{ "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 5: A microstructural foundation for rough volatility, the exponentiation theorem\n", "\n", "\n", "\n", "Jim Gatheral \n", "Department of Mathematics \n", "\n", "

\n", "\n", "$$\n", "\\newcommand{\\wh}{\\widehat}\n", "\\newcommand{\\Ind}[1]{\\mathbbm{1}_{\\left\\{#1\\right\\}}}\n", "\\newcommand{\\Rplus}{\\mathbb{R}_{\\geqslant 0}}\n", "\\newcommand{\\Rpplus}{\\mathbb{R}_{> 0}}\n", "\\newcommand{\\Rminus}{\\mathbb{R}_{\\leqslant 0}}\n", "\\newcommand{\\wt}[1]{{\\widetilde{#1}}}\n", "\\newcommand{\\beas}{\\begin{eqnarray*}}\n", "\\newcommand{\\eeas}{\\end{eqnarray*}}\n", "\\newcommand{\\bea}{\\begin{eqnarray}}\n", "\\newcommand{\\eea}{\\end{eqnarray}}\n", "\\newcommand{\\ben}{\\begin{enumerate}}\n", "\\newcommand{\\een}{\\end{enumerate}}\n", "\\newcommand{\\bi}{\\begin{itemize}}\n", "\\newcommand{\\ei}{\\end{itemize}}\n", "\\newcommand{\\beq}{\\begin{equation}}\n", "\\newcommand{\\eeq}{\\end{equation}}\n", "\\newcommand{\\bv}{\\begin{verbatim}}\n", "\\newcommand{\\ev}{\\end{verbatim}}\n", "\\newcommand{\\E}{\\mathbb{E}}\n", "\\newcommand{\\R}{\\mathbb{R}}\n", "\\newcommand{\\mP}{\\mathbb{P}}\n", "\\newcommand{\\mQ}{\\mathbb{Q}}\n", "\\newcommand{\\sigl}{\\sigma_L}\n", "\\newcommand{\\BS}{\\rm BS}\n", "\\newcommand{\\vix}{\\text{VIX}}\n", "\\newcommand{\\p}{\\partial}\n", "\\newcommand{\\var}{{\\rm var}}\n", "\\newcommand{\\cov}{{\\rm cov}}\n", "\\newcommand{\\mt}{\\mathbf{t}}\n", "\\newcommand{\\mS}{\\mathbf{S}}\n", "\\newcommand{\\mF}{\\mathbb{F}}\n", "\\newcommand{\\tC}{\\widetilde{C}}\n", "\\newcommand{\\hC}{\\widehat{C}}\n", "\\newcommand{\\cE}{\\mathcal{E}}\n", "\\newcommand{\\tH}{\\widetilde{H}}\n", "\\newcommand{\\cD}{\\mathcal{D}}\n", "\\newcommand{\\cM}{\\mathcal{M}}\n", "\\newcommand{\\cS}{\\mathcal{S}}\n", "\\newcommand{\\cR}{\\mathcal{R}}\n", "\\newcommand{\\cF}{\\mathcal{F}}\n", "\\newcommand{\\cV}{\\mathcal{V}}\n", "\\newcommand{\\cG}{\\mathcal{G}}\n", "\\newcommand{\\cv}{\\mathcal{v}}\n", "\\newcommand{\\cg}{\\mathcal{g}}\n", "\\newcommand{\\cL}{\\mathcal{L}}\n", "\\newcommand{\\cC}{\\mathcal{C}}\n", "\\newcommand{\\cO}{\\mathcal{O}}\n", "\\newcommand{\\dt}{\\Delta t}\n", "\\newcommand{\\tr}{{\\rm tr}}\n", "\\newcommand{\\dm}{{\\diamond}}\n", "\\newcommand{\\ui}{{\\textrm{i}}}\n", "\\newcommand{\\sgn}{\\mathrm{sign}}\n", "\\newcommand{\\ee}[1]{{\\mathbb{E}\\left[{#1}\\right]}}\n", "\\newcommand{\\eef}[1]{{\\mathbb{E}\\left[\\left.{#1}\\right|\\cF_t\\right]}}\n", "\\newcommand{\\eefm}[2]{{\\mathbb{E}^{#2}\\left[\\left.{#1}\\right|\\cF_t\\right]}}\n", "\\newcommand{\\angl}[1]{{\\langle{#1}\\rangle}}\n", "$$\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Outline of Lecture 5\n", "\n", "\n", "* A microstructural foundation for affine stochastic volatility models\n", "\n", "\n", "* Exponentiation of conditional expectations\n", "\n", "\n", "* Leverage swap computation\n", "\n", "\n", "* Calibration of rough Heston parameters" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### A microstructural foundation for affine stochastic volatility models\n", "\n", "\n", "- [Jaisson and Rosenbaum][7] first showed that affine stochastic volatility models could arise as limits of Hawkes process-based models of order flow.\n", "\n", "\n", "- In the following, we both generalize and hopefully shed light on their argument." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Hawkes processes\n", "\n", "- Dating from the 1970's, Hawkes processes are jump processes where the jump arrival rate is self-exciting.\n", "\n", "\n", "- One of the first applications was to the modeling of earthquakes." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The Hawkes process-based microstructure model of Jaisson and Rosenbaum\n", "\n", "[Jaisson and Rosenbaum][6] consider the following simple model of price formation:\n", "\n", "- Order arrivals are modeled as a counting process\n", " - Buy order arrivals cause the price to increase\n", " - Sell order arrivals cause the price to decrease\n", " - All orders are unit size\n", " \n", " \n", "- The order arrival process is self-exciting\n", " - The price process is a bivariate Hawkes process.\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The stock price process\n", "\n", "Specifically, with $X_t = \\log S_t$,\n", "\n", "$$\n", "dX_t = m_X dt + dN_t^+ - dN_t^-\n", "$$\n", "\n", "where $N^{\\pm}$ are counting processes with arrival rates $\\lambda^{\\pm}_t$, and $m_X$ is determined by the martingale condition on $S=e^X$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The order arrival rate process\n", "\n", "$$\n", "\\mathbf {\\lambda}_t = \\mu + \\int_0^t\\,\\varphi(t-s)\\,d{\\bf N}_s.\n", "$$\n", "where $\\lambda = \\{\\lambda^+,\\lambda^-\\}$ and ${\\bf N}=\\{N^+,N^-\\}$. The kernel $\\varphi$ is a $2 \\times 2 $ matrix.\n", "\n", "- The order arrival process is self-exciting. \n", " - As orders arrive, the order arrival rate increases.\n", " - In the absence of new orders, the order arrival rate decays according to some Hawkes kernel $\\varphi$.\n", "\n", "\n", "\n", "\n", "- [Jaisson and Rosenbaum][6] show that that in a suitable scaling limit, and with a suitable choice of the kernel $\\varphi$, this model tends to the rough Heston model." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Affine forward intensity (AFI) models\n", "\n", "- In analogy to stochastic volatility models in forward variance form, [Gatheral and Keller-Ressel][6] define the forward intensity model\n", "

\n", "$$\n", "\\beas\n", "dX_t &= -\\lambda_{t} m_X dt + dJ_t^+ - dJ_t^-,\\\\\n", "d\\xi_t(T) &= \\kappa(T-t) \\left(\\gamma^+\\, d\\wt{J}^+_t + \\gamma^-\\,d\\wt{J}^-_t\\right).\n", "\\eeas\n", "$$\n", "where $\\kappa$ is an integrable, decreasing non-zero kernel. \n", "\n", " - $\\gamma^{\\pm}$ are positive constants\n", " - jumps can have various sizes; the jump size measures are $\\zeta_{\\pm}$\n", " - $m_X$ is determined by the martingale condition on $S=e^X$ " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- The $\\wt{J}^{\\pm}_t$ denote the *compensated* order flow processes, i.e. \n", "

\n", "$$\\wt{J}^{\\pm}_t := J^\\pm_t - m_\\pm \\int_0^t \\lambda_{s}ds,$$\n", "

\n", "where\n", "$$\n", "m_\\pm = \\int_{\\Rplus} x \\, \\zeta_\\pm(dx).\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Variance and jump intensity\n", "\n", "Denote the variance per unit time of the process $X_t$ by $v_t$. Then\n", "\n", "$$\n", "v_t\\,dt = \\var[dJ_t^+ - dJ_t^-] \n", "= \\lambda_t\\,\\left\\{v^+ + v^-\\right\\} \\,dt\n", "=: \\lambda_t\\,v_J\\,dt,\n", "$$\n", "\n", "where \n", "$$\n", "v^\\pm = \\int_{\\Rplus}\\,x^2\\,\\zeta_\\pm(dx) - m_\\pm^2\n", "$$\n", "\n", "are the variance of positive and negative jump sizes respectively.\n", "\n", "Continuing the analogy with stochastic volatility, $\\xi_t(u)$ is linked to $v_t$ by\n", "

\n", "$$\n", "\\begin{equation}\n", "\\xi_t(u) = \\eef{v_u}.\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "Setting \n", "$$\n", "\\begin{equation}\n", "J_t^X = J_t^+ - J_t^-, \\qquad \n", "\\wt{J}_t^v = {\\gamma^+} \\wt{J}_t^+ + {\\gamma^-} \\wt{J}_t^-,\n", "\\end{equation}\n", "$$\n", "\n", "the affine forward intensity (AFI) model may be rewritten as\n", "\n", "$$\n", "\\bea \n", "dX_t &= -\\lambda_{t} m_X dt + dJ_t^X,\\nonumber\\\\\n", "d\\xi_t(T) &= \\kappa(T-t) d\\wt{J}^v_t.\n", "\\eea\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### High-frequency limit of the AFI model\n", "\n", "Consider new processes $J^\\epsilon$ such that \n", "\n", "$$\n", "\\lambda^\\epsilon = \\frac 1 \\epsilon \\,\\lambda; \\quad \\zeta^\\epsilon(dx) = \\zeta\\left(\\frac{dx}{\\sqrt{\\epsilon}}\\right).\n", "$$\n", "\n", "Thus in the limit $\\epsilon \\to 0$, \n", "- jump sizes are very small and jumps are very frequent. \n", "- the martingale component of $dX_t$ may be approximated by $\\sqrt{v_t}\\,dZ_t$\n", "- $d\\wt{J}^v_t$ may be approximated by $dY_t$ for some diffusion process $Y$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### High frequency limit of the AFI model\n", "\n", "\n", "In the limit, we obtain\n", "$$\n", "\\beas\n", "dX_t &=& -\\frac 12\\,v_t\\, dt + \\sqrt{v_t}\\,dZ_t,\\\\\n", "d\\xi_t(T)&=& \\kappa(T-t) \\,dY_t,\n", "\\eeas\n", "$$\n", "\n", "where\n", "$$\n", "\\var[dY_t] = \\var[d\\tilde J^v_t] = \\lambda_t\\,\\left[{\\gamma^+}^2\\,v^+ +\n", "{\\gamma^-}^2\\,v^-\\right]\\,dt\\\\ =v_t\\,\\left[\\frac{{\\gamma^+}^2\\,v^+ +\n", "{\\gamma^-}^2\\,v^-}{v^+ + v^-}\\right]\\,dt.\n", "$$\n", "\n", "Then\n", "\n", "$$\n", "d\\xi_t(T)= \\eta\\,\\kappa(T-t) \\,\\sqrt{v_t}\\,dW_t\n", "$$\n", "where\n", "$$\n", "\\eta^2 = \\frac{{\\gamma^+}^2\\,v^+ +\n", "{\\gamma^-}^2\\,v^-}{v^+ + v^-}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "As for the correlation between $dZ_t$ and $dW_t$, we first compute\n", "\n", "$$\n", "\\ee{dJ^+_t\\,d\\tilde J^+_t} = \\lambda_t\\,v^+\\,dt; \\quad \\ee{dJ^-_t\\,d\\tilde J^-_t} = \\lambda_t\\,v^-\\,dt\n", "$$\n", "\n", "so \n", "$$\n", "\\ee{dX_t\\,d\\tilde J^v_t} =\\lambda_t\\,(\\gamma^+\\,v^+ -\\gamma^-\\,v^-)\\,dt\\\\\n", "= \\ee{\\sqrt{v_t}\\,dZ_t\\,\\eta\\,\\sqrt{v_t}\\,dW_t} =:\\rho\\,\\eta\\,v_t\\,dt,\n", "$$\n", "where\n", "\n", "$$\n", "\\beas\n", "\\rho %&=& \\frac{\\lambda_t\\,\\left(\\gamma^+\\,v^+ -\\gamma^-\\,v^-\\right)}{\\eta\\,v_t}\\\\\n", "%&=&\\frac{\\gamma^+\\,v^+ -\\gamma^-\\,v^-}{\\eta\\,v_J}\\\\\n", "%&=& \\frac{\\gamma^+\\,v^+ -\\gamma^-\\,v^-}{v^+ + v^-}\\,\\sqrt{ \\frac{v^+ + v^-}{{\\gamma^+}^2\\,v^+ +\n", "%{\\gamma^-}^2\\,v^-}} \\\\\n", "&=& \\frac{1}{\\sqrt{v^+ + v^-}}\\, \\frac{\\gamma^+\\,v^+ -\\gamma^-\\,v^-}{\\sqrt{{\\gamma^+}^2\\,v^+ +\n", "{\\gamma^-}^2\\,v^-}}.\n", "\\eeas\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Example: The bivariate Hawkes process of of Jaisson and Rosenbaum\n", "\n", "Consider the case of a bivariate Hawkes process $(J^+, J^-)$ with unit jump size (i.e., $\\zeta_\\pm(dx) = \\delta_1(dx))$. Then in the above limit, as $\\epsilon \\to 0$, the process converges to\n", "$$\n", "\\beas\n", "dX_t &=& -\\frac 12\\,v_t\\, dt + \\sqrt{v_t}\\,dZ_t,\\\\\n", "d\\xi_t(T)&=& \\eta\\,\\sqrt{v_t}\\,\\kappa(T-t) \\,dW_t,\n", "\\eeas\n", "$$\n", "

\n", "where $\\ee{dZ_t\\,dW_t}= \\rho\\,dt$ and \n", "

