{ "metadata": { "name": "interpolationPrices", "zanadu": { "authors": [ "Antoine Jacquier" ], "category": "1", "clearance": "Internal", "group_name": "IC MathFin Num Methods", "md5": "8AA7E2857E88BEB40CAC57DD2C72FCD4", "notebook_id": "17D39FE0-C05C-4BDB-8DFE-057052116689", "python_name": null, "reviewer_id": "B81D4EC4-269D-42B3-9975-85BC42EE5712", "status": "Approved" } }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "Linear and quadratic interpolation of option prices\n-----\n*****" }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "We illustrate here the influence of linear/quadratic interpolation of (European) option prices on the shape of the corresponding implied volatility smile." }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Black-Scholes functions" }, { "cell_type": "code", "collapsed": false, "input": "from math import log, sqrt, exp\nfrom scipy.stats import norm\nfrom scipy.optimize import bisect\nfrom zanadu.Groups.ImperialCollege.Root.Tools.BlackScholes import BlackScholes\nfrom zanadu.Groups.ImperialCollege.Root.Tools.ImpliedVolLeeLi import impliedVolCore", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "SVI parameterisation" }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": "We wish to study here the influence, on the implied volatility smile, of linear and quadratic interpolation (in strike) of option prices.\nWe generate a fixed number of option prices, for a given maturity, using the SVI parameterisation:\n$$\n\\mathrm{SVI}(x) = a + b\\left\\{\\rho(x-m) + \\sqrt{(x-m)^2 + \\sigma^2}\\right\\}.\n$$" }, { "cell_type": "code", "collapsed": false, "input": "def SVI(sviParams, x):\n\t########### SVI parameterisation for the implied volatility smile ##############\n ### We return the square root!!!!!!!!!!!!!!!!!!!!!!!!!!!\n\ta, b, rho, m, sigma = sviParams\n\treturn sqrt(a+b*(rho*(x-m) + sqrt((x-m)*(x-m)+sigma*sigma)))", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "prompt_number": 2 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Interpolation of option prices" }, { "cell_type": "code", "collapsed": false, "input": "def interpolationPricesVols(S, v, T, n, nb, minVal, maxVal, sviParams):\n \n