{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "# Rough Volatility\n", " \n", "

" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "### The time series of realised variance\n", "\n", "- Assuming an underlying variance process $v_s$, integrated variance $\\frac 1 \\delta \\,\\int_t^{t+\\delta}\\,v_s\\,ds$ may (in principle) be estimated arbitrarily accurately given enough price data.\n", "\n", " - In practice, market microstructure noise makes estimation harder at very high frequency.\n", " - Sophisticated estimators of integrated variance have been developed to adjust for market microstructure noise. See Gatheral and Oomen [10] (for example) for details of these.\n", "\n", "\n", "- The Oxford-Man Institute of Quantitative Finance makes historical realized variance (RV) estimates freely available at http://realized.oxford-man.ox.ac.uk. These estimates are updated daily.\n", "\n", " - Each day, for 21 different indices, all trades and quotes are used to estimate realized (or integrated) variance over the trading day from open to close.\n", "\n", "\n", "\n", "- Using daily RV estimates as proxies for instantaneous variance, we may investigate the time series properties of $v_t$ empirically.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "First update and save the latest Oxford-Man data:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [], "source": [ "import warnings; warnings.simplefilter('ignore')\n", "import datetime as dt\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import zipfile as zi\n", "from io import StringIO, BytesIO\n", "from scipy import stats\n", "from sklearn.linear_model import LinearRegression\n", "import requests\n", "import urllib\n", "%matplotlib inline\n", "plt.style.use('seaborn-darkgrid')\n", "from scipy.stats import norm" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "data": { "text/html": [ "
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SPX2.rkFTSE2.rkN2252.rkGDAXI2.rkRUT2.rkAORD2.rkDJI2.rkIXIC2.rkFCHI2.rkHSI2.rk...AEX.rkSSMI.rkIBEX2.rkNSEI.rkMXX.rkBVSP.rkGSPTSE.rkSTOXX50E.rkFTSTI.rkFTSEMIB.rk
2002-07-080.0001990.0001920.0001440.0004120.0001190.0000160.0001680.0003210.0003240.000074...0.0003410.0001690.0003280.0000510.0000220.0000980.0000120.0003730.0001170.000209
2002-07-100.0003550.0003750.0001480.0003780.0001200.0000210.0002910.0003970.0003410.000028...0.0003670.0001700.0003350.0000440.0000450.0001790.0000350.0007000.0000970.000178
2002-07-110.0006300.0005440.0001020.0008220.0001970.0000790.0004500.0008620.0006450.000066...0.0007210.0003470.0005580.0000470.0000450.0003150.0000370.0010760.0000590.000328
2002-07-120.0004380.0009230.0001120.0015640.0001300.0000230.0004420.0004660.0007710.000041...0.0007050.0004170.0004050.0000650.0000450.0003400.0000270.0012220.0000450.000473
2002-07-150.0005830.0003700.0001160.0006190.0001850.0000060.0005740.0005960.0005940.000033...0.0004930.0002630.0004160.0000540.0001280.0002660.0000850.0006020.0000650.000513
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5 rows × 21 columns

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" ], "text/plain": [ " SPX2.rk FTSE2.rk N2252.rk GDAXI2.rk RUT2.rk AORD2.rk \\\n", "2002-07-08 0.000199 0.000192 0.000144 0.000412 0.000119 0.000016 \n", "2002-07-10 0.000355 0.000375 0.000148 0.000378 0.000120 0.000021 \n", "2002-07-11 0.000630 0.000544 0.000102 0.000822 0.000197 0.000079 \n", "2002-07-12 0.000438 0.000923 0.000112 0.001564 0.000130 0.000023 \n", "2002-07-15 0.000583 0.000370 0.000116 0.000619 0.000185 0.000006 \n", "\n", " DJI2.rk IXIC2.rk FCHI2.rk HSI2.rk ... AEX.rk SSMI.rk \\\n", "2002-07-08 0.000168 0.000321 0.000324 0.000074 ... 0.000341 0.000169 \n", "2002-07-10 0.000291 0.000397 0.000341 0.000028 ... 0.000367 0.000170 \n", "2002-07-11 0.000450 0.000862 0.000645 0.000066 ... 0.000721 0.000347 \n", "2002-07-12 0.000442 0.000466 0.000771 0.000041 ... 0.000705 0.000417 \n", "2002-07-15 0.000574 0.000596 0.000594 0.000033 ... 0.000493 0.000263 \n", "\n", " IBEX2.rk NSEI.rk MXX.rk BVSP.rk GSPTSE.rk STOXX50E.rk \\\n", "2002-07-08 0.000328 0.000051 0.000022 0.000098 0.000012 0.000373 \n", "2002-07-10 0.000335 0.000044 0.000045 0.000179 0.000035 0.000700 \n", "2002-07-11 0.000558 0.000047 0.000045 0.000315 0.000037 0.001076 \n", "2002-07-12 0.000405 0.000065 0.000045 0.000340 0.000027 0.001222 \n", "2002-07-15 0.000416 0.000054 0.000128 0.000266 0.000085 0.000602 \n", "\n", " FTSTI.rk FTSEMIB.rk \n", "2002-07-08 0.000117 0.000209 \n", "2002-07-10 0.000097 0.000178 \n", "2002-07-11 0.000059 0.000328 \n", "2002-07-12 0.000045 0.000473 \n", "2002-07-15 0.000065 0.000513 \n", "\n", "[5 rows x 21 columns]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "url = 'https://realized.oxford-man.ox.ac.uk/images/oxfordmanrealizedvolatilityindices-0.2-final.zip'\n", "data = requests.get(url, stream=True).content\n", "z = zi.ZipFile(BytesIO(data))\n", "z.extractall()\n", "\n", "df = pd.read_csv('OxfordManRealizedVolatilityIndices.csv', index_col=0, header=2 )\n", "rv1 = pd.DataFrame(index=df.index)\n", "for col in df.columns:\n", " if col[-3:] == '.rk':\n", " rv1[col] = df[col]\n", "rv1.index = [dt.datetime.strptime(str(date), \"%Y%m%d\") for date in rv1.index.values]\n", "rv1 = rv1.dropna()\n", "rv1.head()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "We only extract the realised variance estimators computed via realised kernel, which are denoted by \".rk\"." ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "#### SPX Time Series" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "##### Importing the SPX" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "We can get the corresponding SPX data from the CBOE website directly (see also the SPXHistory notebook)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SPX
Date
1986-06-30250.84
1986-07-01252.04
1986-07-02252.70
1986-07-03251.79
1986-07-07244.05
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" ], "text/plain": [ " SPX\n", "Date \n", "1986-06-30 250.84\n", "1986-07-01 252.04\n", "1986-07-02 252.70\n", "1986-07-03 251.79\n", "1986-07-07 244.05" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "url = r'http://www.cboe.com/micro/buywrite/dailypricehistory.xls'\n", "spx = pd.read_excel(url)#, index_col=0, header=0, parse_dates=True)\n", "spx = spx.drop(spx.index[:4])\n", "spx = spx[[spx.columns[0], spx.columns[3]]]\n", "spx.rename(columns={spx.columns[0]:'Date', 'Unnamed: 3': 'SPX'}, inplace=True)\n", "spx.set_index('Date', inplace=True)\n", "spx['SPX'] = spx['SPX'].apply(pd.to_numeric) ## make sure the SPX data is really of Float type\n", "spx = spx[:-25]\n", "#spx.index = pd.DatetimeIndex(data=spx.index)\n", "spx.index = pd.to_datetime(spx.index, errors='coerce')\n", "spx.head()" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "##### Adding the variance time series" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [ { "data": { "text/html": [ "
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SPXRV
Date
2002-07-08976.980.000199
2002-07-10920.470.000355
2002-07-11927.370.000630
2002-07-12921.390.000438
2002-07-15917.930.000583