\n", "$$\n", "\\eta^2 = \\frac 12 \\left[{\\gamma^+}^2 +{\\gamma^-}^2\\right];\n", "\\quad \\rho = \\frac{\\gamma^+ -\\gamma^-}{\\sqrt{2\\,\\left({\\gamma^+}^2 +\n", "{\\gamma^-}^2\\right)}}.\n", "$$\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Near instability of Hawkes kernel in the limit\n", "\n", "- So far, we have shown how AFV models arise naturally as limits of AFI models.\n", "\n", "\n", "- Now we show that in order to get stochastic (as opposed to constant) volatility, the AFI model Hawkes process needs to be nearly unstable." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Consider the (generalized) Hawkes process\n", "\n", "$$\n", "\\beq\n", "\\lambda_t = \\mu + \\int_0^t\\,\\varphi(t-s)\\,dJ^v_s \\\\= \\mu + \\hat \\gamma\\,\\int_0^t\\,\\varphi(t-s)\\,\\lambda_s\\,ds+ \\int_0^t\\,\\varphi(t-s)\\,d\\tilde J^v_s\n", "\\eeq\n", "$$\n", "where $\\hat \\gamma = {\\gamma^+} m_+ + {\\gamma^-} m_-$. \n", "\n", "Following [Bacry et al.][3], we rewrite this last equation symbolically as\n", "\n", "$$\n", "\\lambda = \\mu + \\hat \\gamma\\,(\\varphi \\star\\lambda) + \\varphi \\star d\\tilde J^v.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Rearranging gives\n", "\n", "$$\n", "(1- \\hat \\gamma\\,\\varphi \\star) \\lambda = \\mu + \\varphi \\star d\\tilde J^v\n", "$$\n", "

\n", "and applying the Laplace transform gives\n", "

\n", "$$\n", "(1- \\hat \\gamma\\,\\hat \\varphi ) \\hat \\lambda = \\hat \\mu + \\hat \\varphi \\,\\widehat {d \\tilde J^v}.\n", "$$\n", "

\n", "which may be rearranged as\n", "

\n", "$$\n", "\\hat \\lambda = \\hat \\mu + \\hat \\psi\\,\\hat \\mu + \\frac{1}{\\hat \\gamma}\\,\\hat \\psi \\,\\widehat {\\tilde J^v}\n", "$$\n", "where\n", "$$\n", "\\hat \\psi = \\frac{\\hat \\gamma \\hat \\varphi}{1- \\hat \\gamma\\,\\hat \\varphi }.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Then \n", "\n", "$$\n", "v_J\\, \\hat \\lambda = v_J\\,\\hat \\mu +\\hat \\gamma\\,\\hat \\kappa\\,\\hat \\mu + \\hat \\kappa \\,\\widehat {\\tilde J^v}\n", "$$\n", "\n", "where \n", "\n", "$$\n", "\\hat \\kappa = \\frac{v_J}{\\hat \\gamma}\\,\\hat \\psi =\\frac{v_J \\hat \\varphi}{1-\\hat \\gamma\\,\\hat \\varphi}.\n", "$$\n", "\n", "Inverting the Laplace transform, and recalling that $v_t = v_J\\,\\lambda_t$, we obtain\n", "\n", "$$\n", "v_u= v_J\\,\\mu + \\hat \\gamma\\,\\mu\\,\\int_0^u\\,\\kappa(u-s)\\,ds+ \\int_0^u\\,\\kappa(u-s)\\,d\\tilde J^v_s.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Taking a conditional expectation wrt $\\cF_t$, \n", "\n", "$$\n", "\\xi_t(u) = \\eef{v_u}\\\\= v_J\\,\\mu +\\hat \\gamma\\, \\mu\\,\\int_0^u\\,\\kappa(u-s)\\,ds+ \\eta\\,\\int_0^t\\,\\kappa(u-s)\\,\\sqrt{v_s}\\,dW_s\n", "$$\n", "and so \n", "$\n", "d\\xi_t(u) = \\kappa(u-t)\\,d\\tilde J^v_t\n", "$, the dynamics of an AFI model." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Now\n", "\n", "$$\n", "\\hat \\kappa =\\frac{v_J \\hat \\varphi}{1-\\hat \\gamma\\,\\hat \\varphi} \\implies\n", "\\hat \\varphi = \\frac{\\hat \\kappa}{v_J +\\hat \\gamma\\,\\hat \\kappa}.\n", "$$\n", "\n", "Recall that the kernel of our generalized Hawkes process is $\\hat \\gamma\\,\\hat \\varphi$. The stability condition is then\n", "\n", "$$\n", "\\hat \\gamma \\int_{\\Rplus} \\varphi(\\tau)\\,d\\tau = \\hat \\gamma\\,\\hat \\varphi(0) = \\frac{\\hat \\gamma\\,\\hat \\kappa}{v_J +\\hat \\gamma\\,\\hat \\kappa} \\to 1 \\text{ as } \\epsilon \\to 0\n", "$$\n", "\n", "since in that limit, $v_J \\sim \\epsilon$ and $\\hat \\gamma \\sim \\sqrt{\\epsilon}$. \n", "\n", "Conversely, $ \\hat \\gamma\\,\\hat \\varphi(0) \\to a < 1$ as $\\epsilon \\to 0$ only if $\\kappa \\sim \\sqrt{\\epsilon}$. Then in the limit, $\\kappa \\to 0$ and volatility is deterministic." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "

\n", "Near instability

\n", "
\n", "
\n", "
\n", " The high frequency limit of the AFI model is a non-trivial AFV model if and only if the Hawkes process is nearly unstable.\n", "
\n", "
\n", "\n", "
\n", "\n", "
\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Diamonds and the exponentiation theorem\n", "\n", "- We now turn our attention to diamonds and the exponentiation theorem.\n", "\n", "\n", "- The exponentiation theorem is effectively a generalization of both the Alòs decomposition formula and the Bergomi-Guyon expansion.\n", "\n", "\n", "- Diamond functionals are generalizations of the Bergomi-Guyon autocovariance functionals." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The Alòs decomposition formula\n", "\n", "Following [Alòs][1], let $X_t = \\log S_t/K$ and consider the price process\n", "\n", "$$\n", "dX_t = \\sigma_t\\,dZ_t - \\frac12\\,\\sigma_t^2\\,dt.\n", "$$\n", "\n", "Now let $H(X_t,w_t(T))$ ($H_t$ for short) be some function that solves the Black-Scholes equation.\n", " \n", "- Specifically, \n", "$$\n", "-\\p_w H_t + \\frac12\\, \\left(\\p_{xx} - \\p_x\\right) H_t = 0\n", "$$\n", "which is of course the gamma-vega relationship.\n", "\n", " \n", "- Note in particular that $\\p_x$ and $\\p_w$ commute when applied to a solution of the Black-Scholes equation.\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Variance swaps\n", "\n", "We now specify the variance swap $w_t(T)$ as the integral of the expected future variance:\n", "\n", "$$\n", "w_t(T) = \\int_t^T \\,\\eef{\\sigma_u^2}\\,du = \\int_t^T \\,\\xi_t(u)\\,du,\n", "$$\n", "\n", "where the $\\xi_t(u)$ are forward variances. \n", " \n", "Notice that\n", "$$\n", "w_t(T)=M_t-\\int_0^t \\sigma_s^2 ds,\n", "$$\n", "where the martingale $M_t:=\\eef{\\int_0^T \\sigma_s^2 ds}$. Then it follows that\n", "$$\n", "d w_t(T) = -\\sigma_t^2\\,dt + dM_t.\n", "$$\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The Itô Decomposition Formula\n", "\n", "Applying Itô's Formula to $H$, taking conditional expectations, simplifying using the Black-Scholes equation and integrating, we obtain\n", "\n", "#### The Itô Decomposition Formula of Alòs\n", "\n", "(1)\n", "$$\n", "\\bea\n", "\\eef{H_T }\n", "&=&\n", "H_t +\\eef{ \\int_t^T\\, \\p_{xw} H_s\\,d\\angl{X,M}_s}\\nonumber\\\\\\\n", "&& \\quad\\quad+ \\frac 12\\,\\eef{\\int_t^T\\,\\p_{ww} H_s \\,d\\angl{M,M}_s}.\n", "\\eea\n", "$$\n", "\n", "\n", "- Note in particular that this decomposition is *exact*." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Diamond notation\n", "\n", "Let $A_t$ and $B_t$ be semimartingales (here some combinations of $X$ and $M$). Then\n", "