prices, strikes, myStrikes, vols, volsSVI, pricesSVI, volsLin, volsQuad, pricesQuad, pricesLin= [], [], [], [], [], [], [], [], [], []\n counter = 1\n \n ################## Initialisation #########################\n X = minVal\n strikes.append(X)\n vol = SVI(sviParams, log(X/S))\n P = BlackScholes(True,S,X,T,0.0,0.0,vol)\n prices.append(P)\n vols.append(vol)\n \n ################## Loop #########################\n \n for i in range(1,n):\n X = minVal + 1.0*i*(maxVal-minVal)/(1.0*n)\n strikes.append(X)\n vol = SVI(sviParams, log(X/S))\n P = BlackScholes(True,S,X,T,0.0,0.0,vol)\n prices.append(P)\n vols.append(vol)\n \n if (i % 2 == 0):\n a = (prices[i]-prices[i-2])/(strikes[i]-strikes[i-2])\n b = prices[i]-a*strikes[i]\n \n for j in range(1,nb):\n X = strikes[i-2] + 1.0*j*(strikes[i]-strikes[i-2])/(1.0*nb)\n P = a*X+b\n myStrikes.append(X)\n myVol = impliedVolCore(True, 1.0, S, X, T, P, tolerance=1e-6, itermax=100)\n pricesLin.append(P)\n volsLin.append(myVol)\n \n ## Price by quadratic interpolation\n P = prices[i-2]*(X-strikes[i-1])*(X-strikes[i]) \\\n / ((strikes[i-2]-strikes[i-1])*(strikes[i-2]-strikes[i])) \\\n + prices[i-1]*(X-strikes[i-2])*(X-strikes[i]) \\\n / ((strikes[i-1]-strikes[i-2])*(strikes[i-1]-strikes[i])) \\\n + prices[i]*(X-strikes[i-2])*(X-strikes[i-1]) \\\n / ((strikes[i]-strikes[i-2])*(strikes[i]-strikes[i-1]))\n \n myVol = impliedVolCore(True, 1.0, S, X, T, P, tolerance=1e-6, itermax=100)\n \n pricesQuad.append(P)\n volsQuad.append(myVol)\n volsSVI.append(SVI(sviParams, log(X/S)))\n pricesSVI.append(BlackScholes(True,S,X,T,0.0,0.0,SVI(sviParams, log(X/S))))\n return myStrikes, pricesLin, pricesQuad, pricesSVI, volsLin, volsQuad, volsSVI", "language": "python", "metadata": { "zanadu": { "is_hidden": true } }, "outputs": [], "prompt_number": 4 }, { "cell_type": "heading", "level": 3, "metadata": { "zanadu": {} }, "source": "Numerical tests" }, { "cell_type": "code", "collapsed": false, "input": "S, v, T = 100., 0.2, 1.\nn = 10 ##has to be an even integer\nnb = 10 ##number of interpolated points between two strikes\n\nminVal, maxVal = 40., 300.