREQARHIJQHM0QJM0lq5fKfeJQIikDmB44nCxhQ9iXZIEp2NQdoVjUZ1aGeU\nSdiAh1lDLfxue3+q6pDJS/WsCIiACIiACIiACOSKAN3r3q51/vxcvU/vKWgCJdXFLtUWjoIu\nkSSJs9noeqJL0KFoOpqG5iIba9QVdUcDUB9k5ugc9BbKJHzDw5sh+7CkEqzV6l5kpkpBBERA\nBERABERABAqeAL8uL6DiYr1vFERABIqQwGDS/AAygxTfmmOLxI5Hf0f9UT7CUF5q6UrVUOUj\njXqnCIiACIiACIiACKwiQAvSv9Ftq05op5wJqAWpCEt/Amk+NpJuazWy9Y+sO5stHLsQKYiA\nCIiACIiACIiACLSNwHxakaynjoIIlBSBUu9il6iwrGudSUEEREAEREAEREAERCB9Ap/S/WXT\n9B/XkyIgAsVAYASJ/ASdluPEqotdjoHrdSIgAiIgAiIgAiIgAoERKKkudqW+DlJbS70XD9iE\nCbZVEAEREAEREAEREAEREAERKDMC5djFLlkR/4OLj6KZyW7SNREQAREQAREQAREQAREQgdIk\nIIPUtFzNGMkcNWWiIxEQAREQAREQAREQAREoGwLqYlc2Ra2MioAIiIAIiIAIiIAIiIAItEag\nHA2SLWg2EG2M+qHOSEEEREAEREAEREAERKANBMY5X8U6SDfNcL5TGx7TrSIgAgVCYGvScQey\ndY/iF4q142/RragHykfQLHb5oK53ioAIiIAIiIAIpE1gofPda533K523Ca4UyptASc1iVw5F\n+WcyGTVFk9l/Gz2NHkTPodHoO2T3zEHHoVwHGaRcE9f7REAEREAEREAEMiLwH+fbY5Aa0G4Z\nRaSHS4FASRmkUp+k4Sg+cReh59Ef0BiUKLAQtNsVXYXuR5OQGalcB/twKWSXQGV2o1fsIiAC\nIiACIlAeBI52IYc5WjzTzbblUQp9yEJteZRK3nJZUnXYUjdIh/MxmYBsuzLJR8Zaj15H+yFr\nZfo5yqVBin5pF/NeBREQAREQAREQAREoCgJ/c5fTLefJ/xRFYpXIXBCoycVLsv0Oazkp5fAp\nmfsE/awNmXyTe+ejQ9vwTBC3bkskat0IgmTLcYzkUhd0N1IoPwLDIlm+u/yyrhxDYFiEwt2R\nrTblRWBYJLt3l1e2ldsIgWFsl6CRSCF7BMwcfZi96HMXc6m3INnYom2QGY9oK00yujbDnQ00\ntAkbch0+yPULy/B99nmwcHvjRv+WGYGdI/lV+ZdZwUeyq/Ivz3KP5lrlHyVRntto+b9TntlX\nrttKoNSn+f4XQDZB/0U7JIETHYNkY5VsqsrHk9yrSyIgAiIgAiIgAiIgAiIgAiVKoNRbkP5N\nufVElyDrMjcdTUNz0SLUFXVHA1AfVIfOQW8hBREQAREQAREQAREQAREQgTIjUOoGySZfuAY9\ngS5FNg1lfEvSMs7NQFeh69BUpCACIiACIiACIiACIiACIlCGBErdIEWL1GayOzZyYK1Ga6IO\nyBaOXYgUREAEREAEREAEREAEREAERMCVi0GKLWrrWmdSEAEREAEREAEREAEREAEREIEmBEp9\nkoYmmdWBCIiACIiACIiACIiACIiACCQjIIOUjI6uiYAIiIAIiIAIiIAIiIAIlBUBGaSyKm5l\nVgREQAREQAREQAREQAREIBkBGaRkdHRNBERABERABERABERABESgrAiU4yQNZVXAymwTAjVN\njnRQbgRU/uVW4k3zq/JvyqPcjlT+5VbiTfOr8m/KQ0ciIAIisIqALQpsUihPAir/8iz3aK5V\n/lES5blV+ZdnuUdzrfKPktBWBERABERABERABERABERABERABERABERABERABERABERABERA\nBERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERA\nBERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERA\nBERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERA\nBERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERABERA\nBERABERABERABERABERABERABERABERABERABERABERABERABERABAqLQPvCSo5SIwIZE7DP\n9FC0PapD81AmoS8P74NmoeWZRKRnc0IgiPLvREqHoJ3RWmgRWokUCpNAEGW+LlnbHdnWvuu1\nSKE4CARR/oPJqv3d2CyS5bnFkXWlEgJBlH8syL046IOmxp7UvgiIgAgUM4ENSfwXyMdoHPv9\nUTrB/uN9G1l89sdTobAJBFH+PyeLM1HsZ8gM0hmFnfWyTV0QZX4R9MwQRcvcflg5t2yJFlfG\nMy3/3mT3cRQt++j2Fc6ZaVIobAKZln987g7ihH0GXoi/oGMREAERKFYCIRL+OrLK7M/QBuhk\ntAxNRp1RW8OfeSD6B1MGqa30cnt/EOW/L0luQBPR+WgLZMboS2SfgxOQQuEQCKrMrWwfRVsj\na3l+Htm5XyOFwiWQafm3I2uvIivrh9CBaHd0J7L/Bz5DHZBCYRLItPzjc9WDE98j+zzIIMXT\n0bEIiEDREhhByu0/tlPjcmAmKdH5uNuaHVpFyX5Vtu429rwMEhAKOARR/qPIn5X1fnH53C5y\n3lojFQqHQKZl3omsTETTkLUWR0MVO3beutjEno9e17YwCGRa/ruTDfu+Wy+B+PAMJ+zaUfEX\ndFwwBDIt//iMPMGJ6N97GaR4OjoWAREoWgKjSfkKZGNGYkNXDmzs0PuxJ1vZt9am8egNdCWy\nP5Q7IoXCJZBp+duvye8hM0GJKsXWimRdrxJd47RCHghkWuYHkmb7bl+eIO2XRq4dnOCaThUG\ngUzL/0SyMRENT5Cdn3LOPhsXJrimU4VBINPyj83FKRxYeR8e2T4fe1H7IiACIlCsBCpJ+Eo0\ntoUMfMT5GmT3pRJu4ybrqjcIWeXJ/uOUQQJCgYagyz8+m9bNZiH6Jv6CjvNGIIgyt8qvfbd/\nnCAXP4pcs3sUCo9AEOWfLFcXcNE+G9ZdW6HwCARZ/huSvSXoRmT/11u5yyABodyD/WqqIALF\nTqAbGbBuMS3NPDSPa/Yfag/UWrCK0cnoN2hiazfrekEQCLL8E2XoPE5aS+R/E13UubwQCKLM\ne0VSnuj/Dfs/w0K/xo3+LTACQZR/S1lahwtnIfuR7H8t3aTzeSUQVPlXkIv7kXWz1cQseS3S\nwnu5fTgURKDYCVjl1cKcxk2zf6OVHes6lyz05uId6Al0V7Ibda2gCARV/okydTQnbbIO63I5\nEikUBoEgyjxZHKn+n1EYNMovFcnKzmikW372N+JpZCZpOPoeKRQegaDK31qIt0Y7oWXIWpAU\nRCBMQAZJH4RiImD/Kca3eq7gnMlC/LXGs6vHjdRHT7SwNVNksxdZC5JC4RHIdvnH53gYJ6y7\n5WxkLYs2lk2hMAgE8Z1PFkd0rFlr/2cUBo3yS0WysjMa6ZSfmaIn0Q7oemSz2SkUJoEgyt9M\n0fnoL+j9wsymUpVPAi1VKPOZJr1bBFoiYGOJ5sdpJMf2K5/1G+6OEoXo+YWJLkbO/YqtDdo+\nAy1FNsOVybrmWbBfluzYphZVyA+BbJZ/fI6s1eifaBraDX2BFAqHQBDf+RmR7ET/f4jNXfRc\nsv8zYu/Xfm4JBFH+sSlen4N3kM1Weik6EykULoFMy38NsnYfGouuQdG/97a1YAbb9q3rvkKZ\nElALUpkWfJFm+xXS/Xlc2r/kuA7NQtFKTdwt4fPWfL4g/kLM8U8i+w/GnIvdHRU52ITtV7EX\ntJ8zAtks/2gmzABfi8wo26+Kh6KZSKGwCATxnU/FIE0vrGwrNRECQZR/FKatd/YisjGqp6Db\nkUJhE8i0/K1bnU3CZCHRjyD7cN5+KLX6wLFIoQwJyCCVYaEXcZaTdX2zX/h3QdZNInYskv3R\n2xTZr4PJuss8xvXPUHzYmRND0MPIfrWajxTyQyCb5W85shZ161YzDD2OjkdmrBUKk0Cm3/lo\nq+DuZM++/7HBzll4r3GjfwuQQKblb1naFr2AKtHByIySQnEQyKT87ceRGxJk0+rEI9AU9AQa\ngxREQAREoKgJ/JjUe3RuXC5+Hzl/ZNz5VA8vjzy/Y6oP6L68EAii/O0Po32GHkXWxUKhsAkE\nUeZjyeJ3qGtMVtdk334M+QjpR8QYMAW2m2n5dyQ/E5GNZ7GudQrFRSDT8k+U2w6ctL8Bzye6\nqHMiIAIiUIwE7Nd/635nrUR/QdZEfknk2Cq88cHO2X+ER8RfiDuWQYoDUqCHmZb/2uTLWgft\nM/EyshakROrCeYXCINCWMt+SJFvZfhKXdOs+Y+c/RPYjylFoDLIuPEOQQuESyLT8LyZrVvbW\njTLRd93ODUcKhUkg0/JPlCsZpERUdE4ERKDoCaxDDp5DDcj+8Jms+0RvFB9kkOKJFP9xJuX/\nI7If/cwk23YrfkwllYNUy7wlg2QwrCvlPBQtd9v/JVIofAKZlL+1EEbLvKXtdYWPoKxTmEn5\nJwIng5SIis6JgAiUDAGboWYblMgYlUwmlZEWCaj8W0RTshcyLXObnGMDtDmqLllKpZuxTMu/\ndMmUR85U/uVRzsqlCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiA\nCIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIiACIhAgATaBxiXohIBERAB\nESg9ApuTpV3QUrSo9LLXYo7W4MrBqBrNjNy1PVvTBFQfOZeNTaJ3Z+M9ilMEREAEREAEREAE\nREAERKCNBC7nfo+Ob+NzhXZ7JQn6HTomxYSZMbR83xRz/8ORcz1izmVjN9G7s/EexSkCIiAC\nIpCAQLsE53RKBERABERABEqNwNFk6ArUJcWMLeG+Z9BnKd6v20RABERABEqEQEWJ5EPZEAER\nEAEREIEgCUwmskOCjFBxiYAIiIAIFAcBGaTiKCelUgREQASKiYB1EdsXDUAT0evoY5QodODk\n7mhPNAU9jUJoD/Q/NB21Fvpww5FofTQLjUPW+lOHLOwake3vhOz8Y8i63ZkJegtZy9JR6CP0\nHLJrP0JfotGopWBptdYpy8eryIxVNGzIzl5oYzQJvYrGonTDpjxoY6DmoyfTjUTPiYAIiIAI\niIAIiIAIiIAIpE+grWOQruZVZkAa0IzI1iY0sPPxP8ptwjmr7NtYn9moBs1DtyI7dwBqLezD\nDSuQ3T8HrYzsv8+2H7JwP7LrUVnazLRsEzl3KdsFkX27Z2eUaBzQw5F7erC1YObodmTP3Ina\noWg4hx1Li71rKjImxsHeZc8lC4nevRUPzEWWxyHJHtY1ERABERABERABERABERCB7BFoi0H6\nBckws/A86hVJ0jpsrbXDzptpiIau7FjrjFX4rZXFQkd0C7J7TQei1oLNKDcbbRa50VqCzITY\n85b2aLBJJuzcL6Mn2EYNUi37j6CDUDSNiUxKrEEykxNN683sx5qeQzm2d72G+iILNjPdv5Gd\nPxElC/Hv/gE3Wx5noi2TPahrIiACIiACIiACIiACIiAC2SWQqkEyg2CtQdbKsWZckjpz/B1a\njGzfwghkZuE0O4gJ1gpjEyPYtdYMUgfusVaZV1GsQanm+HwU+3wygzSNe+2Z2BBvUuzaw8jS\n1RPdFNm/hm18MONn95kBiw2W92XIWtZi0xt7j+3Hvtv2rdugPbMpUhABERABEcgygdjuAFl+\nlaIXAREQAREoYQIDyNtayMb+LIzL51KOH0PWurNJ5FrUPNj52GBd0v4be4J9a22yuGNl5mgF\negvtjt5GZyEzEda17a/IxhKlEj7hJnsm1WCm6HT0JrJ3xgZL48ZoPLKWKWvxicrGSL2P+qBo\nyxK7LQaL52VkXfp+jr5ACiIgAiIgAlkmIIOUZcCKXgREQATKhIBV5i1Mbtw0+zd6foPIla3Y\nmoGY2ezOxjE7sac/4mB+nEZGbrDJGUahHdHV6HNk3e5GoiqUSpiYyk0x9xzHvrWU7YzMnMWG\nDSMHtjXjFa/dItejHCKHCTd7c7YicuX3bJO1OiWMQCdFQAREQATaTiD6H2/bn9QTIiACIiAC\nIrCagLUSWbBuZInCGpGT1upjYQmqRHbeut7FhjVjD9h/BZnxiQ1fRg6s+5mNYdoIWZe6A9Ae\n6EI0FO2PWgs2OURbwkhufhR9iO5C1kIUzX80fy9w7krUUrBuhK2FSdywJ/or+ik6Df0DKYiA\nCIiACIiACIiACIiACOSJwOW816PjW3m/Tcpg9z3fwn1mKOz6DyPXraJvx7tEjmM390aumeFJ\nFsyM2fPR1qvovWuzMw1Z/NGubJZ+O040SYO1PMWHzTlh998Uc+HhyDnr8mbhYmT33GgHkdCR\nbQP6IHoibrsDx9uiZK1b8e+2981BZiQHIgUREAEREIEsElAXuyzCVdQiIAIiUEYErKvcu2g/\nZAYgNmzBwWFoIrIuZxZuQWYuLkLVKBpsCmtrLUklWDe1N9B9cTdb97fJyCZwWBG5Zt35LJip\nCipcQkTWsmXjkaylx8Jy9CKyMVYHodhgxud1dCeyvKcaZnPjb5CN4bIWqxBSEAEREAEREAER\nEAEREAERyAOBaAuSdSd7vAUdEEmXmQLrrrYAnYNsDM2ZyAyLaSsUG6zlxozCp+gydDuyWd7M\nENj5VLrHWfc7u9fSdiI6Gt2D7Nx/UTTswY6d+xr9DfVHll47l24LEo+Gu/GZEZuAzMBYsBYt\nM0qmC9G+6Fz0DbL1kOINJKeaBDNSlq7Y1iu74bnIeTNkCiIgAiIgAiIgAiIgAiIgAnkgEDVI\nVmFvSafFpGtr9j+IudcMz/9QS4ubnsq1t9BC9BGyyr+1zNi7dkathbW54d/IjEc0fYvYt25v\nNsYpGirYeRBZS5LddyQKwiARjbsOWZw320EkbMLWWovMPEXTNY39E1FroSWDtB4PLkZL0KDW\nItF1ERABERABERABERABERCBwiHQlaRsiVoaa2OtLe1bSK61nJipMJORarD4zFhsiJJ1QbMx\nQj1RrkInXvRDNAC1lN9cpUXvEQEREAEREAEREAEREAERKFACw0mXdcf7ZVz6enM8D81BGicb\nB0eHIiACIiACIiACIiACIiACpUlgINmyrnBmhK5Eh6M/oLHIussdgxREQAREQAREQAREQARE\nQAREoGwI7EZOP0DRMTor2R+NjkYKIiACIiACIiACIiACIiACIlCWBLqTaxs/1KEsc69Mi4AI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAI\niIAIiIAIiIAIiIAIiIAIiIAIiIAIiIAIiEDGBP4faZt24353OdIAAAAASUVORK5CYII=", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "yrange <- c(0.05,.35)\n", "curve(vol(params.rHeston)(x),from=-.5,to=.5,col=myCol[1],ylim=yrange,lwd=2,ylab=\"Implied vol.\",xlab=\"Log-strike k\")\n", "rho.vec <- params.rHeston$rho - c(0.05,0.10,0.15,0.20,0.25)\n", "for (j in 1:5)\n", " {\n", " \n", " curve(vol(sub.rho(rho.vec[j]))(x),from=-.5,to=.5,col=myCol[j+1],lty=2,add=T)\n", " }" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Figure 4: The dotted lines are smiles with $\\rho \\mapsto \\rho-\\{0.05,0.10,0.15,0.2,0.25\\}$. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Sensitivity of the rough Heston 1 year smile to $H$\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "sub.H <- function(H.in){\n", " tmp <- params.rHeston\n", " tmp$H <- H.in\n", " return(tmp)\n", "}" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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Xj5PxMvlGmUu/AXjQdz0P1ZyjkznStvPA/uI4AAAggggAACCBS0AAVSQe/e7Gxc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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "yrange <- c(0.05,.35)\n", "curve(vol(params.rHeston)(x),from=-.5,to=.5,col=myCol[1],ylim=yrange,lwd=2,ylab=\"Implied vol.\",xlab=\"Log-strike k\")\n", "H.vec <- params.rHeston$H + seq(0.1,0.4,0.1)\n", "for (j in 1:4)\n", " {\n", " curve(vol(sub.H(H.vec[j]))(x),from=-.5,to=.5,col=myCol[j+1],lty=2,add=T)\n", " }" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Figure 5: The dotted lines are 1 year smiles with $H \\mapsto H +\\{0.1,0.2,0.3,0.4\\}$. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Sensitivity of the rough Heston 1 week smile to $H$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "A function to draw the 1-week smile:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "vol <- function(params)function(k){\n", " phi <- phiRoughHestonDhApprox(params, xiCurve, dh.approx= d.h.Pade33, n=20)\n", " sapply(k,function(x){impvol.phi(phi)(x,1/52)})}" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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RJGDwciSYJproTToUufxRYEIAABCEAAAhBIBQEEUioeU38iP6OFCR8TQpv37xrw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", "text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "yrange <- c(0.05,.4)\n", "curve(vol(params.rHeston)(x),from=-.15,to=.15,col=myCol[1],ylim=yrange,lwd=2,ylab=\"Implied vol.\",xlab=\"Log-strike k\")\n", "H.vec <- params.rHeston$H + seq(0.1,0.4,0.1)\n", "for (j in 1:4)\n", " {\n", " curve(vol(sub.H(H.vec[j]))(x),from=-.15,to=.15,col=myCol[j+1],lty=2,lwd=2,add=T)\n", " }" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Figure 6: The dotted lines are 1 week smiles with $H \\mapsto H +\\{0.1,0.2,0.3,0.4\\}$. The smile flattens as we increase $H$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Ease of calibration of rough volatility models\n", "\n", "- Rough volatility models are typically very parsimonious.\n", "\n", "\n", "- Moreover, from the above sensitivity analyses, the effect of changing each parameter is clear.\n", " - Contrast this with the classical Heston model where volatility of volatility and mean reversion are competing effects." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Dynamics of the rough Heston volatility surface\n", "\n", "- All rough stochastic volatility models have essentially\n", "the same implications for the shape of the volatility surface.\n", "\n", "\n", "- Recall from Lecture 2 that we can differentiate between models by examining how ATM skew depends on ATM volatility keeping model parameters fixed.\n", "\n", "\n", "- In Figure 7, we that rough Heston dynamics are not consistent with empirical dynamics, in contract to rough Bergomi." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "

" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Figure 7: Blue points are empirical 3-month ATM volatilities and skews (from Jan-1996 to today); the red line is the rough Bergomi computation with the above parameters; the pink curve is the rough Heston computation." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Summary of Lecture 4\n", "\n", "* We introduce forward variance and affine models.\n", "\n", "* We showed how to compute the characteristic function for any affine forward variance model.\n", "\n", "* We applied these general results to the classical Heston and rough Heston models.\n", "\n", "- We explained the idea behind the Padé approximation to the rough Heston solution.\n", "\n", "- We explored the effects of the rough Heston parameters on volatility smiles.\n", "\n", "\n", "\n", "- However, though rough Heaton is highly tractable, its dynamics are unreasonable.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### References\n", "\n", "
\n", "\n", "
\n", "\n", "
    \n", "\n", "
  1. ^\n", "Elisa Alòs, Jim Gatheral, and Radoš Radoičić, Exponentiation of conditional expectations under stochastic volatility, available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2983180, (2017).
    2. \n", "\n", " \n", " \n", "
  2. ^ Lorenzo Bergomi and Julien Guyon, The smile in stochastic volatility models. *SSRN* (2011).
    3. \n", " \n", "
  3. ^ Peter Carr and Dilip Madan, Option valuation using the Fast Fourier Transform, *Journal of Computational Finance* **2**(4), 61–73 (1999).
    4. \n", "\n", "\n", "
  4. ^ Omar El Euch and Mathieu Rosenbaum, The characteristic function of rough Heston models, *Mathematical Finance*, forthcoming (2018).
    5. \n", "\n", "
  5. ^Jim Gatheral, *The Volatility Surface: A Practitioner’s\n", "Guide*, John Wiley and Sons, Hoboken, NJ (2006).
    6. \n", "\n", "
  6. ^\n", "Jim Gatheral and Martin Keller-Ressel, Affine forward variance models, available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3105387 (2017).\n", "\n", "
  7. ^\n", "Jim Gatheral and Radoš Radoičić, Rational approximation of the rough Heston solution, available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3191578 (2018).\n", "\n", "
  8. ^ Alan L. Lewis, *Option Valuation under Stochastic Volatility with Mathematica Code*, Finance Press: Newport Beach, CA (2000).
    9. \n", "\n", " \n", "\n", "
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