\n", "$$\n", "(A \\dm B)_t(T) = \\eef{\\int_t^T d\\angl{A,B}_s}.\n", "$$\n", "

\n", "When $(A \\dm B)_t(T)$ appears before some solution $H_t$ of the Black-Scholes equation, the dot $\\cdot$ means act on $H_t$ with the appropriate combintation of $\\p_x$ and $\\p_w$.\n", "\n", "\n", "So for example\n", "$$\n", "\\beas\n", "(X \\dm M)_t(T) \\cdot H_t &=&\\eef{\\int_t^T d\\angl{X,M}_s}\\,\\p_{x w} \\,H_t\n", "%\\left( M \\dm M \\right)_t(T)\\,H_t &=& \\eef{\\int_t^T d\\angl{M,M}_s}\\,\\p_{w w}\\,H_t\\\\\n", "%\\left(X \\dm (X \\dm M)\\right)_t(T)\\,H_t &=& \\eef{\\int_t^T d\\angl{X,(X \\dm M)}_s}\\,\\p_{x x w}\\,H_t,\n", "\\eeas\n", "$$\n", "\n", "and so on. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Diamond functionals as covariances\n", "\n", "- Diamond (or autocovariance) functionals are intimately related to conventional covariances.\n", "\n", "\n", "- Covariances are typically easy to compute using simulation.\n", "\n", "\n", "- Diamond functionals are expressible directly in terms of the formulation of a model in forward variance form.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Bergomi-Guyon in diamond notation\n", "\n", "According to equation (13) of [Bergomi and Guyon][1], in diamond notation, the conditional expectation of a solution of the Black-Scholes equation satisfies\n", "\n", "$$\n", "\\beas\n", "&&\\eef{H_T}\\\\\n", " &=& \\bigg\\{ 1+ \\epsilon\\,(X \\dm M)_t + \\frac{\\epsilon^2}2\\,(M \\dm M)_t \\\\\n", " &&\\qquad+ \\frac{\\epsilon^2}2\\,\\left[(X \\dm M)_t \\right]^2 + {\\epsilon^2}\\,(X \\dm (X \\dm M))_t + \\cO(\\epsilon^3) \\bigg\\} \\cdot H_t \n", "\\eeas\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "- We notice that \n", "$$\n", "\\beas\n", "\\eef{H_T}\n", " &=& \\exp \\bigg\\{ \\epsilon\\,(X \\dm M)_t + \\frac{\\epsilon^2}2\\,(M \\dm M)_t \\\\\n", " &&\\qquad \\qquad + {\\epsilon^2}\\,(X \\dm (X \\dm M))_t + \\cO(\\epsilon^3) \\bigg\\} \\cdot H_t ,\n", "\\eeas\n", "$$\n", "the exponential of a sum of `connected diagrams'.\n", "\n", "\n", "- Motivated by exponentiation results in physics, we are tempted to see if something like this holds to all orders. \n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Freezing derivatives\n", "\n", "Freezing the derivatives in [(1)](#eq:AlosJG) gives us the approximation\n", "\n", "$$\n", "\\beas\n", "\\eef{H_T }\n", "&\\approx &\n", "H_t +\\eef{ \\int_t^T\\,d\\angl{X,M}_s}\\,\\p_{xw} H_t\\nonumber\\\\\\\n", "&& \\quad\\quad+ \\frac 12\\,\\eef{\\int_t^T \\,d\\angl{M,M}_s}\\,\\p_{ww} H_t\\\\\n", "&=&\n", "H_t +(X\\dm M)_t(T)\\, H_t + \\frac 12\\,(M\\dm M)_t(T)\\, H_t.\n", "\\eeas\n", "$$\n", "\n", "- In Theorem 3.3 of [Alòs] for example the error in this approximation is bounded in the context of European option pricing." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The idea of the exponentiation theorem\n", "\n", "\n", "- The essence of the exponentiation theorem we prove in [Alòs, Gatheral and Radoičić][2] is that we may express $\\eef{H_T }$ as an exact expansion consisting of infinitely many terms, with derivatives in each such term frozen. \n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Trees\n", "\n", "- Terms such as $(X \\dm M)$, $(M \\dm M)$ and $X \\dm (X \\dm M)$ are naturally indexed by trees, each of whose leaves corresponds to either $X$ or $M$.\n", "\n", "\n", "- We end up with diamond trees reminiscent of Feynman diagrams, with analogous rules.\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Forests\n", "\n", "

\n", "The forest recursion

\n", "
\n", "
\n", "
\n", " Let $\\mF_0 = M$. Then the higher order forests $\\mF_k$ are defined recursively as follows:\n", "$$\n", "\\mF_k =\\frac12\\,\\sum_{i,j=0}^{k-2}\\,\\mathbb{1}_{i+j = k-2}\\,\\mF_i \\dm \\mF_j + X \\dm \\mF_{k-1}.\n", "$$\n", "
\n", "
\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The first few terms\n", "\n", "Applying the recursion, we have\n", "\n", "$$\n", "\\bea\n", "\\mF_0 &=& M \\nonumber\\\\\n", "\\mF_1 &=& X \\dm \\mF_0 = (X \\dm M) \\nonumber\\\\\n", "\\mF_2 &=& \\frac12 (\\mF_0 \\dm \\mF_0) + X \\dm \\mF_1 = \\frac12 (M \\dm M) + X \\dm (X \\dm M)\\nonumber\\\\\n", "\\mF_3 &=& (\\mF_0 \\dm \\mF_1) + X \\dm \\mF_2 \\nonumber\\\\\n", "&=& M \\dm (X \\dm M) + X \\dm \\frac12 (M \\dm M) + X \\dm (X \\dm (X \\dm M))\\nonumber\\\\\n", "\\eea\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The exponentiation theorem\n", "\n", "\n", "