\n##################SVI parameters#################\nsviParams = 0.04, 0.4, -0.4, 0., 0.1\n\nstrikes, pricesLin, pricesQuad, pricesSVI, volsLin, volsQuad, volsSVI = interpolationPricesVols(S, v, T, n, nb, minVal, maxVal, sviParams)", "language": "python", "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": "plot(strikes, pricesLin, 'b', label=\"Linear interpolation\")\nplot(strikes, pricesQuad, 'g', label=\"Quadratic interpolation\")\nplot(strikes, pricesSVI, 'r+', label=\"True price\")\nlegend(loc=1)\ntitle(\"Linear and quadratic interpolations of option prices\");\nshow()", "language": "python", "metadata": { "zanadu": {} }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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37l1pO1X56quvsHv3bhgYGCAoKAh+fn4Knyn/+bJtTp48GYMGDYKLiwvc3d0xcuTIKuen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\n6JhU+jFLS+DYMfkljx4eQFgYMGECUOb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"text": "" } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": "plot(strikes, volsLin, 'b', label=\"Linear interpolation\")\nplot(strikes, volsQuad, 'g', label=\"Quadratic interpolation\")\nplot(strikes, volsSVI, 'r+', label=\"True smile\")\nlegend(loc=1)\ntitle(\"Implied volatility outputs\");\nshow()", "language": "python", "metadata": { "zanadu": {} }, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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xY4IZMgR69IA8OK8i8pHevXtjZmbGwYMHJcHnsILyIW9MkuBzi1bLwH8caP5T\nc8YMG4uVlTlr10Imm72LQu556rHi8WQrwCeTEk0ua7SwEUNfHor52df5+GM4dAjkPfl8iup7SRRu\nsmVfATSoziC+PfQtbdro16fZscPYEQkhigpJ8LmsY5WOnLx6ktPXTjF6NEyebOyIhBBFhST4XFbM\ntBj9XuzH3MNz6dIFoqJg715jRyWEKAqkBp8HLt26RK15tbg0/BJLFpZi3TrYvNnYURVcRfm9JAov\nqcEXUG6l3Wjg1oBlJ5bRqxccOwbZuFZECCGeiyT4PDLIbxDfHv6W4sUVw4bBZ58ZOyIhMtqzZw8+\nPj6G2x4eHuzatcuIEYnnJQk+jzTzbMadxDscuHyAAQNg0ybIZJ0oUYBZWlpiZWWFlZUVJiYmWFhY\nGG6HhIQYO7wnatiwoWHtF5B55oWBJPg8YqIxYaDfQOYcnoPNMR1vvgnp1pgSOSknVuJ7hj4SEhK4\nc+cOd+7cwd3dnY0bNxpup19pNSUl5fnjEyIbJMHnod41e7PhzAbu7djM8OGwaBHcuGHsqAohIyX4\nx3elw9XVlRkzZuDk5ESfPn348ccfadiwYYZ2JiYmnD9/HtAv8/v+++/j7u5OuXLlGDhwIPcfs9Fv\nREQEjRs3xsbGhjJlyhAUFJShzzlz5uDt7Y21tTUTJkzg3Llz+Pv7Y2NjQ1BQkGGv2Mw24H5AKcW0\nadPw8vLCwcGBLl26cEPevPmeJPg8ZG9hT7vK7TgaexRXV2jbFubMMXZUIi/ExcVx48YNLl26xHff\nfffEWRGjRo0iIiKC8PBwIiIiiI6O5qOPPsq07fjx42nRogU3b94kOjqaoUOHZrh/+/btHD16lAMH\nDjB9+nT69+9PSEgIly5d4sSJE9kqH82aNYv169fz+++/Exsbi62tLe+88072XwBhFLIWTV7R6UCn\nY/Jtc1wW7iSt/ARmWJjw9mda7r+rlQ1Bntf/X18AJk367/darf4