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" ], "text/plain": [ " SPX RV\n", "Date \n", "2002-07-08 976.98 0.000199\n", "2002-07-10 920.47 0.000355\n", "2002-07-11 927.37 0.000630\n", "2002-07-12 921.39 0.000438\n", "2002-07-15 917.93 0.000583" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "spx[\"RV\"] = rv1['SPX2.rk']\n", "spx = spx.dropna()\n", "spx.head()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "spx[\"SPX\"].plot(color='blue', grid=True, label='SPX',figsize=(8, 5));\n", "spx[\"RV\"].plot(color='red', grid=True, label='SPX realised variance',figsize=(8, 5), secondary_y =True);\n", "plt.title(\"SPX and realised variance\");" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "###Smoothness of the volatility process\n", "\n", "\n", "For $q\\geq 0$, we define the $q$th sample moment of differences of log-volatility at a given lag $\\Delta$.\n", "($\\langle\\cdot\\rangle$ denotes the sample average):\n", "$$\n", "m(q,\\Delta):=\\langle\\left|\\log \\sigma_{t+\\Delta}^2 -\\log \\sigma_{t}^2 \\right|^q\\rangle.\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "###Scaling of $m(q,\\Delta)$ with lag $\\Delta$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "source": [ "nbDeltas = 100\n", "lags = np.linspace(1., 100., nbDeltas, dtype=int)\n", "qq = np.array([0.5, 1., 1.5, 2., 3.])\n", "nq = len(qq)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "source": [ "def mqd(col, q, ll):\n", " return [np.log(pow(abs(np.log(rv1[col]) - np.log(rv1[col].shift(l))), q)).mean() for l in ll]" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "#### Choose the index" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Index: SPX2.rk\n" ] } ], "source": [ "col = rv1.columns[0]\n", "print(\"Index: \", col)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7,5))\n", "colors = ['red', 'black', 'blue', 'brown', 'green']\n", "mqds = []\n", "for i in range(nq):\n", " mqds.append(mqd(col, qq[i], lags))\n", " plt.scatter(np.log(lags), mqds[-1], marker=\"+\", c=colors[i], label=\"q=%.1f\" %qq[i])\n", "plt.legend(loc=4)\n", "plt.xlabel(\"log($\\Delta$)\")\n", "plt.ylabel(\"log(m(q, $\\Delta$))\")\n", "plt.title(col)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "##### Linear fit" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "data": { "image/png": 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interceptCoef
q
0.5-0.5420420.061590
1.0-1.0840840.123180
1.5-1.6261260.184770
2.0-2.1681680.246361
3.0-3.2522520.369541
\n", "
" ], "text/plain": [ " intercept Coef\n", "q \n", "0.5 -0.542042 0.061590\n", "1.0 -1.084084 0.123180\n", "1.5 -1.626126 0.184770\n", "2.0 -2.168168 0.246361\n", "3.0 -3.252252 0.369541" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "regrInterc, regrCoef = np.zeros(nq), np.zeros(nq)\n", "logLagsx = np.log(lags).reshape(-1, 1)\n", "colors = ['red', 'black', 'blue', 'brown', 'green']\n", "for i in range(nq):\n", " y = np.array(mqds[i]).reshape(-1, 1)\n", " regr = LinearRegression()\n", " regr.fit(logLagsx,y)\n", " regrCoef[i] = regr.coef_[0][0]\n", " regrInterc[i] = regr.intercept_[0]\n", " plt.scatter(logLagsx,y, marker=\"+\", c=colors[i], label=\"q=%.1f\" %qq[i])\n", " plt.plot(logLagsx,regr.predict(logLagsx), c=colors[i], linewidth=2)\n", "\n", "plt.legend(loc=4, fontsize=10)\n", "plt.xlabel(\"log($\\Delta$)\")\n", "plt.ylabel(\"log(m(q, $\\Delta$))\")\n", "plt.title(\"Linear fits for %str\" %col)\n", "plt.show()\n", "\n", "linearFitsDF = pd.DataFrame(index=qq)\n", "linearFitsDF[\"intercept\"] = regrInterc\n", "linearFitsDF[\"Coef\"] = regrCoef\n", "linearFitsDF.index.name = \"q\"\n", "linearFitsDF.head()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "###Monofractal scaling result\n", "\n", "- From the above log-log plot, we see that for each $q$, $m(q,\\Delta) \\approx \\Delta ^{\\zeta_q}$.\n", "\n", "\n", "- How does $\\zeta_q$ scale with $q$?" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "qqx, y = qq.reshape(-1, 1), regrCoef.reshape(-1, 1)\n", "regr = LinearRegression()\n", "regr.fit(qqx,y)\n", "plt.scatter(qqx,y, marker=\"o\", s=40, c='blue')\n", "plt.plot(qqx,regr.predict(qqx), 'r', linewidth=2)\n", "plt.xlabel(\"q\", fontsize=15)\n", "plt.ylabel(\"$\\zeta_q$\", fontsize=15)\n", "plt.title(\"Linear fit $\\zeta_q = qH$, with H=%.2f for %str\" %(regr.coef_[0][0], col), fontsize=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "###Testing over a longer range of powers $q$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "col = rv1.columns[2]\n", "qq = np.linspace(0.2, 10., 30)\n", "nq = len(qq)\n", "mqds = []\n", "for i in range(nq):\n", " mqds.append(mqd(col, qq[i], lags))\n", "\n", "regrInterc, regrCoef = np.zeros(nq), np.zeros(nq)\n", "logLagsx = np.log(lags).reshape(-1, 1)\n", "for i in range(nq):\n", " y = np.array(mqds[i]).reshape(-1, 1)\n", " regr = LinearRegression()\n", " regr.fit(logLagsx,y)\n", " regrCoef[i] = regr.coef_[0][0]\n", " regrInterc[i] = regr.intercept_[0]\n", "\n", "linearFitsDF = pd.DataFrame(index=qq)\n", "linearFitsDF[\"intercept\"] = regrInterc\n", "linearFitsDF[\"Coef\"] = regrCoef\n", "linearFitsDF.index.name = \"q\"\n", "qqx, y = qq.reshape(-1, 1), regrCoef.reshape(-1, 1)\n", "regr = LinearRegression()\n", "regr.fit(qqx,y)\n", "plt.scatter(qqx,y, marker=\"+\", s=30, c='blue')\n", "plt.plot(qqx,regr.predict(qqx), 'r', linewidth=2)\n", "plt.xlabel(\"q\", fontsize=15)\n", "plt.ylabel(\"$\\zeta_q$\", fontsize=15)\n", "plt.title(\"Linear fit $\\zeta_q = qH$, with H=%.2f for %str\" %(regr.coef_[0][0], col), fontsize=15)\n", "plt.show()\n", "#print regr.coef_[0][0], regr.intercept_[0]" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "###Estimated $H$ for all indices\n", "\n", "We now repeat this analysis for all 21 indices in the Oxford-Man dataset.\n", "We only use $q=2$, and compute the optimal H as well as the constant." ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "We consider the model \n", "$$\n", "\\sigma_t = \\exp(\\nu W_t^H),\n", "$$\n", "where $W^H$ is a fractional Brownian motion with Hurst parameter $H \\in (0,1)$ and $\\nu>0$ the volatility of volatility parameter.\n", "With $q=2$, can therefore compute\n", "$$\n", "m(2, \\Delta) = \\mathbb{E}\\left[\\left|\\log\\left(\\sigma^2_{t+\\Delta}\\right) - \\log\\left(\\sigma^2_{t}\\right)\\right|^2\\right]\n", " = 2\\nu^2\\mathbb{E}\\left[\\left|W_{t+\\Delta}^H - W_{t}^H\\right|^2\\right].\n", "$$\n", "Since\n", "$$\n", "\\mathbb{E}\\left[\\left|W_{t+\\Delta}^H - W_{t}^H\\right|^2\\right]\n", "= \\mathbb{E}\\left[\\left|W_{t+\\Delta}^H\\right|^2\\right] + \\mathbb{E}\\left[\\left|W_{t}^H\\right|^2\\right] - 2\\mathbb{E}\\left[W_{t+\\Delta}^HW_{t+\\Delta}^H\\right]\n", " = \\Delta^{2H},\n", "$$\n", "we therefore deduce that\n", "$$\n", "\\log m(2, \\Delta) = 2H\\log(\\Delta) + \\log(2\\nu^2).\n", "$$\n", "We therefore perform a linear regression of $\\log m(2, \\Delta)$ against $\\log(\\Delta)$ to estimate the coefficients $H$ and $\\nu$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [ { "data": { "text/html": [ "
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NameHnu
0SPX2.rk0.123180.239152
1FTSE2.rk0.1539880.181062
2N2252.rk0.105730.228443
3GDAXI2.rk0.1561180.1931
4RUT2.rkNaNNaN
5AORD2.rk0.08359540.261631
6DJI2.rk0.1255410.229289
7IXIC2.rk0.1218260.207692
8FCHI2.rk0.1403790.198766
9HSI2.rk0.1011650.19879
10KS11.rk0.1160120.20715
11AEX.rk0.1420780.204152
12SSMI.rk0.1729750.152719
13IBEX2.rk0.1408790.193962
14NSEI.rk0.1193130.219514
15MXX.rk0.1059980.205725
16BVSP.rk0.1029420.216939
17GSPTSE.rkNaNNaN
18STOXX50E.rk0.1323260.214822
19FTSTI.rk0.1034130.159045
20FTSEMIB.rk0.1343510.210811
\n", "