\n", "The exponentiation theorem

\n", "
\n", "
\n", "
\n", " Let $H_t$ be any solution of the Black-Scholes equation \n", "such that $\\eef{H_T}$ is finite and the integrals contributing to each forest $\\mF_k, k \\geq 0$ exist.\n", " \n", "Then\n", "$$\n", "\\eef{H_T}= e^{\\sum_{k=1}^\\infty\\,\\mF_k }\\cdot H_t.\n", "$$\n", "
\n", "
" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### If $H_t$ is a characteristic function\n", "\n", "Consider the Black-Scholes characteristic function\n", "\n", "$$\n", "\\Phi_t^T(a) =e^{\\ui\\,a\\,X_t - \\frac{1}{2}a\\,\\left(a+\\ui\\right)\\,w_t(T)}\n", "$$\n", "\n", "- Applying $\\mF_k$ to $\\Phi$ just multiplies $\\Phi$ by some deterministic factor. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- Then\n", "$$\n", "e^{\\sum_{k=1}^\\infty\\,\\mF_k}\\,\\Phi_t^T(a)=e^{\\sum_{k=1}^\\infty\\,\\tilde {\\mF}_k(a)}\\,\\Phi_t^T(a)\n", "$$\n", "

\n", "where $\\tilde{\\mF}_k(a)$ is $\\mF_k$ with each occurrence of $\\p_x$ replaced with $\\ui\\,a$ and each occurrence of $\\p_w$ replaced with $-\\frac12\\,a\\,(a+\\ui)$. \n", "\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The characteristic function under stochastic volatility\n", "\n", "Applying the Exponentiation Theorem, we have the following lemma.\n", "\n", "Let \n", "\n", "$$\n", "\\varphi_t^T(a) = \\eef{e^{\\ui\\,a\\,X_T}}\n", "$$\n", "\n", "be the characteristic function of the log stock price. Then\n", "\n", "$$\n", "\\varphi_t^T(a) = e^{\\sum_{k=1}^\\infty\\,\\tilde {\\mF}_k(a)}\\,\\Phi_t^T(a).\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The cumulant generating function under stochastic volatility\n", "\n", "As a corollary, the cumulant generating function (CGF) is given by\n", "\n", "$$\n", "\\psi_t^T(a) = \\log \\varphi_t^T(a) = \\ui\\,a\\,X_t - \\frac{1}{2}a\\,(a+\\ui)\\,w_t(T) + \\sum_{k=1}^\\infty\\,\\tilde {\\mF}_k(a).\n", "$$\n", "\n", "- An explicit expression for the CGF for *any* stochastic volatility model!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Variance and gamma swaps\n", "\n", "The variance swap is given by the fair value of the log-strip:\n", "\n", "$$\n", "\\eef{X_T}= (-\\ui)\\,{\\psi_t^T}'(0) = X_t - \\frac{1}{2}\\,w_t(T)\n", "$$\n", "\n", "and the gamma swap (wlog set $X_t=0$) by\n", "\n", "$$\n", "\\eef{X_T \\,e^{ X_T}} = \\left. (-\\ui)\\,\\frac{d}{da}\\,\\psi_t^T(a)\\right|_{a=-\\ui}.\n", "$$\n", "\n", "- The point is that we can in principle compute such moments for any stochastic volatility model written in forward variance form, whether or not there exists a closed-form expression for the characteristic function." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The gamma swap\n", "\n", "We can compute the gamma swap as\n", "\n", "$$\n", "\\eef{X_T \\,e^{ X_T}} = \\left. (-\\ui)\\,\\frac{d}{da}\\,\\psi_t^T(a)\\right|_{a=-\\ui}.\n", "$$\n", "\n", "It is easy to see that only trees containing a single $M$ leaf will survive in the sum after differentiation when $a = - \\ui$ so that\n", "\n", "$$\n", "\\sum_{k=1}^\\infty \\,{\\tilde \\mF_k}'(-\\ui) =\\frac12\\,\\sum_{k=1}^\\infty \\,(X \\dm)^k M\n", "$$\n", "where $ (X \\dm)^k M $ is defined recursively for $k>0$ as $(X \\dm)^k M= X \\dm ( X \\dm)^{k-1} M$. \n", "\n", "- For example, $(X \\dm)^3 M = (X \\dm (X \\dm (X \\dm M)))$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Then the fair value of a gamma swap is given by\n", "\n", "$$\n", "\\cG_t(T) = 2\\,\\eef{X_T \\,e^{ X_T}} = w_t(T) +\\sum_{k=1}^\\infty \\,(X \\dm)^k M.\n", "$$\n", "\n", "- This expression allows for explicit computation of the gamma swap for any model written in forward variance form. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The leverage swap\n", "\n", "We deduce that the fair value of a leverage swap is given by\n", "\n", "(2)\n", "$$\n", "\\cL_t(T) = \\cG_t(T) - w_t(T) = \\sum_{k=1}^\\infty \\,(X \\dm)^k M.\n", "$$ \n", "\n", "- The leverage swap is expressed explicitly in terms of covariance functionals of the spot and vol. processes.\n", " - If spot and vol. processes are uncorrelated, the fair value of the leverage swap is zero.\n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "- The leverage swap may be easily estimated from the volatility smile along the lines of [Fukasawa][5] \n", "or alternatively by integration if we have fitted some curve to the smile.\n", " - We use two different Vola Dynamics (http://www.voladynamics.com) curves below.\n", "\n", "\n", "\n", "- We will now use [(2)](#eq:leverage) to compute an explicit expression for the value of a leverage swap in the rough Heston model." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The rough Heston model in forward variance form\n", "\n", "\n", "Recall that in forward variance form, the rough Heaston model reads\n", "\n", "$$\n", "\\beas\n", "\\frac{dS_t}{S_t} &=& \\sqrt{v_t}\\,dZ_t\\\\\n", "d\\xi_t(u) &=& \\frac{\\nu}{\\Gamma(\\alpha)} \\,\\frac{\\sqrt{v_t}}{(u-t)^\\gamma}\\,dW_t.\n", "\\eeas\n", "$$\n", "\n", "- The rough Heston model (with $\\lambda=0$ turns out to be even more tractable than the classical Heston model!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Computation of autocovariance functionals\n", "\n", "Apart from $\\cF_t$ measurable terms (abbreviated as `drift'), we have\n", "\n", "$$\n", "\\beas\n", "dX_t &=& \\sqrt{v_t}\\,dZ_t + \\text{drift}\\\\\n", "dM_t &=& \\int_t^T\\,d\\xi_t(u)\\,du \\\\\n", "& =& \\frac{\\nu}{\\Gamma(\\alpha)} \\,\\sqrt{v_t} \\,\\left(\\int_t^T\\,\\frac{du}{(u-t)^\\gamma}\\right)\\,dW_t\\\\\n", "& =& \\frac{\\nu\\,(T-t)^\\alpha}{\\Gamma(1+\\alpha)} \\,\\sqrt{v_t} \\,dW_t.\n", "\\eeas\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The first order forest\n", "\n", "There is only one tree in the forest $\\mF_1$.\n", "\n", "$$\n", "\\beas\n", "\\mF_1=(X \\dm M)_t(T) &=& \\eef{\\int_t^T d\\angl{X,M}_s}\\nonumber\\\\\n", "&=& \\frac{\\rho\\,\\nu}{\\Gamma(1+\\alpha)} \\,\\eef{\\int_t^T \\,v_s \\,(T-s)^\\alpha\\,ds}\\nonumber\\\\\n", "&=& \\frac{\\rho\\,\\nu}{\\Gamma(1+\\alpha)} \\,\\int_t^T \\,\\xi_t(s) \\,(T-s)^\\alpha\\,ds.