nr/p4DBMTEyZNmoS5uTnm5uZZ\ntlVKMX/+fI4fP27YIW306NF0796dKVOmPNK+WLFiREZGEh0djYuLC/Xq1ctw/4cffoilpSVVq1bl\nhRdeoGXLlnh4eADQsmVLjh49atg56XHmzZvH7NmzcXZ2BvRL7Lq7u7NkyZI82ZlIPBtJ8Hnl/0nC\nWSnmR2ymbNfatPNpR9IlWLwY3nrL2AEWcA8n4WfZKCEn+niMMmXKUKxYsWy1vXr1Kvfu3aN27dqG\n3ymlSEspXHFKAAAgAElEQVRLy7T9jBkzGD9+PC+99BK2tra89957vPnmm4b7028ZV7JkyQy3S5Qo\nQVxc3BNjioyMpEOHDhmSuZmZGXFxcTg5OWXreYm8Jx+9eUyj0VDXpS5fHfwKgA8/1E+ZTE01cmAi\nVz08GyWrbfscHBwoWbIkJ0+e5MaNG9y4cYObN28+dtclR0dHvvvuO6Kjo5k3bx6DBg0y1PKfNq7H\ncXNzY+vWrYZ4bty4wb179yS553OS4I3A5/W3OX3tNMfjjtOwIdjZQSabvYtnlRPbQebylpK+vr78\n9ddfhIeHc//+/Qxbs5mYmNC/f3+GDx/O1atXAYiOjn7sfqWrVq3i8uXLANjY2KDRaLIsm6Sv/2f3\nCsm3336bMWPGGPaAvXr1KuvlTZvvSYI3AvOmzRjoN5BZB2eh0cAHH8D06SBX3+eQfJjgHx4pV6pU\niQkTJvDqq69SuXJlGjZsmKHN9OnT8fLyom7dupQuXZpmzZpx5syZTPs+fPgwdevWxcrKinbt2jFr\n1ixDjT2zEXr63z081/1xI/phw4bRtm1bmjdvjrW1Nf7+/rmyGbfIWbIWjZFcvXuVSrMrcWbwGexK\nlMHHBxYsgIdmzolMyHtJFEayFk0hUqZUGTr6dOS7P77D1BTefx9mzDB2VEKIwkRG8EZ0PO44LZe2\nJHJYJClJ5lSoALt2QbVqxo4sf5P3kiiMZARfyNRwrEEl+0qsPrmakiVhyBBZhEwIkXMkwRvZsJeH\n8eVB/aI0AwfCunUQHW3koIQQhYIkeCNrU6kNV+9e5cDlA9jZQY8e8PXXxo5KCFEYSA0+H/gi9AvC\nYsIICQzh/Hl46SW4cAGsrIwdWf4k7yVRGOVGDV4SfD5w6/4tKnxVgRMDT+Bi7ULnzlC/PgwbZuzI\n8idZo1wUVpLgC6khm4dgXdyayabNOFhSS5cuEBEBZrJakBBFmsyiKQSGvjyU+Ufmk7xrBy+/DOXL\nw88/GzsqIURBJgk+n/C29+Yll5c48c8JQH/h02efyfIFQohn98QEv3XrVnx8fPD29mb69OmZttHp\ndNSqVYvq1aujzeVFmgolnQ6Cg/nqgC0vfrcBNXEibY8EUylGx549xg5OCFFQZVmDT01NpXLlyuzc\nuRMXFxfq1KlDSEgIVapUMbS5efMm9evXZ9u2bbi6uhIfH4+Dg8OjB5Ia/BMppZjbuhyes36iuWdz\n5s3Tb84ti/YJUXTlWg0+LCwMLy8vPDw8MDc3JygoiHXr1mVos2zZMgIDA3F1dQXINLmL7NFoNPiX\n92dm6EwAevaEgwfh9GkjByaEKJCyTPDR0dEZNuF1dXUl+qHLLM+ePcv169dp0qQJfn5+/PTTT7kT\naRFRtdMgTsSd4HjccUqW1F/d+vnnxo5KCFEQZTkJLzvzjZOTkzly5Ai7du3i3r17+Pv7U7duXby9\nvR9pm35TA61WK/X6TBRr2pwhxYbweejnLGq/iEGDoHJl+PhjKFvW2NEJIXKbTqdD92Bv4OeUZYJ3\ncXEhKirKcDsqKspQinmgfPnyhi3GSpYsSaNGjQgPD39ighePN8BvAF6zvIi5E4NzWWe6dIFvvsm4\nD7QQonB6ePA76Tn+4WdZovHz8+Ps2bNERkaSlJTEihUraNu2bYY27dq1Y+/evaSmpnLv3j0OHjxI\n1apVnzkgAXYl7ehRowdfH9QvSjNiBMydC+m28BRCiCfKMsGbmZkxe/ZsAgICqFq1Kl26dKFKlSrM\nmzePefPmAeDj40OLFi2oUaMGL7/8Mv3795cEnwOG1x3O/CPzSUhKoHJlqFsXFi82dlRCiIJElirI\nxzqt6kRDt4YMfXkoe/ZA377w99+QxX7KQohCRpYqKKTe83+PLw58QUpaCg0agI0NbNxo7KiEEAWF\nJPh8rK5rXVysXPjl1C9oNPDuuzJlUgiRfZLg87n3