" ], "text/plain": [ " Name H nu\n", "0 SPX2.rk 0.12318 0.239152\n", "1 FTSE2.rk 0.153988 0.181062\n", "2 N2252.rk 0.10573 0.228443\n", "3 GDAXI2.rk 0.156118 0.1931\n", "4 RUT2.rk NaN NaN\n", "5 AORD2.rk 0.0835954 0.261631\n", "6 DJI2.rk 0.125541 0.229289\n", "7 IXIC2.rk 0.121826 0.207692\n", "8 FCHI2.rk 0.140379 0.198766\n", "9 HSI2.rk 0.101165 0.19879\n", "10 KS11.rk 0.116012 0.20715\n", "11 AEX.rk 0.142078 0.204152\n", "12 SSMI.rk 0.172975 0.152719\n", "13 IBEX2.rk 0.140879 0.193962\n", "14 NSEI.rk 0.119313 0.219514\n", "15 MXX.rk 0.105998 0.205725\n", "16 BVSP.rk 0.102942 0.216939\n", "17 GSPTSE.rk NaN NaN\n", "18 STOXX50E.rk 0.132326 0.214822\n", "19 FTSTI.rk 0.103413 0.159045\n", "20 FTSEMIB.rk 0.134351 0.210811" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "optimalH, optimalnu = [], []\n", "\n", "q = 2.\n", "for col in rv1.columns:\n", " try:\n", " mqds = mqd(col, q, lags)\n", " regr = LinearRegression()\n", " regr.fit(logLagsx,np.array(mqds).reshape(-1, 1))\n", " optimalH.append(0.5*regr.coef_[0][0])\n", " optimalnu.append(np.sqrt(0.5*np.exp(regr.intercept_[0])))\n", " except:\n", " optimalH.append(\"NaN\")\n", " optimalnu.append(\"NaN\")\n", "\n", "dataCoefdf = {\"Name\": rv1.columns, \"H\": optimalH, \"nu\": optimalnu}\n", "Coefdf = pd.DataFrame(data=dataCoefdf)\n", "Coefdf" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "The value of H seems to be consistent throughout all indices." ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "#### What about the distribution of $(\\log \\sigma_{t+\\Delta}-\\log \\sigma_t)$?" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [], "source": [ "def plotScaling(col, llags):\n", " ## llags : array of lags (in days)\n", " \n", " def xDel(x, lag):\n", " return x - x.shift(lag)\n", " \n", " def sdl(lag):\n", " return (xDel(np.log(rv1[col]), lag)).std()\n", " \n", " sd1 = (xDel(np.log(rv1[col]), 1)).std()\n", " h = Coefdf.loc[Coefdf[\"Name\"] == col][\"H\"].values[0]\n", " f, ax = plt.subplots(1,len(llags),sharex=False, sharey=False, figsize=(15, 5)) \n", " \n", " for i in range(len(llags)):\n", " la = llags[i]\n", " hist_val = xDel(np.log(rv1[col]), la).dropna()\n", " \n", " k2, p = stats.normaltest(hist_val)\n", " ax[i].set_title('%str ; Lag = %s Days' %(col, la))\n", " n, bins, patches = ax[i].hist(hist_val.values, bins=100,normed=1, facecolor='green',alpha=0.2)\n", " #.hist(bins=20)\n", " ax[i].plot(bins, norm.pdf(bins,hist_val.mean(),hist_val.std()), \"r\")\n", " ax[i].plot(bins, norm.pdf(bins,hist_val.mean(),sd1 * la ** h), \"b--\") ## scaling\n", " height = 1. / (hist_val.std()*np.sqrt(2.*np.pi))\n", " right = max(hist_val)\n", " ax[i].text(0.6*right,height,\"pval=%.1E\" %p, horizontalalignment='center',verticalalignment='center')\n", " ax[i].set_xlim([min(hist_val), max(hist_val)])\n", " hist_val.plot(kind='density', ax=ax[i])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "col = rv1.columns[15]\n", "llags = [1, 20, 200] ## in days\n", "plotScaling(col,llags)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "### Summary: A natural model of realised volatility\n", "\n", "- Distributions of differences in the log of realized volatility are close to Gaussian.\n", "\n", " - This motivates us to model $\\sigma_t$ as a lognormal random variable.\n", "\n", "\n", "- Moreover, the scaling property of variance of RV differences suggests the model:\n", "\n", "(1)\n", "$$\n", "\\log \\sigma_{t+\\Delta} - \\log \\sigma_t =\\nu\\,\\left( W^H_{t+\\Delta}-W^H_t\\right)\n", "$$\n", "where $W^H$ is fractional Brownian motion." ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "### Remark: Is it the same for the stock price?" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "source": [ "spx[\"returns\"] = spx[\"SPX\"].pct_change(1)\n", "def mqdspx(q, ll):\n", " return [np.log(pow(abs(np.log(spx[\"returns\"]) - np.log(spx[\"returns\"].shift(l))), q)).mean() for l in ll]\n", "\n", "nbDeltas = 100\n", "lags = np.linspace(1., 100., nbDeltas, dtype=int)\n", "qq = np.array([0.5, 1., 1.5, 2., 3.])\n", "nq = len(qq)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7,5))\n", "colors = ['red', 'black', 'blue', 'brown', 'green']\n", "mqds = []\n", "for i in range(nq):\n", " mqds.append(mqdspx(qq[i], lags))\n", " plt.scatter(np.log(lags), mqds[-1], marker=\"+\", c=colors[i], label=\"q=%.1f\" %qq[i])\n", "plt.legend(loc=4)\n", "plt.xlabel(\"log($\\Delta$)\")\n", "plt.ylabel(\"log(m(q, $\\Delta$))\")\n", "plt.title(\"SPX index\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "Not really convincing for the index itself (actually reassuring...)" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "# Fractional Brownian motion" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "- *Fractional Brownian motion* (fBm) $\\{W^H_t; t \\in \\mathbb{R}\\}$ is the unique Gaussian process with mean zero and autocovariance function\n", "$$\n", "\\mathbb{E}\\left[W^H_t W^H_s\\right] = \\frac12\\,\\left\\{ |t|^{2\\,H}+|s|^{2\\,H}-|t-s|^{2\\,H} \\right\\}\n", "$$\n", "where $H \\in (0,1)$ is called the *Hurst index* or parameter.\n", " - In particular, when $H=1/2$, fBm is just Brownian motion.\n", " \n", " - If $H>1/2$, increments are positively correlated.% so the process is trending.\n", " - If $H<1/2$, increments are negatively correlated.% so the process is reverting.\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "### Paths of the log-volatility process" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "source": [ "col = rv1.columns[10]" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "zanadu": { "code_type": "", "is_hidden": false } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "logrv = pd.DataFrame(np.log(rv1[col]))\n", "logrv.plot(color='blue', grid=True, title=\"log($\\sigma$(%str))\" %col,figsize=(12, 4));" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "### Paths of fractional Brownian motion" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "We simulate the paths of fractional Brownian motion on the same daily time grid as the volatility paths above, in order to visually distinguih the different levels of `roughness' of the paths.\n", "The simulation is performed using Cholesky decomposition, so is slow." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [], "source": [ "from math import sqrt\n", "from random import gauss\n", "def covFrac(s, t, H): ## covariance function\n", " return 0.5*(np.power(s,2.*H) + np.power(t,2.*H) - np.power(np.abs(t - s),2.*H))\n", " \n", "def fbmmatrix(T, nbTimes, H):\n", " tt = np.linspace(0., T,nbTimes)[1:]\n", "\n", " covMatrixFrac = np.matrix([[covFrac(tt[i], tt[j], H) for j in range(nbTimes-1)] for i in range(nbTimes-1)])\n", " cholMatFrac = np.linalg.cholesky(covMatrixFrac)\n", " gaussianVec = np.matrix([np.random.normal(0., 1.) for i in range(nbTimes-1)])\n", "\n", " pathFrac = cholMatFrac * gaussianVec.T\n", " return np.insert(tt, 0, 0.), np.insert(pathFrac.A1, 0, 0.)