\n", "\\eeas\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The second order forest\n", "\n", "There are two trees in $\\mF_2$. The first tree is\n", "\n", "$$\n", "\\beas\n", "(M \\dm M)_t(T) &=& \\eef{\\int_t^T d\\angl{M,M}_s}\\nonumber\\\\\n", "&=& \\frac{\\nu^2}{\\Gamma(1+\\alpha)^2} \\,\\int_t^T \\,\\xi_t(s) \\,(T-s)^{2\\,\\alpha}\\,ds.\n", "\\eeas\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The second tree $\\left(X \\dm (X \\dm M)\\right)_t (T) $ is more complicated. \n", "\n", "Define for $j \\geq 0$\n", "\n", "$$\n", "I^{(j)}_t(T):=\\int_t^T\\,ds\\,\\xi_t(s)\\,(T-s)^{j\\,\\alpha}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### In terms of $I^{(j)}_t(T)$\n", "\n", "We may then rewrite the above expressions as\n", "\n", "$$\n", "\\beas\n", "(X \\dm M)_t(T) &=& \\frac{\\rho\\,\\nu}{\\Gamma(1+\\alpha)} \\,I^{(1)}_t(T)\\\\\n", "(M \\dm M)_t(T) &=& \\frac{\\nu^2}{\\Gamma(1+\\alpha)^2} \\,I^{(2)}_t(T).\n", "\\eeas\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "A little more computation gives\n", "\n", "$$\n", "\\beas\n", "\\left(X \\dm (X \\dm M)\\right)_t (T) &=& \\eef{\\int_t^T d\\angl{X,I^{(1)}}_s}\\nonumber\\\\\n", "&=& \\frac{\\rho^2\\,\\nu^2}{\\Gamma(1+\\alpha)} \\,\\frac{\\Gamma(1+\\alpha)}{\\Gamma(1+2\\,\\alpha)}\\int_t^T\\,ds\\,\\eef{\\int_s^T \\,v_s\\,(T-s)^{2\\,\\alpha}\\,ds}\\nonumber\\\\\n", " &=& \\frac{\\rho^2\\,\\nu^2}{\\Gamma(1+\\alpha)\\,\\Gamma(\\alpha)} \\,\\int_t^T\\,ds\\,\\eef{\\int_s^T \\,v_s \\,\\frac{(T-u)^\\alpha}{(u-s)^\\gamma}\\,du}\\nonumber\\\\\n", "&=& \\frac{\\rho^2\\,\\nu^2}{\\Gamma(1+2\\,\\alpha)} \\,\\int_t^T\\,ds\\,\\,\\xi_t(s)\\,(T-s)^{2\\,\\alpha}\\nonumber\\\\\n", "&=& \\frac{\\rho^2\\,\\nu^2}{\\Gamma(1+2\\,\\alpha)} \\,I^{(2)}_t(T).\n", "\\eeas\n", "$$\n", "\n", "One can be easily convinced that each tree in the level-$k$ forest $\\mF_k$ is $I^{(k)}$ multiplied by a simple prefactor. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The third order forest\n", "\n", "For example, continuing to the forest $\\mF_3$, we have the following.\n", "\n", "$$\n", "\\beas\n", "\\left(M \\dm (X \\dm M)\\right)_t (T) &=& \\frac{\\rho\\,\\nu^3\\,\\Gamma(1+2\\,\\alpha)}{\\Gamma(1+\\alpha)^2\\,\\Gamma(1+3\\,\\alpha)} \\,I^{(3)}_t (T)\\\\\n", "\\left(X \\dm \\left(X \\dm (X \\dm M)\\right)\\right)_t (T) &=& \\frac{\\rho^3\\,\\nu^3}{\\Gamma(1+3\\,\\alpha)} \\,I^{(3)}_t (T)\\\\\n", "\\left(X \\dm (M \\dm M)\\right)_t (T) &=& \\frac{\\rho\\,\\nu^3\\,\\Gamma(1+2\\,\\alpha)}{\\Gamma(1+\\alpha)^2\\,\\Gamma(1+3\\,\\alpha)} \\,I^{(3)}_t (T).\n", "\\eeas\n", "$$\n", "\n", "In particular, we easily identify the pattern\n", "\n", "$$\n", "(X \\dm)^k M_t = \\frac{(\\rho\\,\\nu)^k}{\\Gamma (1+ k \\,\\alpha )}\\,I^{(k)}_t(T).\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The leverage swap under rough Heston\n", "\n", "Using [(2)](#eq:leverage), we have\n", "\n", "$$\n", "\\beas\n", "\\cL_t(T) &=& \\sum_{k=1}^\\infty \\,(X \\dm)^k M\\nonumber\\\\\n", "&=& \\sum_{k=1}^\\infty \\,\\frac{(\\rho\\,\\nu)^k}{\\Gamma (1+ k \\,\\alpha )}\\,\\int_t^T\\,du\\,\\xi_t(u)\\,(T-u)^{k\\,\\alpha}\\nonumber\\\\\n", "&=&\\int_t^T\\,du\\,\\xi_t(u)\\,\\left\\{E_{\\alpha }(\\rho\\,\\nu\\,(T-u)^\\alpha)-1\\right\\}\n", "\\eeas\n", "$$\n", "\n", "where $E_\\alpha(\\cdot)$ denotes the Mittag-Leffler function.\n", "\n", "- A closed-form formula for the leverage swap!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### The normalized leverage swap\n", "\n", "Given the form of the expression for the leverage swap, it is natural to normalize by the variance swap. We therefore define\n", "\n", "$$\n", "L_t(T) = \\frac{\\cL_t(T)}{w_t(T)}.\n", "$$\n", "\n", "In the special case of the rough Heston model with a flat forward variance curve, \n", "\n", "$$\n", "L_t(T) = E_{\\alpha ,2}(\\rho\\,\\nu\\,\\tau^\\alpha)-1,\n", "$$\n", "\n", "where $E_{\\alpha,2}(\\cdot)$ is a generalized Mittag-Leffler function, independent of the reversion level $\\theta$. We further define an $n$th order approximation to $L_t(T)$ as\n", "\n", "$$\n", "L_t^{(n)}(T) = \\sum_{k=1}^n \\,\\frac{(\\rho\\,\\nu\\,\\tau^{\\alpha})^k}{\\Gamma (2+ k \\,\\alpha )}.\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Implement the approximate formulae" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "ltT.raw <- function(H,eta,rho,n)function(tau){\n", " k <- (1:n)\n", " alpha <- H+1/2\n", " x <- rho * eta * tau^alpha \n", " vec <- x^k/gamma(2+k*alpha)\n", " return(sum(vec))\n", "}\n", " \n", "ltT <- function(H,eta,rho,n){Vectorize(ltT.raw(H,eta,rho,n))}" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### A numerical example\n", "\n", "We now perform a numerical computation of the value of the leverage swap using the forest expansion in the rough Heston model with the following parameters, calibrated in [Roughening Heston][4] to the SPX options market as of May 19, 2017:\n", "\n", "$$\n", "H = 0.0474;\\quad \\nu = 0.2910;\\quad \\rho = -0.6710.\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "H.20170519 <- 0.0236\n", "nu.20170519 <- 0.3266\n", "rho.20170519 <- -0.6510\n", "params.rHeston <- list(H=H.20170519,nu=nu.20170519,rho=rho.20170519)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Plot of successive approximations" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "library(repr)\n", "options(repr.plot.width=10,repr.plot.height=7)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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348MO93NZWS98faHPG+qVw8g9dIYM0g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\ng/qSt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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "curve(ltT(H.20170519,nu.20170519,rho.20170519,1)(x),from=0,to=3,col=\"brown\",lwd=1,lty=2,\n", " xlab=expression(paste(\"Time to expiry \",tau)),ylab=expression(L[t](T)))\n", "curve(ltT(H.20170519,nu.20170519,rho.20170519,2)(x),from=0,to=3,col=\"blue\",lwd=1,lty=3,add=T)\n", "curve(ltT(H.20170519,nu.20170519,rho.20170519,3)(x),from=0,to=3,col=\"dark green\",lwd=1,lty=4,add=T)\n", "curve(ltT(H.20170519,nu.20170519,rho.20170519,20)(x),from=0,to=3,col=\"red\",lwd=2,add=T)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Figure 1: Successive approximations to the (absolute value of) the normalized rough Heston leverage swap. The solid red line is the exact expression $L_t(T)$; $L_t^{(1)}(T)$, $L_t^{(2)}(T)$, and $L_t^{(3)}(T)$ are brown dashed, blue dotted and dark green dash-dotted lines respectively. " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Calibration of rough Heston using the leverage swap" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "We get leverage swap estimates from Vola Dynamics." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "vd.Data.C14PM <- read.csv(\"/Users/JGatheral/Voladynamics/VolCurveType.C14PM20170519FittingMode1.csv\",header=T)\n", "vd.Data.C15PM <- read.csv(\"/Users/JGatheral/Voladynamics/VolCurveType.C15PM20170519FittingMode1.csv\",header=T)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