/N/js9DPUEoRGAjnz8Mffxg7KiFEQSAJPp9r\nW7kt1/+9zr6ofZib69eIl1G8ECI75CRrAfDtoW/Zfm47a8sN51YtLRUqQHi4fklhIUThJidZC7ne\nNXuzP2o/1zavoXRp6NVL9m0VQjyZJPgCwMLcggG1BxB6ORTQl2l++AHu3DFyYEKIfE02hMvvdDrQ\n6RiZ9C+WIX9w1+MDPIqVYsgLWhYs0Mq+rUKIx5IafAGyoWttwvq34uNXPubAAejaVb9vq6mpsSMT\nQuQWqcEXEfXK12PuH3NJSEqgbl1wdoa1a40dlRAiv5IEX4DYtwpE66Hl+yPfA/oLn2bONHJQQoh8\nS0o0Bcyh6EMErgzk3NBzmGCOtzcsXQr+/saOTAiRG6REU4TUcamDl50Xy/9cjqkpDB8uFz4JITIn\nI/gCaFvENt7f8T7H3z5OQoIGDw84fBgqVDB2ZEKInCYj+CKmuWdzTDWmbInYgpWVfhnhWbOMHZUQ\nIr+REXwBtezEMub9MY/fev/G5ctQowZcuAClSxs7MiFETpIRfBHUuVpnLt68yIHLB3B1hRYt9Fe3\nCiHEA5LgCygzEzPe83+PGftmAPp9W7/6ClJSjByYECLfkARfgPWp1Ye9l/ZyOv40deroV5f85Rdj\nRyWEyC+kBl/ABeuCuXz7Mt9b92DNNS0zZ8L+/caOSgiRU6QGX4QNfmkwP5/6mTvbNtC+PVy5AgcP\nGjsqIUR+IAm+gHOwcKBHjR4cuHwAU1MYOhS++MLYUQkh8gNZLrgg+/9Swh/dN8FmyX7uu49iYGoJ\ndm/WcumSFjc3YwcohDAmqcEXEj93qcHpwV0Z3XA0776rX0L400+NHZUQ4nk9T+6UBF9I/PPBIGo4\n/syFYReIiy5J7dpw8SJYWho7MiHE85CTrIKyr3XmJZeXWHhsIR4e8MorsHChsaMSQhiTjOALkdCo\nULr93I2zQ84SdsCMnj3h9GnZ8UmIgkxG8AIA//L+uJd2Z/mfy/H3B3t72LjR2FEJITKl0+X6IZ6Y\n4Ldu3YqPjw/e3t5Mnz79kft1Oh2lS5emVq1a1KpVi08++SRXAhXZM6rBKKbtnYYijREjZK14IfIt\nYyf41NRUBg8ezNatWzl58iQhISGcOnXqkXaNGzfm6NGjHD16lHHjxuVasOLJAjwDMDc1Z9OZTQQG\nwvnzcOSIsaMSoohKl8Rv34Zff4Xp06FjpyR26BJy/fBZJviwsDC8vLzw8PDA3NycoKAg1q1b90g7\nqa3nHxqNhlH1RzF171TMzJRc+CSEEaSmwtGjEDZDR+/eUKWqwrHqGb77eBglNlaidrwVzX6bCcHB\n+p9cGs1neaFTdHQ05cuXN9x2dXXl4EPXwWs0Gvbv34+vry8uLi589tlnVK1aNVeCFdnzetXXGffr\nOPZc2kP//o2oUAFiY8HJydiRCVEI6XT8+7KWsDDYuxf27IHQUCjnfpuxJU5xocnb3K62DTuTJEp6\nBVDO82NerfgqzPhan9xzUZYJXqPRPLGDF198kaioKCwsLNiyZQvt27fnzJkzmbYNTvdktFotWq32\nqYIV2WNqYsqH9T5k6t6pbOneiG7dYM4c+OgjY0cmROFw/74+ie/cCRUX6xh2Q0u16mlUanSMhtW+\n5XXzHVy9d4Weu5PwfqE5nnYtKdOqE5omTZ7Yt06nQ5dDI/osp0keOHCA4OBgtm7dCsDUqVMxMTFh\n5MiRj+2wQoUK/PHHH9jZ2WU8kEyTzFOJKYlUnFWRTd02UfJWTRo10l/4VKKEsSMTouBJ3aXjmI2W\nXbv0ST00FKpVA/9Xr9L67wF836UUuy9ux66kHQGeAbTwakEj90ZYTJ7x+FG6TgfZGOQ+T+7McgTv\n5+fH2bNniYyMxNnZmRUrVhASEpKhTVxcHGXLlkWj0RAWFoZS6pHkLvJecbPijKg7gml7p7Hc4W1q\n19aybBn06WPsyIQoGOLjYetW2LQJaq3TsdBdyyuvpvJq70MENp2Dyd6dXDtwjaa7Eilt9xpz7Lpi\n06J9tpI2kP12zyHLBG9mZsbs2bMJCAggNTWVvn37UqVKFebNmwfAgAEDWL16NXPmzMHMzAwLCwuW\nL1+e60GL7BlQewDT9k7j+qGyDB+u5YMP4M03IRuVNyGKHPWrfpS+aZM+qZ88CU2aQKMWV6lXLJxj\nbbux4tx2nG450fLFlrTsvIRebvXh4