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "data": { "image/png": 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s5NMVB7m9b1N5n+RpE00n2CZW2J2UVDqwmAz/mVmqYOiWYx2dU0RBuY035u/G7nTJ4hjcfo6XfLKS4Z+sVG0PhtNHHRdWVFnHTmR6+Jqv1jJu+lbVtuX7q6zT1mpYxVySRKXnelySxM8bs3ln0V5emrcr4DlKYVTpcy+2HilhwLt/03vCEr99B46Xs/5wEQAv/C7KvqPBCGRgd2ps35hVxJ78MgCKT7IVT6uLO1hQwcTF+9h3rFxj74lRWG7nTzGv1sutKcVh+vvOE/P4bMUBrv5qLdtz/a3NZRq/U5lN/dw8M0fUFMZecooq+Gb1IT+hF4wNWTUb8HpZtDtfczD06YqDDHpvWa3PDNUGXmHs5a+d+bzy5275s9MlMUDhKnPPtM2q48tsDu77eQtPzt7hV7YkSRwrs/Hob9uZsHCvPGsWDpnjF/PsXDHs408nB46Xy22ML//7UX2/vAviSJLErd9uZNSU9Sf8/TdPXc+Fk1Zy3ocrzkgXo1ONLo7/hXy/LovfajlXtM6J886ivfywIZsFu/Ips6o76exiKznFVg4erwhwtprFe47J/7skSdXpO7TUXTUJ5D4RjjieuHgfr8/fzevzd9P/3b9xSRKLdh9TdZaB8C74UFLpUPmdirmljJqyXv5+rwXKy+VfrOE2Twf965ZcgFoREfmlVvLLbIz+biNXf7UWgCLPQCTQ9LnN4WL8gj3ycdUlkEvh16sPceWXa2pUZjDeWriHx2ZuRzxa6rfv1y1HOFZ2aq3W4a78+POmHD5ZfhCAXXn+oqJEQxyXWB1MWLiHAs/0f6hAtwFvLuLdxft4ad6ukPehtgJHQ82e7D1Wzu68sjMuUNXLkj3H/ESe729hdbh47c9dZI5fjCRJnD1xWcDyft1yhKEfrZA/T12bFfBYLWZtza3W8Voof/uDBRUUhuHDXl0u/2KN3MaE4t3F+yi1OtiWW8rmnGJ2aLy71WVPftXAW2tg+V9DF8f/Qt5csIfnf995uqvxj8YlSXy3LqvWhIHd6WLWtqOA27J7RQCRE26shVIMVNpdKnG87nARB46HtjAeOF7OLVM3kFdq9du3PquIrTnFfiL5kk9XkTl+MVd+sUbVOc/YnMPREnc5X68+xI8bspm20W1tK7c5Ka4M3pl4dez4BXt4fq7Ihqwi1f53Fu9Vff55Y5UlT2npfn1+lQDPLg7uOxzsXnstJ8M+XskwRccsSRJFFV4XEG0r/+87jvLduiw+/Hs/+4+Xh+1De7rwXuuuPHUHe7TEygu/7+ShGVu1Tqt1NmcXu6fONZ7HxKjgrgQv/L7T75nXEsc3Tl7P1LVZDP9kFX/vPU7DxKiw6xfK3cN3NuhksTGriGu+XsuXqw6etO+oDr6D0Aemb5VjFLyc+8Fy1efU2Ah+8rzD7yxSr3zoW94qH8v+t2sPsynbv206WWzOLmboRyv4Y8dRSq0ORn6+mqfn+Fu4Txa7A1iT31uyL2yL8W3fbeDmqYGPLfeZUSm16eJYF8c6Ohos31/A+AV7+KiWgh8W7T4W+iBgzHcbQx/kQ7nNwfXfrJM/PzhjK5d/sSak5fTPnXlszinmrh83+01V/u/HzYyauiGgC8G+4+WUeRrQgnIbL/6xiwema4uoUquD33eEP23/29ZcCnysrs1SYlSfCyrsbDtSwrJ9x1VW9B83ZMv/X/rpairsTj76ez+/bz/qZxkNFvU9Zc1hzSCoHm8t4UiJW3QHsqLbPWJz2sYcrvhiDTdNWa9yA3E4XUxYuCdk8FIgfEXBxqwiXpm3q8aW8gSP8PR1Z/C67mzOKZHTp1WXcK3AALd8u4FHf9vOtiMl1PFYdDM84rVBGCL29x1H5f8Ly+2ym40WlQ4X9/2yJWwXDqia1QiEr8vGyXJ/8LptfPT3gVqd/nb786vLK7U6gl5HXqmVkZ+v9tteFkJcHSyomiGbsvawal92cSXPztnB/J3abcbRUhu3fruB//24KehMVm1Z1nd5xOnqg4VykOTKAwXBTqlVrglgTZ62Ue3q4/s7zdmey01T1iNJEuuzitmSU8K0jdmqY2Zvy2XUlPUMnKjODuM7s/lfRBfH/zJCNUpKpq49zB+KDsWL1eFSNZKVdiefLt130qbxHE4Xnyw74Dd6PZ1kFboFUKnVUSv+mMqI+WBW3XK7E7vT5edTW25z4nC6eGXeLj+r1OYcbcukVqelxLsC2L7j5Xy3TnuqMph4OOTp4LwdVEEAsZdTbGX1wcB+neDfsOf7+FzGRpr8zrE5XNwbItvHuR8s57MVB3ly9g7VAOKH9Vly/bV4b8k+npilnSHCaxWrtPt3zEeKKzXdKZQ+4Qt3H2Pq2izeXbzP7zgInarp0s9Ws3z/ce76cRN/7DjKgzO28fOmnBrPckR4AiwPF1by/FxR/h2VYvDWbzdUu9zFe45xzvvL2HC4iHKbk2fnigF9KpUs3Xuc3k2TmXxDV546vzXgf0/6NU/xO297bikOp4sym4NzP1zOhIV7/Y7xZZ/Gu3hOK+3l2K2eQYlLkli85xhbcoqZva1qyt63/fIV0y5J8htwFVXYueTTVexUDNy03FuUzNle1WZ7fU+VOFxS2EGN4Pbd/mtXPgPe/Ztbplb9znmlVga9t4zxC/aQOX4xG3wGG5uyi7ng45UcKvSfodGy2ofLpZ+uZta2ozz623Yyxy/mjwDt7/qsYvq9szSgD7LyHtgcLvbX0F/f++RJVIn6iBMISg6FJEmsPVSIyyVVa/Dz2xa1+8jTs0W2HSlRDSBe/XO36pl9Zo7IVo2ZLd1yrItjwO1X+E9IlRMO4//aE/axExbu5YlZO7A7XSzxWN+cLol+7yzlnPeqfMAmLTvAa7+LKstMbVBpd7Ixq4g/xDwmLT/Ax8v212r5J4K3L/5zZz6Pzdyu6XoQDsWVdqwOl2rQ8vlK/w5NSZ+3l/rleR048W/un76VnzUCgx7+dZtmOcpOa8qaw9w4eZ1q/6sKH+AduaWaDXGwAcsoT0da7hHyJqOBIxquDDs1Ovs1BwvJHL9Y7mzsPt/9oY/FXitPrW8QkBZaliWbw8Ubf+0JOF3pRZkmT4l3kKjlVnHxJ6tUq7p5qVAI6aOeZ0nZ+EqSxE1T1oflwpBbYuWeaVtYdbCQJ2btkC2/B4KIfV8q7U7ZCua9Rz9uyOa3rblMXuO25FUnJdn23BL2e4Sm1eHi/SX7WLrX3aZszinmjx1HmbU1l6c1Aq60GNq2LkLdOM5qkMAF7ery3FBBtb9JcozfOUv3HufjZQd48ffAAZ9aRJrV3WBCABcOr9j6eWMO46Zv5eapG3hmjsjkNYeZu/2onz+4zek2Mny/LotKu5PPPAF1ShejlQcKyC6q5AtPm+BwSdXyqT1SrG6XtuQU03vCEvq8vTTgOQ6XxCO/bpODGB+fuZ1Hft2G1eFSCSXvbMH3693Wxt98UttNWBi4r/Ed3Cp5eHDLgPtqgncwmjl+MS/+vpOCchuZ4xfztyIt5Kt/7uKKL9eofIWdYYpPbxIIh0viiVnu59ccJBuQwyXJg/3sokou+HiF/K6Fw+vzd3PHD5uYtSUnoMFBixf+2Cm7Rnld3EA7CDXUrMbe/PKQrnD/dnRxDFzw4hRGjBmr2vbhhxNrtMTzli2bGTPmJu688xY+/3ySvH3u9qNkjl/MgSP5XHjhYMaOvY2xY2/jhx++PeH6KzmqEHGZ4xfzSADhpOSLlQd5YPpWlu8/LncAZTan/GJ6R5G1bdl98Y+djP5uIzkeQRVqVSqHS5Jf2OyiSrKKwm9wgmFzuFQNqfe7lFQnS4OSwe8vZ/TXa6oVYe1l7zG1eFuxv/pTeSv2u6/r7UV72Z5bKv++/lNwR+k9YYnf+bs1Ap2UFFbYOV7m/k1yiq1c/Mkqv2O00tU96BGBm7Ld1qhQQmxLTlUZWlbD6lBbz/GGrGK+XnUIlySx/1i5HBCoRYXdSanVwcytR2SLZkxElTV85YECth0pYeHuY5p5ltunx/PgoBaaZXvF3Zt/7WHAu4FFkdXhoqTSwYJd+bw8bxcjPnO7nVgd2hZP3+2+/LUzj6dn7+Dyz1dz4+T1XOFx5Rnw7lK+XHWIXza5xZTTJckZSvJ9rNt3/biJiyetBNR+xd0bJwFgNhl5blgbmqaqxXCrNO0V175cdYg/A0zHB+LslqnqzwEsx95n9KjPQPmdRXt5SkP025wu/hTzeHPBHj5ZfkDOeKHMROFtZ7x1Ltew2F3mk/ZQiW/O4JsVlt8jxZWaFuTDhRX8tSufGyevDxhY9vPGbB79TT1zEhOhHjQECzgN1Jb/eHN3Mj2/bW1xtNQmt2czthyRBf5nK6p8sn/zBOXll9kQPTM/V365hvN8fKGVzN1+lE+WH2CuxyVMGdhnNmpLp6MlVnpPWMJ0T3rIWdtyySu18cN6tTvDuOlbWbRbO9+z1xf7gR83sTNE++vLtV+vY0tOMRd63imAz1f4+6aH6s9em7+bwe8Hvjf/Bc64hImRO34iavt3tVpmZdurodeNftuPFFdyzdduf55SqwOrw8XaQ4X0aVbzzvfNN1/hpZdep0GDDB566F5EcQeC0Eb29Vm2fhNDhpzP/fc/DLg7zdwSK/V8lomVJInftuYytE1dIszhj2F8XR98G89X/9zFnG1HWXRPX3nbMY+4OVxYSbt6Vctd2zydpNFjRnVJ7qlBSSOnos3hYtjHK7iicwPuUORgDMYOTyPl/R57gBd2xuYcrA6JgwXlfL8+mx6Nk1jlmaYf2rYuT53XmgizkYW78jEaDaocveHw/tJ9TF2bxRfXdqZD/QTA369zxGer+X5UN5qnxrqXtrW7MBhgyAfLGd2rsSrvJLjzUnoj4VfsO07busGXTx3Sug5/7lT/Vld9uZZfbs2kYVJ0WNdxfps0P9/eu6dt4e7+zeTPOcVWGidHMzpM3+YX/qgK7IyNMPlZIXwDbbSYpzEt6i1n37EKjpfbQvpz7skvJzHKzNmt6nBl5wYsPYGFQcpDpMvrWD+BzTnh+dhOXLKPSoeTHzfkqFwnfKmwO3lrwR65kwb3/ayqU9XzplXO2P7N5Gl9X7zBmV5L+MytRzAbjQxV5IstqrAzRPFbefNE3zJ1g58FfcbmI9zet0nA75u9LZcDx8s1Z0Dyy2x++Z+VA01fNx3ve6x0FRp5Vn25zdEiNTaCZj5i+f3LO3LXT5sDnBGcrg0TVe9Nn6bJPDioBW8uUFtGc0usLNt3HFOYUbMf/b2ftp72dM2hIlkUZxdV0tKTl9l3EK41cPMOfvo1T/F77gsr7BwprmT+znzeXqR2I7n4k1XcM6AZN2Q2QpIknC4Js8moShX4q0ZWI4fTxcQl/i4/MRZ1P2QL8c72bprM4Hb1eNEzcLilZyOapsSofO297V7H+vFszinh7JapLAwSnzG8Qz05G42XbUdKaJhU5ZPuFX5aA25vf7/svn7yrNXhwgrNNvbFP3YGFJGFFXZe+3MXDw9uqXL5OeSxEM/dfpQRnerLVudv12UxuHUdpm3MYVN2MVlFlSzec4xHBrekXnxkwAG/0gWvZZ3YkLNdoA5WBvhhQ7bfMeV2J1EWf1c1v+sst5MUYwl5nNMlYTC4tcLu/DKSoszUiYsMed6ZzBknjk8W+/LLWLDtiGoUPnf7UUqtTrmx+MAjkj6/RjuB+7Rp37NgwXzVtieffJ709HQAyspKsdttZGS4k5T36NGbtWtXIQht5Gj8Q3t3sm/nDsaOvY2kpGT2NR7KzhKT3/Ka83fm88LvO8kqquTOMMUmaAchVHpehCPFlbITv/K4OI8/Z6nVoVqJy9sweDsqSZK4/pt1lFodzBjdQ9UoPPTrVoorHXy24mBY4tjudMnTwN5Rv83pntb7du1hnhvWRhbgL/6hniZdpfBfnbv9KMM71COzcTIPeazkgZYqLbM5kCRUSfSV05jeQYK3Lr5c9eVaMhKjyPKx7PkmZQf/vJRfaAiJQa3qsMAzeHnivNY8MriVanlcgOu/Wcefd/XxO/eG7g35Zo06kCWQH5yyoyuqsENydI0CrDISo6ptyQjF16sP8euWIwGFmJKWabE8eV7rgNN9Q9vWZe720K4/wcTxsvv6MWfbUTbnFHNTj0Z8tUrbBWZw6zrM9wxmvLse+FQAACAASURBVOnEglFpd/kJw89XHuLOfs34ZvWhgP7HHerHsyWnBKckERtGZwbuxSvAfT/sTvdCGXk+Ftu0uAhyiq2anW253cnTs0Uubl9PtX32tlwuaFePZ+YEzhur5f+utJqFmsa+vU8TRvduEvSYX0f38CunR5PkoOeM7d+M9zQEX68myYzoVF9OM7jo7r4YDAaiI/zvtXdKPVx+2XSElF7uAbIyY8m46VtZck9foiwmXvDJKuT7bFpMBm7r04Roi5ExvZvQW8Nd4pJPVwVckGZDVjE3ZMI9P29hzcFClt/fX+Ur75svHeDJ2TuoExtBqVU9M+crprQWnWiWEiP7cbeuG8dNvZsi2Z3sPVbOnf3cg/Q4hQX6lYvb8Yri/B/WZwUVx3f2a0bXhkmq3MUvz9vFXwrDwiueWQpfVy0lBQqL+YjPVvPldV1onx6vOiaUdfWnjTnc2a8pCVFV4lFe+V1SG5YATYPEa57sOs8NE/z2QVUGlLv6NeXSjvWZtzMPA9C2Xpzs1uZrFPktjNR1246UhBVLc+6Hy3l4cEuu6NyAzdnFbM4p9luEJb/MxrCPVjCkdR1eubidHED4zmUd6NMshbWHCrE5XfRuemIzfqeaM04cW9tcjrXN5bVe7nkey8RF7erJlthoxctuzNvNj28/jgV4dWsMFYVHGT36DlUZI0dexciRV8mfJUlSjZ7LysqIiamyEMbExJCd7RZe3qMsSenccsvtZGb25I8/5jD/02+g5ygyxy9m2X39sHgETpFHACzYlV8tcayVI/OxmduZMKKDKrpVmXbIKxZLrQ6V8Bz70yZ+GNVdHv0WVzpkK9X6rCK6NkyS70Mg/8xAKLMKrDnomVp3unhoxlbySm3c1b8ZSdEWng8jgXukObRoWLQ7nwdn+IvnudurGhLlFGQgS6avMAZIj6/ZCPnu/s1kcez9Dcb0bqwSW2U2p6a7wyUd0/3EcTA/OC8vz9vFk+e1kj//r19TPltxUNURTBzZgbunqQPdbuvdhCYp0dUWCOEQyOLaOi1WJcYbJLitQwlRFk1L+x19mwQVxyajgT92HA16DRaTkYs61CM+yszAlqk0T43RFIOt0+JkcRwOZTaHZlBhoJRf4y9tT88myYyb7v4dJEmS3TCiLUaVD3MgRn+7gY3ZxbROi+WKzg1U+3x9uH0HW4v3HFNlAQG3r+KQ1mlBv1PLjcs388ihggp+2JDNNV0z/I697KzALgTPDG3N5uwSIsxGIoDJ13fFhSRH1j91fms/sQlV77tXHJuMBtqnx7Mpu5iEKLNqkO+9x8Pa1uXA8QruPbc13V6e71dmuAR6ttccKvQbzDpckp/lOD7STFykWRaWj53bShZ/t/VpwqRlB4Ku1Ohtu70uWasOFKgs7Fr+8YGe6w+W7mfNwULev6IToDawKGe4vM/01Z7f13c1TG//27aeeoU8qHKnCUS0xUiPJv7HrFBkj/C6dARbBt7rD+9lc3Yxqw8UMH3zEaaP7hF28Hl+mU0ljn2Zsy28OJ1AA85Plh0AYGDLOiTFWPzeY4A+zVL8Zgxb1Inh7REdVG5uPZskyQve3P9L+OkZv117mCs6N+AWT1Cu2WhkeId6RFlM/L79qLxwy58781UDnbnbj9KnWQp3/LAJCGy0OlM548TxyUDZQH216hDXdMsgLtKsEhOutJY4erhdLy45pwXHVvws7xOPlnL9N+sYk3aATauqhEp2cSWHWo1