asOfTimeexpiryTimetimeVvargamlevchi
20170519-160000.000-EDT20170522-160000.000-EDT0.008219178 4.611848e-05 4.529596e-05 -8.225198e-07 0.08251227
20170519-160000.000-EDT20170524-160000.000-EDT0.013698630 1.486447e-04 1.449538e-04 -3.690866e-06 0.04284537
20170519-160000.000-EDT20170526-160000.000-EDT0.019178082 2.525408e-04 2.442417e-04 -8.299132e-06 0.09615161
20170519-160000.000-EDT20170530-160000.000-EDT0.030136986 3.303599e-04 3.184876e-04 -1.187229e-05 0.03175334
20170519-160000.000-EDT20170531-160000.000-EDT0.032876712 3.890970e-04 3.741274e-04 -1.496953e-05 0.06030012
20170519-160000.000-EDT20170602-160000.000-EDT0.038356164 5.156240e-04 4.928132e-04 -2.281081e-05 0.04809755
\n" ], "text/latex": [ "\\begin{tabular}{r|lllllll}\n", " asOfTime & expiryTime & timeV & var & gam & lev & chi\\\\\n", "\\hline\n", "\t 20170519-160000.000-EDT & 20170522-160000.000-EDT & 0.008219178 & 4.611848e-05 & 4.529596e-05 & -8.225198e-07 & 0.08251227 \\\\\n", "\t 20170519-160000.000-EDT & 20170524-160000.000-EDT & 0.013698630 & 1.486447e-04 & 1.449538e-04 & -3.690866e-06 & 0.04284537 \\\\\n", "\t 20170519-160000.000-EDT & 20170526-160000.000-EDT & 0.019178082 & 2.525408e-04 & 2.442417e-04 & -8.299132e-06 & 0.09615161 \\\\\n", "\t 20170519-160000.000-EDT & 20170530-160000.000-EDT & 0.030136986 & 3.303599e-04 & 3.184876e-04 & -1.187229e-05 & 0.03175334 \\\\\n", "\t 20170519-160000.000-EDT & 20170531-160000.000-EDT & 0.032876712 & 3.890970e-04 & 3.741274e-04 & -1.496953e-05 & 0.06030012 \\\\\n", "\t 20170519-160000.000-EDT & 20170602-160000.000-EDT & 0.038356164 & 5.156240e-04 & 4.928132e-04 & -2.281081e-05 & 0.04809755 \\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "asOfTime | expiryTime | timeV | var | gam | lev | chi | \n", "|---|---|---|---|---|---|\n", "| 20170519-160000.000-EDT | 20170522-160000.000-EDT | 0.008219178 | 4.611848e-05 | 4.529596e-05 | -8.225198e-07 | 0.08251227 | \n", "| 20170519-160000.000-EDT | 20170524-160000.000-EDT | 0.013698630 | 1.486447e-04 | 1.449538e-04 | -3.690866e-06 | 0.04284537 | \n", "| 20170519-160000.000-EDT | 20170526-160000.000-EDT | 0.019178082 | 2.525408e-04 | 2.442417e-04 | -8.299132e-06 | 0.09615161 | \n", "| 20170519-160000.000-EDT | 20170530-160000.000-EDT | 0.030136986 | 3.303599e-04 | 3.184876e-04 | -1.187229e-05 | 0.03175334 | \n", "| 20170519-160000.000-EDT | 20170531-160000.000-EDT | 0.032876712 | 3.890970e-04 | 3.741274e-04 | -1.496953e-05 | 0.06030012 | \n", "| 20170519-160000.000-EDT | 20170602-160000.000-EDT | 0.038356164 | 5.156240e-04 | 4.928132e-04 | -2.281081e-05 | 0.04809755 | \n", "\n", "\n" ], "text/plain": [ " asOfTime expiryTime timeV var \n", "1 20170519-160000.000-EDT 20170522-160000.000-EDT 0.008219178 4.611848e-05\n", "2 20170519-160000.000-EDT 20170524-160000.000-EDT 0.013698630 1.486447e-04\n", "3 20170519-160000.000-EDT 20170526-160000.000-EDT 0.019178082 2.525408e-04\n", "4 20170519-160000.000-EDT 20170530-160000.000-EDT 0.030136986 3.303599e-04\n", "5 20170519-160000.000-EDT 20170531-160000.000-EDT 0.032876712 3.890970e-04\n", "6 20170519-160000.000-EDT 20170602-160000.000-EDT 0.038356164 5.156240e-04\n", " gam lev chi \n", "1 4.529596e-05 -8.225198e-07 0.08251227\n", "2 1.449538e-04 -3.690866e-06 0.04284537\n", "3 2.442417e-04 -8.299132e-06 0.09615161\n", "4 3.184876e-04 -1.187229e-05 0.03175334\n", "5 3.741274e-04 -1.496953e-05 0.06030012\n", "6 4.928132e-04 -2.281081e-05 0.04809755" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "head(vd.Data.C14PM)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "expiries <- vd.Data.C14PM$timeV\n", "ls.C14PM <- vd.Data.C14PM$lev/vd.Data.C14PM$var\n", "ls.C15PM <- vd.Data.C15PM$lev/vd.Data.C15PM$var" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Rough Heston parameter optimization" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "obj <- function(data)function(params){\n", " \n", " expiries <- data$timeV\n", " ls.Vola <- data$lev/data$var\n", " \n", " paramvec <- as.numeric(params)\n", " H <- paramvec[1]\n", " nu <- paramvec[2]\n", " rho <- paramvec[3]\n", " \n", " l.theoretical <- ltT(H,nu,rho,10)(expiries)\n", " \n", " res <- sum((l.theoretical - ls.Vola)^2/(expiries)^(-1/2))*1e6\n", " return(res)\n", "}" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "4669.56287459822" ], "text/latex": [ "4669.56287459822" ], "text/markdown": [ "4669.56287459822" ], "text/plain": [ "[1] 4669.563" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "obj(vd.Data.C14PM)(params.rHeston)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ " user system elapsed \n", " 0.024 0.000 0.024 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "system.time((res.C14PM <- optim(params.rHeston,obj(vd.Data.C14PM),method=\"L-BFGS-B\",\n", " lower=c(0.0001,0.01,-1),upper=c(.5,10,1))))" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ " user system elapsed \n", " 0.031 0.001 0.031 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "system.time((res.C15PM <- optim(params.rHeston,obj(vd.Data.C15PM),method=\"L-BFGS-B\",\n", " lower=c(0.0001,0.01,-1),upper=c(.5,10,1))))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Notice how fast the calibration is!\n", "\n", "The optimized parameters are:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "

\n", "\t
$H
\n", "\t\t
0.000835784396700211
\n", "\t
$nu
\n", "\t\t
0.373719584768268
\n", "\t
$rho
\n", "\t\t
-0.652211596123752
\n", "
\n" ], "text/latex": [ "\\begin{description}\n", "\\item[\\$H] 0.000835784396700211\n", "\\item[\\$nu] 0.373719584768268\n", "\\item[\\$rho] -0.652211596123752\n", "\\end{description}\n" ], "text/markdown": [ "$H\n", ": 0.000835784396700211\n", "$nu\n", ": 0.373719584768268\n", "$rho\n", ": -0.652211596123752\n", "\n", "\n" ], "text/plain": [ "$H\n", "[1] 0.0008357844\n", "\n", "$nu\n", "[1] 0.3737196\n", "\n", "$rho\n", "[1] -0.6522116\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(fit.C14PM <- as.list(res.C14PM$par))" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "
\n", "\t
$H
\n", "\t\t
0.0033274407426272
\n", "\t
$nu
\n", "\t\t
0.38222733264668
\n", "\t
$rho
\n", "\t\t
-0.652436353082184
\n", "
\n" ], "text/latex": [ "\\begin{description}\n", "\\item[\\$H] 0.0033274407426272\n", "\\item[\\$nu] 0.38222733264668\n", "\\item[\\$rho] -0.652436353082184\n", "\\end{description}\n" ], "text/markdown": [ "$H\n", ": 0.0033274407426272\n", "$nu\n", ": 0.38222733264668\n", "$rho\n", ": -0.652436353082184\n", "\n", "\n" ], "text/plain": [ "$H\n", "[1] 0.003327441\n", "\n", "$nu\n", "[1] 0.3822273\n", "\n", "$rho\n", "[1] -0.6524364\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "(fit.C15PM <- as.list(res.C15PM$par))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Plot the Roughening Heston and optimized leverage swap fits" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "image/png": 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xDdqEjE3RSb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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(expiries,ls.C14PM,type=\"p\",col=\"red\",cex=1,\n", " pch=20,xlab=\"Time to expiry\",ylab=\"Leverage swap fair value\")\n", "curve(ltT(fit.C14PM$H,fit.C14PM$nu,fit.C14PM$rho,10)(x),from=0,to=3,col=\"red\",lwd=2,add=T,n=1000)\n", "points(expiries,ls.C15PM,type=\"p\",col=\"blue\",cex=1,pch=20)\n", "curve(ltT(fit.C15PM$H,fit.C15PM$nu,fit.C15PM$rho,10)(x),from=0,to=3,col=\"blue\",lwd=2,add=T,n=1000)\n", "curve(ltT(H.20170519,nu.20170519,rho.20170519,10)(x),from=0,to=3,col=\"green4\",lwd=2,add=T,n=1000)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Figure 2: Vola Dynamics (http://www.voladynamics.com) red and blue points are C14PM and C15PM estimates respectively; normalized l|everage swap fits with optimized parameters in red and blue respectively; with smile-calibrated parameters in green." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Summary of lecture 5\n", "\n", "- There is a one-to-one correspondence between AFI models and AFV models.\n", " - Jaisson and Rosenbaum's rough Heston model is one example.\n", "\n", "\n", "- To get a non-trivial stochastic volatility model as a limit, we need near-instability of the Hawkes kernel.\n", "\n", "\n", "- Diamonds and the exponentiation theorem allow easy computation of model quantities that can be compared with market values\n", " - Easy calibration.\n", " - As many matching conditions as market option expirations.\n", " \n", " " ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Rough volatility summary\n", "\n", "- Roughness of volatility appears to be universal.\n", " - The microstructural explanation is cool.\n", "\n", "\n", "- Rough volatility models tend to be parsimonious yet consistent with both time series and implied volatility data.\n", "\n", "\n", "- There should be many applications to trading.\n", "\n", "\n", "- And of course the are many interesting mathematical problems.\n", "\n", "\n", "- Rough volatility continues to be an active and fashionable research topic." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### More resources: The Rough Volatility Network\n", "\n", "- For an exhaustive list of papers and presentations on rough volatility and to keep up with the latest developments, see https://sites.google.com/site/roughvol/" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### References \n", "\n", "
\n", "\n", "
\n", "\n", "
    \n", "\n", "
  1. ^\n", "Elisa Alòs, A decomposition formula for option prices in the Heston model and applications to option pricing approximation, *Finance and stochastics* **16**(3) 403-422 (2012).
    2. \n", "\n", "\n", "
  2. ^\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).
    3. \n", "\n", "\n", "
  3. ^ \n", "Emmanuel Bacry, Iacopo Mastromatteo, and Jean-François Muzy, Hawkes processes in finance, *Market Microstructure and Liquidity* **1**(01) 1550005 (2015).\n", "\n", "
  4. ^\n", "Omar El Euch, Jim Gatheral, and Mathieu Rosenbaum, Roughening Heston, available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3116887 (2018).\n", "\n", "
  5. ^ \n", "Masaaki Fukasawa, The normalizing transformation of the implied volatility smile, *Mathematical Finance* **22**(4) 753-762 (2012).
    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", "\n", "
  7. ^ Thibault Jaisson and Mathieu Rosenbaum, Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes, *The Annals of Applied Probability* **26**(5) 2860-2882 (2016).
    8. \n", "\n", "\n", " \n", "\n", "
\n", " \n", "\n", "\n", " " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "3.5.0" } }, "nbformat": 4, "nbformat_minor": 1 }