yn4PW6UbuQytFzJWsiN3z2el+ZvpvWyP6hWDb75Rv+mFUJA\ncjL89hv8/DN4LQlmjmMwrV5T+DQ+RskLs0nRbePqvauM3pXEH/1b42XnRekW7TIm7gczYXKJLDYm\nHvX/pYTvJt2l1NTPuDPqXU6fsOKXG1om79MaOzohjEOn435dLTt26JP6hg1QsSK06XiXFif78t3r\nVmyO2IyFuQWveb9G60qtaejWkOKfTH3uWvqzyrUavCjAtFrQaikFbLn4O7uaaPhofDAt3aHPOfD0\nNHaAQuSd+/dhyxZIHa+j32Utvr7waocYZlWbCaEbuLjjInV2J5Fi3pxp9h2xbxWYr2rpz0pG8EXA\nrVEjqGD7IxFDI5gxyY779+HLL40dlRC5KzVVf+XosmWwdi3U8FVMKDmQbYNd2B29nojrEbT0aknb\nym1p4dUCm2lfGm2UnhUp0Yis6XT0ubUYDxsP3qw4AV9fiIwEa2tjByZEzlIKTs3RMe+0lpUrwdkl\nlZ61v6XijWWcu32K4dtusbX7y1S2r0z5tm9g1vTV/x6cy7X0ZyUJXjzR6fjTNFzYkPPDztOvpyX+\n/jBsmLGjEiJnxMbC4sX6PRAGxY8nbEh9Ujx/QXdlHY6WjnTw6UAHnw7UmPMzmkmTMu/EiKP0rEiC\nF9ny+srXqV++PnUZQY8ecOaMrBUvCiidjqR6WjZs0Cf1vQcSeSloOyYvrKLJqlWs7/aiIal72qU7\n4ZRPR+lZkZOsIltGNxhNu+XtiBgyCAeH4mzcCO3aGTsqIZ7OqVNwcZSONyL9cay/ndLaVTRw/pnA\ny/ZUS6zGS7vuM7JBM7iUAElRoE2X4PPhCD03yQi+iAlYEkDnqp2xON2X+fNh925jRyTEY6QrmSQl\n6U+UfjM3mRN3d/BJidGMbnGJmk416FS1E4FVAnGy+v9qegVwlJ4V2dFJZNvoBqOZvm86HTqmcvo0\nhIcbOyIhHkOn49IlGDsuDaeX97JycTtaUJoZjgMY9PtxLt/uw2+RTRh8r/p/yV1kICP4IkYpRb0F\n9RhRdwQR6zoTEQELFhg7KiH+c+sWbN4MiZ8MZGDF0pjXCqGsrSV9/LrTtXpXKthWyHqUnk9Plj4r\nqcGLbNNoNIxpMIYJugls79+JSpU0TJ8OZcoYOzJRlMXEwPr1cHbRJmxj5mBW/gijTsbiVLM+Ne+1\nomyTzmgaZnONjUKU3J+XjOCLoDSVhu9cXz5t9ikrp7TA2xtGjzZ2VKKoOXMGfvkFflmrOHkzjLIt\nv+OK7c809XyFgS/1p/lP+zGZ9JhNDArZKD0rMk1SPLWlx5cy7495fFXzd9q2hQsXwEy+z4lcpBQc\nPqxP6mvXwo1/b+DVcQnR5eajKXaP/rX70btmb8pZltM/oJCdLH1WcpJVPLUu1btw+fZlzM58jYeH\n/h+cEDnt3j04/JmOwYOhfHl4o6fiEntwH/EG/w6ogGu9/Xz/+pecHXqGUQ1G/ZfcociM0HOTjOCL\nsLmH52I99XPMg87w9dfw++/GjkgUdHfuwP79+iV4f/8djh2Dr2yDuTDoHZKrLGZ99PcA9H+xPz19\ne+Jg4WDkiPM/KdGIZ3I/5T6zWznQZOF+2tetwYYNULOmsaMSBUlKin6j6U2b4M4GHUsua6ldGxo3\nhkaNFEkuOu5NHEK/Fy/Tzqcd/V/sT/3y9bO137PQkwQvns7/14oHYNIk1nSuTtn4QEKLa/lws9aI\ngYmC4PZt/VZ269frl+CtUAFat4Y3LwbjOCeYe+o6uxaM58qm5ZhqTBm0+Sr/jvmQkuYlDctYi+yT\nBC+e2f1xo3Cxns/WjodoXqciZ8+Cg3xrFg/55x9YtQrWrYMDB6BBA2jbVp/YXV3111dcfrcf4xqn\nsO7vdbSp3IYBtQfoR+uTJsnJ0ucgJ1nFMythVoIBtQew6PRM2reH7783dkQiv/j3X1i5Etq0gUqV\n9LX1cQ10REfrL0R6+22wPbmJQ/1fY26bcpT/cgEDNsQSc+ctfrLtSwO3BlKKMTKZGFfUabUM86uC\nzzc+rHxrAn27OPL++zJlsqhKS9PX1H/6Cdasgdq14Y03ICQELC2BYB1Yafkj5g/mHp7L6lOrebX5\nqwyovRRVew/1MluKV0oyRiP/jIs6rRZHoGv1rvx67yvc3aewbh0EBho7MJGXrl/Xf3ubOxdKldIn\n9ePH9eWXBxKSEjgd8