kyaMXEWUxERsbS0VF1TRIeXk5cXHq0ejUQzHcfVU3AAYMGIRx/NvyvuJKBwlRZnbllcniLNSKWD9vzObjZQeYe0cvDAaD5gpr3qk4ZdChcnrcO8Xqa7zLKbaqAsMmLT8g/3/795tYMLYPZqPBz49w4uK9FJTbua1PE9I9guaN+bvJKa7krREdcEmS7FIByFPYW3NK5I5q3aGisFc2CmeS0yuMocqSDpCn8P+buTUXi8lAenwUU33SCwWjUXJ4bg8AT5/fWs5BrZWeqm29eL9tWsRqWLYC+cEp2Z1fJlscwD2l/I3JqBLHDRKjSY62qETNxR3UVsSTwasXt5X9HHs3TeaJ81oze1uu3IErA6fqxfvfu4TIqk7qwvb1/JL/OxUBNV6Gd6hH32YpPKLwrzQaDAzy+J12aZioWdfq/Obg9umuE2LBCSX9m6dgMBh4ZHAr3luyjy4Nk+Sg0GiLiRGd6ocM3PL6eu/MK/NbldDXKjamTxPWHCr0y0/ry41T1gXdHw6XebKoaGVISY4OLDQuap/ORe3T5c+Cj7gK15d1+X39sDklvlp1kHM8Yv/XMT1U/YTFZOTuAc1IiLbQJSOB9T6r3kWa3e9M14aJrPPJ4nBjZkO+Xu1uP5b7xAnUT4gkp9jK/uMVKuslwAdL9tGrqdoCPsbHit69UdU1poYx3b1w9zE2ZxfLLlE1dT3xsupgITaHi1UHC1SW4wxFW5YSY+F4uZ2UIPWbfXtPOVuOkuapsUEHf5FmE7ERZlaPG8DFk1ZypKRmgdK+CxKNV7jQOJwutoV4D7zkldponlplEPMGSHqltVY2lOrgtdHEaLT3Xno1TSY9PlJ1L/o2S5X7Xi/NU2ODrgYZiFKftG5v/LWbo6VWxvZv5pca7llF/me70/WPTnTwnxDHysCBScsPMGn5AUZ0Sg+4zOee/HKUzaw33+IneU1Y9s51snV32EcroMxGYYWddIuJ3EoDGE1kZR2mQYMMVq1azs0336Yq27z+B2b+4aBOm57s2rgSV1LVFIVyFaA4DSuTF0mS2JVXRuu6cfJLXmZzEhdpVlnDlcwT81TptLSyHlQ3aGzQe+pVjZokR3OgoELuGHbnlzHpqrOIsphkv6dSq4NpG3NU6Yi8KIM4qrPkp5YLBLhT1eWX2rhnYHPV9oIKO/UtVa4kXv7ed9wvMC8cVh8spLDCrmrsLSaDpvVZOTWpNS0ZKNDIFy1/LrOiPN/GMhCxEWYSo82q1EvRFiPnt62rEi+RZiPJMREsv68fby3cq7L8B+OlC9uoBGmg6W2ApikxvHxRWx6fuZ1Sq5N68ZHc3LMxN/Ztxh2T13Jjj0aKequf8+eGCcR7Arqu7ZbBlV0ahLUyVnJMBOe0TqNtvUN09PibK/GdFbi9TxNu6tEIk9HAw4NbMnHx3rCsuNXxke7bLEUeJDZKjua14e2Aqpkup0vihu4N2XusvEZBmlpEW0x8fX1XrvhiNfuDrNKoXEWrtjEbDSHT2AUjxqftqxsXwVfXdZE/v31ZB1bsL8BgMBBpNnBbn6byvvoJUdRP0M6l/MKFbblIEeAE7t9ox9FS7hnY3G8hhtZpVaLd13o5YUQHrv5qLe8s2kv9BPWz9c2aw3Rs4H4G7+rXlEiLict9LIXKAaIlzHRiExbuIUYjXiAUXRomsv1Iid9s5KI9x2T3u7S4CK7r1lD1u315XRf25JcF9RtPC+KP6mu0fXdkB2wOF0nRFlUb9+uYHvR4y39W7UTJL7PxxEz/NI6rxw3wm+k5VmbjeLmNZ2aL9GueIvupb8gq5qU//GcxaoqWMcRLpNnInf2a8sZfu2UhmxStlnaNkqJIiwt/cK6koMLu55t+vMzG4zO3+w0aZyks5X/uzK/W7NqZxn8iW4VSAEVh5XrTPOZsOhDQKuubBUHpL+rNJeqSJNli6hUWV325lp2NLuC5555kzJgbadVKoH37Drw3fwvbfn4HAEf7C3l90lc8/MD/mDT5WxydRgSoc+CG7NctR7jum3WsVHSMXqEqSW4/Ol8en7ldlepJGcHqbTTDFceWANP3vkEN23NL6f/u3yr/wA+X7g8ojkIRyDI0e1uuahpMkiRsDhcTFu7lmzWH/YLr9uSXyXU6EOZyzaFQJmp3SZKmMO6ckSALYmUAiRIta4ov3ts/0mcKWml1ig+xopgXi8nAMEXg1r0Dm1MnNoKx/ZtxVoMqsegVZmaTsVqpmLzWcZPRwGvD23GTQuBqHev1+xvVs+q41LhIPrm6s0q8XNmlAYNbV2UVuKCd27K9etwA7j+7BSkx4XUEXkvl19d35SGN6zIYDIzoVGWtjDAZsZiMGA0GrujcgN/v7B3yO4JZ0LR48BztrBTxHteb67s3pE5cJBNHdmTO7T2ZfENXbsxsFNYMihZvXtJe/v9ExKmXBgk1czPSGixWh9hI9TOfGG1RDSL7NkthXICMH8HQMlRER5iYMbqH/Lz2aZbMb2N6MGN0j6CBTsmKZyGn2H/w6u1Tzmmdpul2ohTHyvc2GJtzSqhBshwiTAY+u6Yz9wxoptqujEvpWD+B67qrfVDrJ0TRr3n1gqKVNPAZpDRNiWFgyzqclaGexTEYDLx6cVuu6uLvanAifLbiIFGe4MPOGeoB85uXtOcGxfU+P1fkjfm7WXGgwC+A05uxIlyCCeC4yMDteaTZxAXt6rFgbN+A92LaLZmyS6Bv6sJw8HVXWp9VpBlo7cuZucB5eNSqOBYEwSgIwkeCICwXBGGhIAi1m9CwhigtkucZ1/Ki5QtmRDxFE4P74ZUULhUARRUO7rzzbi644GLN8u77eQtnK1aUWX2wULZOSylNef2dT9jYdgz7G5zD7vwyvtpwHEevm90Hx6Zi738X9v534egzBqL8rVWhWLHfbQEeO81/iqzE6ggrulSJN3/x9+tDWwOfGdqaabdkau4LJPhyS6qsJ2UBgqHapQd2J1h6bz9WjxvAaxe309z/65Zchn9SZdm59LPV9H2nKnDF17/y/l+20nvCEnpPWMKiPeGtXKdFbISJFy9oA7g7Na+/a6C0ZJOuOkvOyKHMCqK89nAiiL26+9EhreSgqWeHCqosK+Mvba91qh9pcZGM7t2Et0d04KnzW3N994Yey5pRtlq9PaKDX736N0/hsXNbcUuvxn5lKkV6+/R47j+7OXPv6BVwcQWANnXjiLaYaJAYxaoH+ofMOJIYbeGVi9oG3O8V86GsJclhvCuPDWnFjNE9uKh9PUZ2Vg9IAs3ULL6nL309v0eij0/iPQOaMeWGrn7nGIBVD/QPmJ0kwmxk9bgBjOpZdc/rxEUi1I3j7gHNWDVugF9aslC0Soule+Mq0RFIn/p2qIlRZj8RfGffprw+vB1TbuxWrTp4iapBp63EfILiOhC+Fmnf75p3Z2/eGN6e9IQoGiRGMaBFCp9cdZZmWZFmIz2CuH94lz8PNI2uvEdmk5HLNXy0W6XF+qX983V9u1ARbOkrAL04XRKt68ZxQ2bgAa1vWrva4L3LO3L/2VWzfcEs5INbp5HZOHgw5tC2dflSMYMQiumbj+CS4FwhzU+UDmyZqvKhdkr4xT7UlEBuV4H6W+8TqHwWve5gvoYkg8FAZ8/g4strw78XgYgKI87nn05tW44vBaJEUewNPAqMr+Xya4S3YUiliHcj3gNAMB5mdsRjPDekEbf0VL/8O46W0vftJXytEaleVOHg733HVVOpExbuVaVJ8qaI+XNnHqNrsLJUqGtZd1jbb+iPHUcpsTpkC1O4HNZY4UiLt0d04KL26dQNMCUWaIlX5VRsoKnu67r5W0kAfhzVXe6Yg414lblDfacyAy2S4bUeD2kdWLQFIyMxik6KjsWb61TLzeOWXo0xGAzywhHea/nrrj5M8ulIxw1q4bctEE+d35qVD/RXdXbgtt7UDSAMu2QkMKZ3Y1aPG0BMhAmjwUDf5ikM75CuOu78Nmn8cmsmfTXSDL01ogOXdarPlT7Tvld3zWDiyI5c0iGd+89ujsFg4NpuDUNaxFso3EnCtV6GOu6zazrzdYhOMRxLvcFgoEFiFM8MFYiNCO/diraY5E7Ld9XKGzIb0bqufzDSE+e1OmHL7RuXtPez9Pky5/ae8v9Tb+ymuqZAU+EvX9RWtmz1bJLE73f2ZsaYnqweN0C2nnZvnMSgVnWCrh4WESRo9MMrOwWtd3XpX82UjoFQ/iat0mJpUSdGlR4xKcaiSrdpMBjorPBVv1UxgIw0m3j5orZ+qTt90RLkgF9aT1+XMXD/pld1zQh4r18b3o5nFYuqBGpXz2tTZZme97/eKsHqZUuA1TlPhLrxkaqMCMGeGYABLVL4bUwPVo8boCkwb+rRSE6dB27xHQqrw0Wk2ag5+I22nJwJ97QAz0TjAPENP9zc3S/LRbdGSax6oD9tNGJXzm+TxsK7+9DSx3XPt5+4qH09HgkxO6iVj1tJuO6BZzK1/Sv3A+YCiKK4Auhey+XXiOzsv3i87l18G38PAL86ezPXmUmswUrLgkXc2KUqAttrxbM5Jc1cj9dPDh2Qolxqtbp+XoBfDk9wZ5fIL7Uy7KMVmquFgTvVUHGlg/hIE28Mb8eNmY3kXLsA34/qxkXtqxdYpWzEvSIp0PRnoADfcHyv6iheUKW4Vyb/93XnCCT+fNFaHlPJ2AHN5AUItKYyX7u4LdNuyeTRIS15//KO9PRES0+8vCP1E6K4xEdUei3Hl3Ss2u7NOOK1gtT13Nf4KLNf53R11wy6NExkbH+1yHl0iPa0fyBB45uH1Bs00y49QeVvGQiDwRAyx3JqbASPnduKxzx1O1dwv0tPnt/aL+WPF+/j072RwmIZsjbVp1ODhJC5NsMRx9XlLY/V3itkUsMIxGuXHs8lHQNnaqgOoXxR44NE12s9SfPu7M2AFqmyNfNZRZpFcGcJMRkNNE1xPyuBsqY0Sori6+v9LebgXrK5VZr/gKGmfD+qG7f3CZ4Srrp0rJ/A1Bu78d1N3UkM47nxvgsqa6/RQGK0hWm3ZHJJx3Q+CjAgiAogwIwGA10bJvL8BW5RFGjmAiAjwLvb3Kd/MWDgjeHtVO3Nsvv6MUJhIU2Ktsg54L3ERZoC1r82CbVUs8FgkIPPtNKvRZiMqja2p8Lt8MMrtOtfaXcSaTZyrcdoc2NmVVsW7gDZy5fXdmb+XaHdr7T6s2AuSk1TYmR3MiXKwdycO3rxy62Z8nbfus+5oxezbu/F6nED+Pr6LrRKi+W+gc25vHMDRmm4wHkHyNkaLkFKtFw0tXJqn8nUdkBeAqAM3XUKgmAWRVEeZsTFRWI+xSb5ZMd8JqbGM5F46palsP/4EKSy5qwy3kvfrU8i7X+Xpfcvx2CJxumSGPDmIgDiKWfpqkUYkOhi2M06qRXBciNkGnawUWqBjRPrcGN8LL9vL9nP0t35qoTgwUhLiuHSzMZcCjw1vD1Whwubw0V8lJntxyqY6bHeNkyO5rDGkrMt0mLZ40mhpezokpKqGtV+LVNZ6pOPcnjXhrzjk4geCJjDduG4gSwQj/LNioNktqzL+Ms7UWl3IqTHc/nHK/y+08stfZpyTps0EqIsDP9gmd/+6tK4XqLsN373kNZ86wlEW/P4YA4XVNDe43vbqZnbEjWoQ33ySqw08HQ+TRRWwH0lNjnpfc8WdbhnSGu3q4vnOq7q1RSXycgV3RqF9P3qJ9RV+WePzGwsL/msdV+UJCXFcPuA5rz2e1Vg4019mvLynB2YI0whz68OtwxwT+HeMjA8L6olD52N1eFigZjHmkPu5kIyGgPWyWQKvM9LsP2rHzuH/327ntUawWsZaXG1ei8ALu7m7lSSPML8qh6Nefa3qtkLre8zm0NfY7gYNQTTzufPp/XTvwNQVxFd7/udFo1zmzZwD2K+uCmTGRuzadEgUdUBD+0cw47O2gMhJX+NO5uSACunmcy1+0wKDZP9fJBrgvfZ2/jUEMxGY7UWZLp7cCvWZxUxIrMx73syriiv8c0rPfn0PamuLjmrATM80f8pyYEtb9/frhZaI7o04BeFS5z3O76+pQf931jod35aSixJCuFssZi4NLMxkiTx3pJ9nN06jbRU/4FK34RoruvRmCmr3PEqyx85J6QbWDjvbijSUuPC9kfX6mvqJMeQlBTNTb2b0DEjUVWfwR3rw4+b/M4pqnQQGWmmX9t0dr0wVLUvCfj4+q58uGgPGw4V+Z2rZOLVnenb1m0k6dIoifWHAmeLaKh4L7s0SqJz4yRu7Nn4hO5fsHM7ZiTQMqPK/aJ3UgyzhSqx/cTF7enSNIV7f9hIYrSFogo7T1zQlsenb9EqToVWjPLifQXc2M9/9uFkcaLPXm2L42JAac83KoUxQOlJ8FEKxdXnjOeqPd8yNSKaSdunEtPoKySXhUsd6ZzliMSJhPWvazAnNqfIXkRKo2Tsx5qzRnqRyNUwwuMtMNo2jj9d/v50FhwMNa5iosdlY4erEUNtrxJekjE3U27oynXfuK3SRp9Rl7cxChezy0Vhob+QLqy0cUGrVNqP6i5bZF/7c5e8XKWXSMVIPTUmgtcubkd2mV1VZoJnBNkgIVIeRSYY3T6mvpZam8NF3bgIlesDQCwSFwlpXCSk4ay0McBjkT1SXOUW4XsdvrkSR55VX5W/ORRaWRwcFVZ6NU1m2b4CTI6qx1Wy2smIMWveyxhF3SSFH/WVk6oyjnSLOEK9Dd/SeNA4VRkXCWlUlFYSKhSwRWIkL13YhrMyEjlUUAE2B5efVZ8hQppmncBtdS+xOigsLOfyDvUY0iKFp2bt4GBBOXbPAKCs3Bbw/FNBBBBhgIuEOrhsrdiUXcwN3TIC1ikpKSZkfUPtv6tPE0ZpiGOLU/tdqQ4DW6SqfNe95Zk873FRSSW39Gwkryjn3f/8BQLzxXwW7TnG7b0a19pvckixsMdvd/Vl7Z58iooquGdAM+aJeRQpAo59v1Pymf755dZM+Zh6USZu69lIdX51KCwsR5Ikzm+ThktSr5xotTlq5fqfGybwxcqDWMut2CtsoU8IgfLZswHVqWH9aDNzbu+l2hbsGu/p10QWx9W5F48OasHDA5uz8mAh6fGR8rlKJzdlpgVruZVCRaiUw+GUz/l1TA+Soy0Bv/++/k3l/qi8tJLKEG5A4by7oSgpDv95887aebPeAFR6rnesZyahsLCc67s3ZPKawxQVVTDpqrM0l37ffKgwYN271ovjkyvP4p1Fe5m8Rjvt59uXdaBXRoJcxqsXteHmKesDWl0TFAOvVy9qQ/MGSRQWlp+UtnrJPX0xGQ0hy+7TKJHl9/fn5inrKaqwk2gOT9PUjYvgoI8xr6zi1PY73mcvLS289Ki+1LY4/hu4GPhBEIRewIklVawlpKgkkvqO49rCcib81hhTzF7McTsoMBeyLzGLOGcZUSWHKDIaMVnicMYsh7il9JYaMbisnAyHg3PLKujm2KkSx10yEtiYVcij5m+51TxH3t7GeIhLjX8z3dXPry7KRR5SYixc2qk+jZOiVT6I3lWmlKsN+fL8BQJPz9ZOdxYsU4HBYFC5KvRrkeonjuMUwSCvD29HamwEPX0aOa9v1xVdMnhn0V7ZCvrOZR0YNXW9yo/Z7pSIjTDz0ZVt5ITgkwNMrwJBk6r7cnnnBkHFsXdFuw+u6Ehm42SsDhfbjpSoGkN31HM7jpXZgqYfCoSWNSnaYqTF3/dhPrYN1/65cNlv1S4Xqvz+vO4tjwxpFexwfh3TA4fCnSIp2sJEj4/dWo/Voo1G8v3TgdFg4NJO9f0WCagOH1zRMazMFN4Vz5T5m/++t1+1LIGBeP2SdjickioIFKCZx80gKdpCguedVLo1DWtbj2Ftaz9/tHcxm0Gt6tAmPZ70KPe135DZSA6umnx9V82xu6+BLtyly32JjTBxUft63NyzsSpFpcFg4MUL2/KnmKcSx9VNIxmIC9rV05xq/icQzEUiGEaDAaPJIAeAhsJ3xupGRcBdoHR2gb73ZNKmbhw7joaXb9iXgQp/cy23jHsHNudej792l4aJfgsOQc2yp3hXtAT/ANOUmAh+uDmTtYcKaZ4ao1qgA9QxO+Fm26kp4QR+ezEbDVzTLYNn5oiavsRvXdqe3BIr5TYnQt04xKOlXOrJ8HP795vkVTiDuXOdidS2OP4FOFcQhGW4m96ba7n8E0cy4yxrjbOsNVbgvn5n0T0ml5Rvz4HsHOz1unIkr4jdURUsjIpjRlwiGO18lpRI27JtmAs2YSptiVWK5tnYnzkr6nO56N2uBtxqf5Af4iZwt+sXZtj68MzQtuzOL6N+QhTt68fTPj1eFsfNUmOCrn7XsUF8QHFcJzaC0b0a8+kKf6uyoBHsEwitCPGnzm8tv7iB/CVv69OURknRXNi+HhuziuSsBYnRFqbe2I0vVx1iyprDsg9YdISJbooE9sECUqoT8BAqEf6tvRpzscInONJspEvDROb9rzfnKoIooy2mgEIg6efLkMzRFA2fIm+LXfwU0Zu/pPTsV4kwnwNAHOVMjXiJdx2X4YxIxXzMPZVuzFlP2vsNKT53ItbWGqn7JAmcVszHtuOod2KRxMFS/nRrlMQPo7rLvqH/BkJFqntRBnX2b55C2/T4WhHG4BYJERoWlRGd6lM3PpK+zVJwSnC0xMY1AQJPa5M7+jYlMdrit4CEEt8FNLw8P6wNX60+xIxqpqHyZeHdfeX/J111lp9LmO8AvrbE8ZnKmN6NQ/qeh5u3uLr4rmroXVH0+1HdqLS7gmYKOp18eGUnvywboRh/aXtmbc0lwmyUDSPh3FetQFjf1Qq18H1sJ111Fn08S3xrCdBIs1HOKrRgbB++X59FSaWTKWsP13ggeioINuhsnBytCn7tqchWpBzw3TsweKDwmUatimNRFF3AHSEPPAPwrlQUYTKwen8xs9c05p3uB7HkrqMR8MzS9qyIHUh5k34MNK8kKWU+WxKPE91wKhl2B3ekDKLdpiqx9EbU/bxfmInh+H6uX5FMqu0wg+q+ybD7f8VorHqosrOzsCx+D5BI6dSKyuECUVH+o/U0Crnv4HM8GHGcVxzXMteViaQIW4qxmBjduwk9miRTUGHnWJmNyWsOc3OPRtV6yRwa+Xh9V9bRItJslC1+b1yiThsWbTFxZ9+m3Nm3qTyV5xUn3pXLgq34U52I/VBWZt8GKmrrZKK2/4Dp7FerNtorwBQBThumon28cEEb2ahmOrYDS457oGAsPowroSE46U0cuwAAIABJREFUbcRs/gKA+IWPcDtgNV9KJHY6GffxacR48LSrRUM/JmHe3RicNuLn3YO11aXgc30Jv99O5J7Z7uMv/Apb08FhX3910Qr2/C9g8awemBBl5q0RHU7Kd3RpmMhwxUqCBoNBzvdqNqCZ9u5kkBRtqdaS80oaJUfz5HmtT1gcK+nSMNFvpUFfK2lNrab/FIIFwD4ztDVNkk/Oe6m1ZK83i4pyZbfq8NV1XdiVVzOLbnWI8yydXR0GtEiV00B+dGUn1h4qCiuv75jeTXhwhnpJ5VvDeF8ln0y+SiHeJMQqmnGRZm7t1QSH08X5bdPktjlQdoozlWBGhrsHNGPGliN0yUggI/GfdV1n3Ap5fxyew5zDM2u1zGENL+LKpJGqbfGRZnKwykLFntEbW6OmRBxyi7kdlnZUEsElHdKZsaUnLfMy+KP4Yf6OjuKNlGSeKlnCG40zGGhPYXPWuXRsPhzWZWPe8BMvvfcezVc9zGM/iWRPuZ2GN3wif+8HH7yDs1lvXI260aPVMb77bjKjRo0G3I1kbISZh3/dxsPm72huE8EIH0a8wxpXa661PSEH+0m4p32UnY7Wuuuh8FpwfJcLrm0kzxD7yXNbcVe/prVmtTMZDXx69Vnkl9nILbFiNBhYsCtfXtLVdznamDUTMZVmkfL9eaQzkSOkkvpVd5xJLTDYSjAX7OKiET8jxdTBvGsl8X/eLZ+b+k0vigdPwFTiDtirbHMFUTt+BOAe83S/uhUPfhtbiwtxCANxzn6UqF3TMedtxlG3KkLacmiJLIzdnxedVHF8JmPJWoY9PRNM/gMey4EFxC9+ktJ+z2Jrdm61y64bH8kDg1owqJp5gKtDuOn3/gksGNunRgtHhIt3dqh5agzntUljZKfaXcjhn4RySex/Au3S489Ya7OS9IQoLmwfnpvIwJapzLuzN+d+uJwIk4G/7+sf1nla78hbl7Zn5YGCsIW92WSkrSf12qzbegY1HJ0J/DiqO+MX7uFwYQWHCysDph0E7YHxP4UzThyfKrzJ/ytsTrc91hRB8XnvU+ezjkjmKMo84QzntK7DigMF7C5pyIA9Y6jYu4Y2psM0NdjJj0nmt2FF0OInyp2rMFkGEGOSaNasOVLjKfTeeilrVy+jZbfvsDfogTOpOfv378PV3j0N37lTZ9599y25TlWNpEQ/0xZsKe0otTlJKRXpbtzJNxGvMCduJF8eb18t37BgtEuP54trO1Nhd/K/HzfLflixESaGhrkCUzAmjGjP/b9sldOKmU3GoEuHKgnXvcJ35aQym0MWx15fTyQXiTOuxlRatSTyorjHWXr2Lxj/LMKYW5WiL/mXy1TlFQ+egCVnFdHbviVh/v3y9tJ+z1La7zmK5z5F88PTALjTdi+bXM15uW0W7QRPOXF1KR3wAlG7ppP84wUcv3o+zlQBQ8UxEn+7DmdcBgVXziZxzhgsR9a6W9yT7M93pmE+upGk6VfiSGxGwfU+S8LmbCRp5g0AJM6+mcJLvsfgqMDWdEjVMWHcM600fTraVNdiV12apsTQq2kyd/RpQnuNZbv/y7Q/ScLzum4Nmbn1n5VO61RiCTPYTEnf5ilydiNvLuX+LVJrnGO7boj812cCTVNjmDiyI3ani515ZWGlNfwncsaJ4/MaDuO8hsNOWvkpMRbqxUfy9PkCn688SOeMBDblw9q1a7jrwUcw2AeCwYR17xpocz7RFhNfX9+FnKJKsora8MSsHTw4qjONEi1gjuZIeQ5Ljizk+z0/EV33G5yR0ewqEqkXXR9LiwHkL/uK+AUPApA/ah0tW7ZmV85WXE0yWbp0EZWV/pG4Y+ofoH7BcYo7P4mz7ZVc9f63fM9D9DTuoGf5S9x92ypcYeRODRdv/sqZt/WUfYGVPoMnQmtP7tJAqzAFYsHYPjUO+Li+eyPmiXnsyS+nUXI02CuI2fAxEVnutG8FI2cQveETovbMZOD6e1Tnlne5k5j1H8qfy3o+hLXNFViFy7G2vJikX68FoPi895Ei3aLcMHQ8l02/haYpMdzcNYP9x8tp0zJVJdakqGTsaR2x5G0m7u/nKRn0OqlfuxdjsGf0RopOxV73LGI2fkLaB43Iu2MPmM78hrJGuJxEbfma+CVPYWvYDykyQbaem4v2EbXpCwwuO66oZGzNh2H5fJDq9KQZVwFw7KbVuOLqYyzJIvXrnhQN+wxb8/NP+eXoVB+LycjEkaEXY/ivsfy+frWyhLcW953dnPs0FvLQcWOWXa/CF3s9mySz/P7+lFY6Auam/rdiMRlP2kDuTMAgneJAiLy8ktMSeeFN6+FdFU255OK6dWuYMWMazz33irzt8vuf5pAzgS8ev12eQpo27Xv+WjBfFeT95JPPk56ezsI92Ty56A2YsZSI2y0YMVJ3az1a5u5mfPPjxHju875293Luh9swOGyMvfx8Nm/exCuvvAlOO7ErXsWR1pGEeWMByL95PVJMGpnjF5NGAStiHsDkslLa71kqzhp9ku+YmhNJyXPgeDkNEqNOWsBJQJx24hY/QfS2qfKm/FHrkGLrgtNG8rfnYC7ajyOxKSVD3iHi0BLKM+/DWJKNKybVX5xKEtGbPscVnaIdWBcA770zlmaTNO0STKXq7BoFV87BkdYR89FNJP94AQDF576HtfWlNb/2MxTTsR2kfDck4H7JHIPBUfWclWU+QOzqtyjrfh8VHW4kYf59susTQEW7a4jaOR2Dwz3I/FcOKiQJJCcYq2/L0HpvzXmbcaS2A+OZPX17JlAbqcj+y/zT7t9367Lo2yzFbVQ5zfzT7t2ZhiKVW41Gm2ec5fhkYw4zPcuAFqkUmFNUaa9GjryKkSOv0jw+yhSFtWAEicbd/K/+jRyPzuf7n6aS3Tuai5u0596cfVxQWsbGWR/z9QXnkDvgTQ6tnENmZk8i9s8ncdZNclkSUNHpVqSYqijjPJI5evtu6n7VHXNu7S5JfbJpknKKg8AclWCKIHrTZyphXHzeB25hDGCKwNrmSswrX6ey48040rvhSHen6XPFB/B/NBioOOvWGlfLFdeAis53ELf0GQAKL/oGe+OzZQuzo24njl89n5TvBpMwbyyFcem4olJxRSZW1fsfjDlvC8k/VCXUL+98OxEHFmCwFlLW5wkcqW0xVhbIlmGA2NVvISU2prz7PWCKoGj4VAzWYup82g6A6G3fqr4j/q+HKO3/PFJUEmcisUufJ2rbVI6N3hq2OE387XoiDi2itNejSJYY4pc8zfFrF+KKrgOSEynaPYVrsJUiRQTPVGM+spbkaZdQ1v1e7OndsTcaoItkHR0PV+uuVzoe/nPiOFwsJiOZjZPCntrv3iiJEZ3S6df/GSZ/+B4ul4vLe15N75F9eWfNGzy86BgvXNmARhRxbPpqLAtHEZ+RSvtLGvLeihkcq1uHXRYLJRHRFBkk+sW5OOvAzzSJa4rBXIjkjMNsNGBv0IOoXdOx5K6n8LJpuGJrGMwhucDlcGdpOMU4JSc7Crexp3g3x6z5tE1qT2JEIkcrcokxx2AymMm35lHpqCQ1qg7p0elEGCOpE1WHaLO20LYc/pu4xU9isJer/IrtaZ0ovGKWpj9qebexWJudhzNF8Nt3sqhofx1ITirbXaspZJypAiWD3iR+wYMk/XK5e1tcfY7ftPqU1bHWkVwkzLqZyAPz5U0F/2fvPgOjqtIGjv/v9JKZ9IQkEAhtgID0JkWwYW+oKFYW24q7tl23+OoWd3Vtu7rq2lERFEFBFARR6U2K9DLU0BPSJ2Um0+77IRAIBAgzSSYhz+8Tc++de5/7cJJ5cubcc276Gn9KH8oGPVPt0ACQ96sNKF4X9p8eR394FcHMkdXaqWq0400fhmHfAgC8aRdS3udRYmaMwrR9Gqbt0ygZ9i88mXfW/715y0BvqdUYcY1rP5b17wEQtfCPlA7+O+hP00OlqliX/QNN6WEM+ytX7IxacXyGlbjPhlX9O//e1Zi2fI515asU3PYDgfjO1U5l3PYlxqy5lPd4EPPmiQBYV79etb/omk/xta4+dEUIIZqzZjesIhKCapDlR5ayNn81P2cv5qDn+EMRehW0apAYrZkOif2wG2PRoGHe4R8p81efLseuj2aQvTOXbfmW6GCQDl4fJS16U2KMIn/gU3iCXkrKDpNyeC2+DtfjIwAqGLRGct057C7ZhcvnQqdoYd98Oh3ZhuWilyjW6ojSR3HEfYSKikJa2NvRwtyC/Ip8ovRRdI29gPhYW9j5K6jIZ3H2AqZlTWV/2bmt+gdgUPT0SOjDhUmDuSjlYqINxx/ES3yr5uVr3Z1HUXrxqyHHXBdCaXtRC/+MedOEqtdFN36FL7V/XYdW77R5W7Cufq3ajByFt8zCn3T2mR00xVlEz74f9Ya3KTKdtDS1qoIaxLjrOypaXwwGK6ZNE7Et/GPVIXlj1oLWgOWXt3Bn3oWuwEnAVtkzFLSm1Ni7rHgKUSpcBKNPP0cwVPbA2mc/gLa8cin22vz/mNd/QNSSv1bbVjB6AYHY6vemeAqJmzQUjef4in5BUxwaTwEAng7XY9ox47TX8aYPo3TQXwjEdSAmcAj9O/2q7Q+aEyHoQ1NxfCnbvLGbGm1veyTJV9vhkfyFTnIXnnCHVUhx3MCCahBl8sV4XFnYg0FigkHcXUZTOvylasepqkqu5wh7S7M44smhwJPPwfIDLDj8E95g6Mui2vQ2KgIV6PweyjW1GwNs0VmINcbSwpxKQA2gQUOiKYkMW1vK/GVolMrXWkWLikpADeDyFrPTtYM8Ty6FFQUECJBdfhgVlba29tzW9g66xl2ARWtlp2s77oCbRFMSOe5sovRRJJqS0Ck6DpTtp9hzBMu8J9lm0DMvpQsHyw+g1xjobO9IZoWPXqWFDN6/BmOLPiieQio6joSAB8P+xZQM+xeBhC4h56suhNr2NGU5KO584r64HICC234kEN+prsOrV7GfXYyucHvV68KRM6qGr9RWbfOneEuJPdqjqi3LxtPuGox751Ubw3wi1+VvUdHh+uMbVJX4DzLReF3kPrC9skf4NOLf74LG66p6HbC3puCupWeML3rGbWhKD1M4egEJ73VA8VeuIll8xbt4210Nqopl5SvVenXdnUZRduGfUSpcmLZNxd3zQVRjNLrsNah6C9aVr2LcPacyfEWLolZOsO1NG0ggzoF548cAVGSMwLjne4Cq2VKgesFecPs8AnEdz3gPzU1j+dxoqiR/oZPchUeK41pqTA3t2NP1x5xLwVBUUUiu5whHPDkUrnwRe8FOrKqKJRjEqKrYgkHytFpUwHD0/7bUlor18g9ItbbEqrcSM/VqdEfWk63VkqfVYgsGyddqaeX3Yw0G2a/XsbPPI0S1uZxcTy4bCtbhoZQ9RVnoNHpUNUiOO4f8ijw0aAgSrDHWFHMq8aYEYg1xGLQGWlpbMbTFcDJs5/DEtKpi/uWtqq+Uc8duYs+RlXy/ezJbCtezQ6+nQqNBp6p0jc7khvZ3Mih5CFql8YyjDLftRc17EvPWLwia48kfs67JTPOmKd5L/MTjs57k3be5aoaPc3FO+Qt4QWvAPvOeasM4Tif34f1V+Yxa+DTmTZ9U7Su+6qMa51TWH1xOzNe3AOC69DW0xfuwrvo3+XcuPX2Ps89NwoddcXe9h7LBz57yYGLe2I1oyrKJm3z8erkP7Dj9sIsT6A6vRp+9moqMEcRPqnl+1txxB6q+Xckdd+D4Dr+bxHePL0me+9CeGueZbq4a0+dGUyT5C53kLjxSHNdSY2topg3jsS1+lrK+j1Pe78mQzqGU56HL34L+8GqsqyrnS/a2HIIvuQemrVMo7/sYuiPrMW+djD+2PUU3Tcf+wyMY9lWOYcx9YAf6I2uxzfs9WtfeU85/4lfFNeUv15OLXW9HQaHAm1+10IdG0aBRtCSaEk8557ky7vgW+9xfV70OmuPRuPOrXvuAdSYjPw58jAVHFnGo/CCJpiQuTR3BzRmjiDXGhR1DuOqi7dlnjcGY9QOqzkTBnUsJWo+vxKYpzsL+/a8pHf4y/sT6Wf3tXGmLdhM3qXJ1roCtJf6ETFxXfRjSuUIaljLvd5i3TgbAnXkX2qKdlAx/mfiJgwlYW+DpPArr6tcJRKVRNuD3+FoOJvaz4ajGGBS/B407F4DSAX/E3fsRlAoXmtJDqAZb1R+2RddOwpd+EZriLOInDqb0wmdw93yweiCqimH3d0TPqdxeNb5XVTGv/wBd/hZM26ZS0eZy9AeXofGVUjhyBqoxhkBsu3NLlKoSNf/3KN5SdAXb0RVuRzXaKLpmIv4WvdEfWoGqM58ypEVTchD77PvR526g/IJfUTbk7+d23fNYY/vcaGokf6GT3IVHiuNaaowNTfGWoBrqd55ApewICR/3OmV7ta+NVRXrin+hP7ickuEvosvbgv3HRykd+DTuXpWF6TnnTw2CcnzYhuIpRDXGnLHXU3doJca98/B0urlqHGb0tJEYDv9M/j2rMK97v+qBpmMKRs1FNdgI2lsRUAMsyV7InAOzWJW3EpPWyNWtrmdYysV0iu5Sb/OHnk1dtD3FnU/C+ONFTXnPh3Bn3ol5y+dYfnkLqCwCS4e9cLpTnBNt0W4Ub2m11fzOhX32/Rh3zwag6Iap+NIGhhxLKPkzbv8a+w+PUNb3Ccr7PlbVFhV3fuUcypYkor++BcOhn6veo+rMFN00HX9iV6LmP1U100lZn0erhjocG55QdO3EyplGjsX4xRVoSw9SOGouwaiUqu1R8/+AecvxZeZP6Q0O+on7pB/a8iNA5cOFxTdMOad7PZPa5k6b7yRu8iU1Dg/RFO0h5uubcV35Af7knnUWW1PQGD83mhLJX+gkd+GR4riWmnND0x/6mZjpx5fPPtYbdibxH2SiqSgm7/6tqHorsa51FNp71uorfW3BdmKnXoM7czSBmPZoC5xYNn4EgKfTrZT1e5Lg0QejlAoX5nXvYt74MZqK4qpz5I47UNUj5+5yB6XDXwTAsPt7zBs/pqz/7zHsX0R5n0drjGlf6V7Gb3+XZTlL8Kt+YgwxJJlaMLrdXQxpMaxBC+W6bHuG3XOInl3zHNe+5J4U3fxtWOe3rHoN/eFVVTMk5P46CzQ6tIU7CUS3OeNcuxrXAbSlB6vamrflYEoufb1aL3coQs6fr/yM44ZPfkCu2qwNqkrMV9ehz1l76mlryLN1yd+r/nAr6/Mohqyf8KUPxfLL/wAoHfQsns63oRpPXQzHuuwfWNa+g8cxkpJLXz9lfzjOJXfH4sgbsw7VkoB+30KiZ96FolYOmwqa4vDHd6p82C8xs07jbKya8+dGXZD8hU5yFx4pjmupuTc008aPsS36PyraXI7r6vFnPT5qwZ8wb/602rbiq8bjzbj8+IagH/PGT/Cl9K3qYVS8pSS8f+aHxlStkeKrxuNPuoDoGbejz9t0xuPdnUZRekloM06U+kpYlrOEdQW/sKVwE/vK9pJubc0DncYxMGlQgxTJdd32LD+/XO2hLU/76whGpWBZ9y65D+4E3bkvLW44OptE9JwHTtlX0eZyjFlzCeqtFN46h2BMBkp5LlGLnsFwaAVF105Cl7cJ24I/oAT9Ve8rvvIDvG2vOOV856refnaDAbT52zBvnkhF2xHVeoIBUFUS/9cKAG/aIHQFTjTuvBrbo+IpJOHDmld8O+vQqUAFuoId+BO6VPu2pS6cS+70+5cQ881tlAx/iYqMK0gYf/pvDZrL7BbN/XMjXJK/0EnuwiPFcS01+4amquhy1uJP6Ay6Wqz+4y0j8f3q8/+qGgMlF7+Mt82l6HLWEvPt8Xlki0e8g8ZThGq0Y5/7cNVKZ/7ojMoZFgKVM2yU9xqH/YffoC09SHn3+7Cs/wAAT6dbKBn+CqhB4j4dgLYsp+rcx1YKDJc/6OeHg3OYsudz9pbuIcmUzG8yn2BQcs0PMdWVOm97fjexky9HU55LwZ1LUM1x6PctJGbmXbi73UvpoGeqrxIX9GNZ9RqBuA5UtL2q8v/CYAUqhxnYfnwM47751S6hao0ogYoaL++65D/Yf3q8xn0BWyuClkTK+j1ZucBEHfzxEcmfXcvq17H+/DJ5YzeiVBQT8/UoXCP+V/MDtGqQqAV/wLBvAdrSw6haI6VD/obHMbJ2P3P14JxyFwwQN6E//uQeVTNgVLS+GF3BDjxdRmPY8z26AieK303RdZ/ja1W/PzeNQbP/3AiT5C90krvwSHFcS9LQzp22aDemjR+jde3H4M5GydkIgC+lL/rDp1+UImiMIf9X69EWZxGwtqgqxI4xr3mz2oIGrsveOGU5ZvPad9DlbqS8z2ME4jpQl3xBHz8e/J7pe79kp2s7I9Ku4s7295JmrXmu5HA1VNuL+fJa9DlrqUgfjuvao73+AW9lgXe0p9mbNhDDweVUtLsa14h3Kr9RWHx8IQ5Ph+sp6/c7VHMcxu3TUYIBVEXBn9QD67J/Yjj8c02XBiqXei7v90Td31ckf3bVIPjcp7Ths/K7QdFFfOaHc82d7YffYNo+ver1yVPanfgMQ0XrSzDsX4RrxNt18g1BYySfG+GR/IVOchceKY5rSRpaeGLsBvQvnLqEsafdNZh2zay2rbzXOMoG/um051LK84j/uBeKGqR4xDt4219T5/HWhifgYcKOD/kqawq+oI9e8X0YlnIxw1IuJUp/5mV4z0VDtT3T5onYFlQughGwp1PW7wnsPz522uOLR7yDcedMTLtm4kvqTiC2PaWDnq1ajvhkStkRrKtfw7Tlc3xpF+Ia8TaKOx9d/hbMmz7FNeJtVFNsnd+X/OyG7lxzp8tZh33uuKMLiTxT4xCdmC9GoM/bXPVa1ejI+3VWXYTb6EjbC4/kL3SSu/BIcVxL0tDCExNjoaigBMVXSsIHmbi73UPp0H8CYNw2FVVnRrUkENTbavWwjjZvC4rffc4LQtSHI+4cfjg4h5n7Z1QuQqKzMTLjVoa2GEbrqAw0YY4DbbC2p6qYNn6EbfGz1Ta7u91LWZ9HSfiocqaBgL11tan7PI6bKbn0tfqPL0Tysxu6+sid4i5Af3gVgdj2RM+4FU2Fi7z7NlUfyhMOVUXxFKAa7E2u511UJ/kLneQuPFIc15I0tPCcmD/FW4qqM4Om8Sy0URdUVcVZvJVJuz5hac5iANKtrbm61XUMT72UhBDnbW7otqct2I55w0eYN3+KqjGQ9+vdABh2zyZ69v0U3PYTxl0zsa76D3B8vt7GSn52Q1ffuTPsnUf0zLsp7zaGsgF/PPfhJzUwbZqAbeGfCdhb4205GFVvRX9wKb60gQTiOuLpMroOIq8daXvhkfyFTnIXHimOa0kaWniaW/72le5lY+F6Zu37hm3FWwDoEtOVUW3vYHDy0HOa5SJSuTNtnog/vnPNvfN+D8ZdswhEt2kUvfdn0tzaXl2q99wF/SS8nYGCWjnW/cr3QVVrtbLfKfxuDAeWYV32HLrCnac9rCFnypC2Fx7JX+gkd+GR4riWpKGFpznnb19pFouyFzD3wGwOlO8nM7Ybd7S7m84xmUQbzv4h3ZxzVxckf6FriNzpcjdhXf5C1dzYQYONgtELUa1JoKoYt08jaEsjaLATSOhS4zns343FuOf7qtclQ/9JICYD27wnCcS0x3BgcdU+T4cbKLn8zXq9p2Ok7YVH8hc6yV14pDiuJWlo4ZH8QSDoZ87B7/ho+/sUVFQuYd3W1p5USxrt7R3oYHfQIbrjKcMvJHfhkfyFrsFyd9LUj8VXvIu33dXo984nZuZdVdvL+jyKN30YQWsLgvZWlYutfHkN+iPrq53u5N5h4/avUXylmJzT0B9eSf5dywja0+v9tqTthUfyFzrJXXikOK4laWjhkfwd5/aXs6FgPVuKNuEs3sbh8oMcKNuPSmXTjjXE0THaQfe4nqRYUkmMjqOFNp04Y1yEI2+apO2FriFzpy3YgeJ1ETP9FlStAU+3u6tWCDxZUB9VObOJ6kdberhqe/EV7+KP70IwJqPmaxxd5hqgZPhL9T7+WNpeeCR/Z6AGAeW0c8FL7sITbnF8+rVghRA1Muss9E8aSP+kgVXb3P5ydrl24izeyk7XDjYXbuTn3OXV3jcgaRBjOz5AO3vdztssRGNwbD5yX8sLMexbUK0wdl38b2zzf1e1FLXGVwq+0qr9Rdd/ga/loFpco2PVv23znyIQ0w7FU4RqiKrV+8X5QVNyCMVTWDlMpwFWOa0r1sXPoivYTvF1nxM/vgcVba+kdPiLpxxn2DsPZXcetL01AlEKkJ5jUUuSv3NX4nOR484mYPCwKGsp0/d+SUXAw7CUS/hVxwfqbdGR8420vdBFIneKpxDbT0/gj++EL21g5UqJgKbkIKCg+Moqxyf7PaAzE7Amn/Nc58dWLgwaY9BUFAGQO+5AXd+KtL2zUYPoctYSteRvlAz71yljyuslfwEvie+0BaBk2It4Mu+o2/PXlxpWnT3G0/5aNN4SSof8HfO69zBvnghULqzkvmBMvcwff76TYRW1JL/kwiP5C92x3OV78vgy6wu+2Tsdd6CcEWlX8XjXpzBoDZEOsVGTthe68zl3hqwfiZ51b9Xr/HtWEoxKrdNrnG/5U7ylqIoGjacI07YvMOxbSHmvcXgzLgvpfJYVL2Fd818Ayns8SNmgZ6rtr8v8aYt2Y5/zANrCXShBX9X2gtELCVqTUA22OrlOfTHsnEn09w+F9N7CW+fgT+xaxxGd38ItjsNb3UAIUWvxpgQe7DSOj4d+xi0Zt/P9we94atVjlPhckQ5NiCbH2+ZSiq/8EHfn2wAw7pwV4YgaP9vccSS+15H4Cf2wrnwVffZqor8bg+6kByIB9IdWYNg9B8VTCAFftX1KhQvTxo+rCmMA/YEldRqrcesUEt9qiX5/5Uwlxp2z0OVvAzVIea9xlPesLDTjPruImK9uqNNrh0rxFFYuxrThI8zrP0CpcIHk4+xaAAAgAElEQVSqYvvxMaK/fwh/bEcKb55J0fVfkPvgTgpun4+n/bWnnKeizaUErngVX1J3AGKnXIF+7/yGvp1mTXqORa1I/kJ3utz9dGguL234J2atmd9mPsnFqaH13pzvpO2FrlnkTlWJ/Xw4usKd+JJ6ELQk4sm8E2+bygf38HvQlGUTjG4DVD44GIhtX6uxqudV/nxuEt87/ryDu+vdmDdNqHpd3uNBygb+CcuaNzDsX4T+8Kpqb3d3uaNyfKyqEvPV9ehzfgGgZMhzaNz5WFe/Rt6v1ldbfj7GbqQovwitay9BczyqpeaFlAx75uJLHYBqtFdtS3zr+LCzkouex7LqddDqKbh7ReVGv4fEd9tXHZN335Zq7wcqV1t056F17cOf1B0ULdHfjEY12ii56F+o5rp7SFqXs47YL6/BH9v+tPN059+1gqC9+nA6Telh4j/pi+viV9EfWokS9FFy2X+r2p5tzkOYds1E1RrJv3fNuc/x7S3DtG0Knsw7I77iZEOSYRW1dF79kosAyV/ozpS7X/JW8962/7HdtY1HujzGTW3kAYyTSdsLXXPJne7IemKnXl1tW/GVH+LNuIyoBX/CvGUSJcNfxh/TjtjpN1Fy0fN4ut591vOeT/mLWvR/mDd+THmPB/GlDqgaSmHYNYvoOQ8CoOosKP7T32/BHYvQFmcRPfNugnorJZe9gTfjcnTZvxD71XUAuLvcTnmvR1D85cRNrv4Hf9G1E/GlD4OAF23xXoKWRKIWPY1pxwwCtlYU3jIL1RyHtmg3cZOG1hjDiWPLDbvnoMvbgnXVv3F3vYfSi/5Z7Vjz+g+JWvKXqtcBe2u0rr3H47nuc3ythtQie5W9wqrWVPMCNwEfie/UPMPKMfn3riZobVHzzkDFKcuvV7U9VcWwZy7Rs8dWxnzDVHxpA2s6S42iFvwJ8+ZPcV3yGhWdbq7cqKpoi3YTiG1X6/M0NVIc19L59EsuEiR/oTtb7rwBL8+te5alOYu4quW1DE0ZTo+4XjIW+Shpe6FrTrkzbfwY26L/O+1+VaPHm34RxqwfASjr/VvKBzx1xnM2qfz5PViXP4/id1PR8UZ8aRdW7TJtmoht4R+paH0Jrms+OeWthqwfsc17Eo27cv52X0o/Si56HtP26XhbDiYQ14H4j/tUXia2PRp3Pvn3/nK8JzIYIHbKFejyt54xRFVnprznr9EfWo7h4PJT96OgoKJq9ChBH8VXvo9x50xMO2YAUDr4b7i7jz3pTUES/1c553VFxghcV7wHGi26nLXEfnnqkIUTeTpcj+L3oD+8Eo2nEABvq6GoWiOuy/9XWQgHKrAu/QeWjR8dz82wFwnEdUB3ZAO2eU9Wu++K9OG4e4/DlzoA/YGlGHfPpvTC/wOd6YyxnOzkthf3UW+05TkA5D6wHW3RHlSDteobkdOJ+7g32rIcgqY48sesBY0W05bJ2Ob/rtazxDRFjaY4djgcCnAA2HF003Kn0/mnk4+T4rhpkvyFrja58wV9vL7pFX489D3eoJd4YwI3tr6Zq9OvJ9oQ3UCRNk7S9kLXLHOnqpg2f0rU0r+j+D0AuDPvxLR1MkrQX+3Q/DuXHC8ufOVoPIUEbWlV+xtT/ozOaWiL91De78nj27ZPh4AP84YP0edtrnZ8RburUBUd7h73Y587Dq1rHwV3LCIQ07bG8yveEozbpuJLHVDjSobHeiAB3Jl3UTrsheoHBCowbf4M86YJ6AorywDVEo9Snk95r4fxx3XC/uNva7x2ea+HCVqSiFryVwD80RmUDn2uspcZ0B3ZgKpoCSRm1vj+E3uIfck9Kb7mU2KnXo3WtRd3t3sp734fiq+cmG9ux931btxd7yFu8mVo3Lk1nu8Yd9d7MG869Y8JAHe3ezFv/LjqtapoKLhn5el7h8/RKW0vGMD688tYfqm+OmTBqLmnXXlSU3KI+An9qm2ryBiB1rUPXf5WfAmZFF//RYMtx96QGlNx3B74j9PpPOOfalIcN02Sv9CdS+4qAhWsyVvF9KyprMlfhUFjYFjKJdyaMZq29