wcDvvPj2r/X6P9if069c+q/qY2avZl3LgneaKQGLwC4cOMCfvP9mFn+PAvn\nlua334wdkcgL4eHw9df60XrbtjB4MPgl6NA00RraXPhlISdXfcuf//zJyF33OTu4G552npg0eSVj\n8i5CV5fmJVmLRjy3CrYVaOHVghiHuZw7N5LwcPD1NXZUIjekpOgvbJs1C86f19fST5+GsmX/3yBY\nR2JDf9acWsOcw3M4f+M8/fr3o3/tX+Dz7/F+3AlTSe75jozghcHxuOMELAlgwL8XuBxZQk64FjL3\n78MPP8D06eDuDkOGQIcOYG7+X5vzN85zbugbdK9xFt9yvgz0G0ibSm0wN/1/I1k+IM/JLBqRI2o4\n1qC2U21K1V/EmjVw7ZqxIxI54d49+OIL8PSEbdtg9WrY87GOzp31yT1NpRG2dAbLAiuxunN1mi3Z\nz6mrXdhxrj4d4+z+S+4go/QCRkbwIoO9l/bSa20vGhw9TVUfM0aONHZE4lnduQPffqtP7vXrw7hx\nUKvW/+8MDubmqOEsOraIbw59g2UxS4a8NISu1btScvJ0GaXnIzKCFzmmgVsDnCyd8Om4mm+/hdRU\nY0ckntbduzBlin7EfuwY7NypP4n6ILn/9c9fbDyzkQpfVSAsOowf2//IkbeO0KdWH/3VpqLQkJOs\n4hGjG4xm7O6xlHPqwqZNGtq2NXZET+fGDf1iV7/+ClFR+rndaWn6D6v0/1++vH5kW78+VK4MJgV8\nuJOaCosXw/jx+uf0++/g46O/TynFoWWfcnr1POLuxvH+jrtccn8XqxNWYJ8E5dNdkCRlmELjiSWa\nrVu3Mnz4cFJTU+nXrx8jH/Od/dChQ/j7+7Ny5Uo6duz46IGkRFNgKKWoMbcGg872YN3JkWzdauyI\nsnbnDuzZo0/ou3fD2bPg7w+vvAJeXmBqqk/eJib//b9Go59Bsm+f/ufWLahX77+EX7duxpOP+d3O\nnfD++/o57DNn6uNHp+Pf+i+z9MRSvjjwBWYmZrxb912CqgdR/JOpUoYpIJ4rd6ospKSkKE9PT3Xh\nwgWVlJSkfH191cmTJzNt16RJE/Xaa6+p1atXZ9rXEw4l8pkl4UvUD23cVJkySp05Y+xoMvfnn0p1\n6KBUqVJKabVKffSRUnv2KJWY+PR9xcQotWqVUsOHK1W7tlLlyys1a5ZSd+/mfNw56c8/lWrZUilP\nT6VWr1YqLU3/+7iEOPVrr8aq7KdlVaulrdTOcztV2oM7lVJq4kSjxCue3vPkziy/lIaFheHl5YWH\nhwfm5uYEBQWxbt26R9p9/fXXvP7665SRjT0Ljc7VOnM76RYBfQ8wd66xo8koMhJ69dKP0Bs00C+E\n9euv+tJEgwZQrNjT9+nkBK+/rj8hefiwfqbJ7t1QsSJMnaof4ecn16/DwIHQpAk0bw4nT+qvPr54\nK5J3Nr1D5dmVSUhK4Lfev7Gp2yaaVmyacV0YKcMUCVkm+OjoaMqXL2+47erqSnR09CNt1q1bx8CB\nAwFkcaGCTqeD4GDMP57M8G23CDj5Jo5zgrm/VWfsyIiLg6FD9eujeHjoSzHvvgsWFjl/rJde0m8t\nt2uXPnl6esLYsXD1as4f62koBcuWQbVq+lLTuR90DB8OEbdO0vOXngwdWYMOK8KJutWX1iF/4DN7\nub4U82B56AckwRcJWZ5kzU6yHj58ONOmTTPUiVQWtaLgdDU/rVaLVt5k+U+69bqTUpMYYT2f6ubd\ncYjxpo+RQrp9Gz79VD/l74034NSpdFdd5rJq1fQLb50/r4+hcmUYNUpf787rk7LnzulH7XFx+g+f\nunUh+t2l9Lz3FaFRoQx9eSiDvrqETQkb/QOKWUqdvQDS6XToHv5AflZZ1W9CQ0NVQECA4faUKVPU\ntGnTMrSpUKGC8vDwUB4eHsrS0lKVLVtWrVu3LkfrSMJIJk5U43ePVy2/GaBefPG/+m5eOndOqSpV\nlOreXanIyLw//sMiI5Xy91fqtdeUio/Pm2MmJio1ZYpS9vZKzZihVFKSUqFRoarZ4mbq8+bWataB\nWepuUiYnC6TOXig8T+7M8pHJycmqYsWK6sKFCyoxMfGxJ1kf6N27t1qzZk2OBymM5NdfVVxCnLKZ\nZqPcql5RBw7k7eH37lWqXDmlvvkmb4/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