vP3K7AzkbYXumadu6Af3ZH1BC1JBG0tsax5A+O2qZT3ewKjcxrGffPxpfSl6KbpaMqyiZ4xGl3hdoqvGo8343Kg8eRPU7SH+EmVX/+X9X8K3ZH1BGI7nFIoQeXQB+uSv2Hc+1O17eXd76Ns8F/DisOy6jWsK185Y0EGEDPlSvS5G/GP+YkSVyn+5F6AWtXDC1B81Xj8cQ5M26bi7n4fqtGOxrUPbVk2vpT+5zZ/saqiKT9C/Me9q20uumFKtR70E+n3LSTm28pp4PLu34YudyOa0kOgaIla9DSaiuJqx+fftQxt0R7sPzxS1ct8jD++M65LXz9jTs7V6dpezLQbq40HD1iSKRiz5tQTBHzEfHUd+tyNFF/5Ibb5v0fjKajafWwaRFVrJO+hXXUWd2PRmIrjUcAfgGLADTzudDqdJx/ndntVnU5bJ9c8F1qthkAg2ODXPV9I/kIXau52Fe1k8vbJzM76jnJ/OcNaDuN3vZ8i1Vq301U1dtL2Qie5Oz3trEfRrPsU1RyL4j5e7Khx7fE/uBw0WrRaDeqq8SjbZhC4dTLojGc44xkU7oHodNCc+2efkrUI3aQzz8YQuPQ5gv3HHd9Q4UL/Spuql8EuNxG47J8QlXzO168m6K+8l/izLGSUuw3N+okolz1HQFWqbVcOrkJt0R1aXBBeLDXJ34H+nf6oeiuBq19DzRx5+mPVIJp5f0Nt2R/VcVX1fQEfmiUvo13yCmryBfhvnwrW4w8TKus+RSkvQG19IWpa37q/D87ws+stg9IciGuLZvaTaH/5iMBFT6PsmU/g5olgruwF1k6+Fc2uHwmm9iJw71xQNOD3oGydgWbPAgIX/xXduwNQPMX4frsZbCmnXErZvwLyd6D2uOuUfY3dsfzp9dqGK44dDsdY4PGTNo8DkpxO51SHwzGYyl7kU1qN9Bw3TZK/0IWbO5fXxbSsKUzdM5l4YzzP9XmR1lFt6i7ARk7aXugkd6d34oNoAOW9HiFga4lt4R8pvHU2/vguxB6ei+7r+wEovPlb/Mk9z+kampJD2L/7Ffq8Tbgz76Ki4/X4WvQBTe0Wp9W49hP75TVo3PmU93qEijaXEP3d2KoewILbfiQYlVo5x+9JPa1KeR5oDahaPehqeIisATT19qc/sJRAdJtqQ20aSm1yp5QdIeHjXtW2edMvwtP+OuzzniRgb03BnYsrC+MaaPO3Ejf5MlwXv0pF51Gn7D82Y0jJ8JfxdLm9doEH/aBo0B9eRcDeqs7nHq+txtRzbAH8TqfTe/T1ISDN6XRWu4AUx02T5C90dZW7TYUb+fOq3+EOlDO63d3c1X4Mulp+yDZl0vZCJ7k7PU3JQeIn9KeizWW4rhoPioK2YAdxnw+v8fiAJYmikd+gGm2oxuPPAWhzN6PqLdjm/x5Pl9upcFT2VuoPLifm61tqPFfemHWoloQTTu7FvO49dHlbKLn0P1UzF0TPuB199ioKb51TOf0cVM40ULwHpTwPf2q/Gs7eeEj7C11tcxf105OYt31BRfpwjPuqz4VcfM0EvK0vPv2bVZXE/7UCjo5dju+EcedMvK2GolQUEz/x+MN6Bbf9QCC+8xnPFf31zRgO/Vxtc/kFYykb8rez3kdda0zF8YtAvtPpfMnhcHQH3nU6nQNOPk6K46ZJ8he6usxdUUUhb297gx8OzqFTdBee7vHX834Zaml7oZPcnZnizkc1xR3vdVVV7N8/iHHXd1XHuC5+FduCP1ZblS3/7pUEbano9y8m5pvqPWrlPR9C8bsxbf2i6oHA8l4PY/nlf9WOC0SlUnzNBALxnTD/8hZRyysfcCu8eSb+5B5oSg8R/0k/yrvfT9ngv9AUSfsL3bnkTqlwoRrtaIt2E/PV9fhS+lHeaxz+Fr3O+t64CQPQlhwgYG+NL7U/pm1Tqu0P2FqhLdkPgK9FH4qv+QTVYMe0aQK+lL5V46yPtdea1MfS7mfTmIrjWGAiEAX4gXFOp3PbycdJcdw0Sf5CVx+5W3B4Hv/e+CJ+1c/QFsPoHJPJpakjsOqtdXqdxkDaXugkdyFQVRLe64jidxPMGEb+FZ+gP7gM6/Ln0eduBKBk2IsEjdHVlgP2xznQFVR/zKas7+P4WvTBl34RcOrX4J4O16P4yjg2vdwxBaPmYp/7CLrC7RTeMqtyAYsmSNpf6Boqd5qSg9h+fBTDoRWn7POmX0TxtZOInTQUXdHuU/YHTbHkj90I3jLMmyYQtfyfFN34JapGjz+pB9Hf3Ib+8Bpcl/0Xf2LXs047V5caTXFcW1IcN02Sv9DVV+6OuHP496aX2Fy4gTJ/GWathatbXcuVra6lTVQGyrk87d2ISdsLneQuNPbZ92HcPQffY06KfMf/4DRum4r9p5Mft6lUfOX7GHd9h2n7dAL2dALRbSi++qNTFndQKlwkfFB9VgN/bHtcl/+PuC8uP+W8uQ/tabIrm0n7C11D5k7jOkDcZxcRNMejLT1Utf3YWGPjjm/RH1qOtmD7KUW0L6k7+hOWH8+7fxuqIQoAbdFuYj8bhqIGK1dgHPRMg9wPSHFca/JDGh7JX+jqO3eqqrKteCvTs6Yw7/BPBNUACaZEUi1ptLKm087Wgfb2DrSzt8ess9RbHPVF2l7oJHehUbwlaAt2ENVp8Cn5M236FNvCP6HqTJT1fRJ39/tQ/O7jSxeraq2mIdMfWErMjFG4O99G6cWvVG47YXoxAE+nWym55N91d2MNTNpf6Bo8dwEvaA0o3hIUTxHa4qzKBUJOfJgv4IOgD23pYUybJ2JZ/361U1S0vhjXNROqbbN/Nxbjnu8puegFPF0bbtYLKY5rSX5IwyP5C11D5i7Hnc2ynCVsLdpMjjubvaVZuHyV83UqKKRHtaFPQj+uanUtGbaaFwNobKTthU5yF57T5q+WBfBZ1XAe69Ln0B1ZT9mgZ/DHd4YmvFKmtL/QNfbcacqysa54EVXRgM5E6cCnQX9q54viKcS8aSLubvcc/wOyAUhxXEuNvaE1dpK/0EUyd6qqkufJZYdrOztd29lStIm1+WvwBX2kWVrSMboTqZY0rmh5daN9sE/aXugkd+GR/IVH8hc6yV14wi2Oz/95oIRoxhRFIdGcRKI5iQuTBwOVM178dGgu6wvWsbVoM4uy5zNp1ye0t3cg1ZLGkORhDGoxFJPWFOHohRBCiIYnxbEQzUyMMZaRGaMYmVE56Xu+J49Z+79hU+EGthVtZVH2AvQb9QxIHMRYx4OkR7WOcMRCCCFEw5HiWIhmLt6UwN0dfgVAQA3wS95qVuauYPaBb1m2eDG3tb2DMR0fQHOaVZaEEEKI84l82gkhqmgVLX0T+zOuy6N8etEULk0dwaRdE/jz6t/j8roiHZ4QQghR76Q4FkLUKNYYx1MXPM0jXR5nbf4anvj5EQorCiIdlhBCCFGvpDgWQpyWoijc1OYW/tn7JQ6W7efxFePI8+RGOiwhhBCi3khxLIQ4qz6J/fhXv3+T68nlsRUPk1WyJ9IhCSGEEPVCimMhRK10j+vJK/1fp8Tn4r7Fd/Hsmj8xLWsKnoAn0qEJIYQQdUaKYyFErXWOyeSToZO5oc3N7HA5eXPLazy0ZAybCjZEOjQhhBCiTkhxLIQ4JzHGWB7p8hifD5/Gy/1ep8xfxm9XPMRvlz/E/tJ9kQ5PCCGECIsUx0KIkPVO6MuEiybzSJfH2Ve6l4eXjWXFkaWRDksIIYQImRTHQoiwmHUWbmpzC+8MHk+KJY2nVz/Fm1tewxvwRjo0IYQQ4pxJcSyEqBMtzCm8MfBdrm89kmlZUxizeDSz98/EF/RFOjQhhBCi1qQ4FkLUGaPWyG8zn+DFvv8hSmfj5Y3P8/DS+2TxECGEEE2GFMdCiDrXN7E/7wwaz196/oN9ZXsZu/hOlufIWGQhhBCNnxTHQoh6oSgKF6VczNsXfkiCKZGn1/yer7O+QlXVSIcmhBBCnJYUx0KIetXW3o43B77HgMQL+e+WV/nz6t+R7T4c6bCEEEKIGklxLISodwatkef6vMjDnR9lfcE6frXoDqbu/pxA0B/p0IQQQohqpDgWQjQIraLl5oxRjB86ke5xPXl72xs8vOx+thc7Ix2aEEIIUUWKYyFEg2phTuH5Pq/wbM/nyK/I4+GlY3l321sE1ECkQxNCCCGkOBZCNDxFURiWcgkfD/2MK1tdwxe7J/Hc2mfxyzALIYQQESbFsRAiYqL0Np7s9kd+3ek3LMqez6sb/0VQDUY6LCGEEM2YLtIBCCHELW1vpzxQzic7PsQbrODO9vfSJqotiqJEOjQhhBDNjBTHQohG4e72v0Kn6Ph4xwfMP/wTjuhOXJt+IzdGXRfp0IQQQjQjUhwLIRoFRVG4o/09XNnqWhYenseMvV/xysYX+GjHe/RLGMig5KH0SeiLQWuMdKhCCCHOY2EVxw6H40bgFqfTOfro6wHA64AfmOt0Ov8WfohCiOYkzhjHjW1u5obWI1lfsJaZh6az+PBCZh+YSawhlmd7/oPu8T0jHaYQQojzVMgP5DkcjteBF046xzvAaGAw0N/hcPQKLzwhRHOlKAo94nvxypBXmX7pLP7a859YdFYe/3kcb255jTJfWaRDFEIIcR4KZ7aKZcCvj71wOBx2wOh0Onc5nU4V+B64JMz4hBACrUbH0JThvDf4Y25sfTPTsqZwx4KRfLXnC5ndQgghRJ0667AKh8MxFnj8pM1jnE7nFw6HY9gJ2+yA64TXJUDbk88XFWVEp9OGEGp4tFoNMTGWBr/u+ULyFzrJXXhOzF8MFp5J+D9GdrqRN9e/yVtbX2dp3iJGtr+Zvsl9SLIkRzjaxkXaXngkf+GR/IVOcheecPN31uLY6XR+CHxYi3O5ANsJr21A0ckHlZZW1Dq4uhQTY6GoqDwi1z4fSP5CJ7kLT035S9Vm8M+erzDnwCzGb3+PZ5Y/DYAjujP9EweSZm1J97ieJJmbd7EsbS88kr/wSP5CJ7kLz7H8JSbazn5wDepstgqn0+lyOBxeh8PRDtgNjADkgTwhRL1QFIUrW13DiJZXsbtkJ2vyVjP3wHdM2Dm+6ph4YwKtotLpEtOVy9KuoHVUm8gFLIQQokmo66ncHgImAVoqZ6v4uY7PL4QQ1WgUDe3tHWlv78iotqPxBirYV7aX9flrcRZvY3/ZPibvmshnuybQOiqD1lFtiDHEUOIrIaAG6J3Ql57xvUmztJRFR4QQQoRXHDudzgXAghNerwAGhBeSEEKEzqA1VhXLxxRU5PPToR9Yk7eK3a6duHwuTFoTAIuy5wOQGduNy9OupEtMV9rYMtAqDf9shBBCiMiTRUCEEOe9OGM8t2Tcxi0Zt1XbrqoqO1zb2VCwjmlZU/jPppcAiDbEcEnq5aSYUyjyFrK/bD/Z5YfRarTEGxOIN8aTZE4mw9aWPgn90WnkV6kQQpwv5De6EKLZUhSFjtEOOkY7GNnmVg6WH2Br0WaW5Szhm73T8Kt+tIqWJHMyccZ4jBojB8r2sb7gF0p8JQAkmZIZmDSIngl96BHXC5veJsMzhBCiCZPiWAghqCyUW1pb0dLaisvSrqDUV4o/6MOmt6GtoWe4sKKAjQXrmXNgFnMPzmHGvmkAJJtbcFf7MVzZ8hopkoUQogmS4lgIIWoQpY864/5YYxxDU4YzNGU4/qCfzYUb2VK0iWVHlvDKxheYuW8Gbe3tsOujSTYnE29MoF/iQAxaQwPdgRBCiFBIcSyEEGHSaXR0j+9J9/iejGp7B9/u+5qZ+2aw4sgySnwufEEfAFadla6xF5BqSaNDtIM2URlYdBYCapB4YwJ2gz3CdyKEEEKKYyGEqEMaRcP1rW/i+tY3AeAL+iiqKCSrdDeLshewpXAT6wvWMX3vl6e8t62tHd3ietDe3oFusd1pZU2XoRlCCNHApDgWQoh6pNfoSTQnkWhOom9i5UyXlbNkOCmoyKfMV4Y36CWvIpcNBev4/sB3zAi4AegaewFdY7sxIGkQ3WK7S6EshBANQIpjIYRoYJWzZHSqcV9QDXKgbD9LchYy98BsvsqawuTdk0gxp9Le3pE0axp2fTQtra3oHJNJvCmhgaMXQojzmxTHQgjRiGgUDelRrRkddTej292N2+9mUfZ8luQsZG/pHpYfWYJf9Vcdn2xugUVroVVUOhcmDWFQ8lCsemsE70AIIZo2KY6FEKIRM+vMjGh5FSNaXgWAP+inIlBBVuluNhduZFvxVoq9RWwt2sKi7AUAmLQmWllbMzx9GCNbjkav0UfwDoQQommR4lgIIZoQnUaHTqMjM7YbmbHdqrarqsrmwo2sL1hLkbeIHS4n7216l++z5nJ7uzu5LPUKGbMshBC1IMWxEEKcBxRFoWvcBXSNu6Bq27rSn3lz7Vv8a/1zzDv0A090/QNJ5uQIRimEEI2fJtIBCCGEqB/DWg7nvcEf85suT7ChYB1jF9/Jd/u/RVXVSIcmhBCNlhTHQghxHtMoGm5sczMfDPmUDnYHr2x8gT+sepwcd3akQxNCiEZJimMhhGgGUi1pvNL/vzya+SSbCjcydvGdvL31DQoq8iMdmhBCNCpSHAshRDNRuXrfSD4c8imZMd2Yuudzxiwazac7P6LMVxbp8IQQolGQ4lgIIZqZFEsqL/b7D+OHTKJrbHc+2v4+YxffyaLsBQTVYKTDE0KIiJLiWAghmqk2tgz+2ecl3hj4Lmadmb/+8mfuW3wXH2//QHqShRDNlhTHQgjRzGXGduODwRP4U/dnseqjmLBzPOOW3ceekt2RDk0IIRqcFMdCCCHQanRclnYFbwx8l1f7v0Gxr5j7l9zDKxtfYLdrV6TDE0KIBiOLgAghhKimZ3xvPhoyiU93fsTM/d/w3f5v6RKTydWtrqeFJYVczxFyyrMp9hVh1pppaU0n1ZJG19gLZBU+IUSTJ8WxEEKIU8QYY/lN5hPc3WEscw98x7f7vubljc9XO8aqi8ITcBNQAwC0t3dkTIf7GZB0oRTJQogmS4pjIYQQpxVtiOaWtrdzU5tb2OHajjvgJsGYSLI5GYPWiC/o43D5IVbn/cz0rC95es3v6Rnfm7EdH6RLbNdIhy+EEOdMimMhhBBnpdXo6BTT5ZTteo2e9KjWpEe15rr0m/h239d8unM8jyx/gC4xmTze9Sna2TtEIGIhhAiNPJAnhBCiTug0Om5sczOThn3J3e1/RbY7m18vHcuHzndkJT4hRJMhxbEQQog6ZdZZuLfjfXw4ZCJDWgxj0q4J3D5/JNOypqKqaqTDE0KIM5LiWAghRL2INkTzTM+/8+bA9+id0Jc3t/yHv699RnqRhRCNmow5FkIIUa+6xHblH71fZPKuiXyy80NW5a3ggrieXN3qOgYmDUKjSD+NEKLxCKs4djgcNwK3OJ3O0Udf3wS8DOw/eshfnE7nwvBCFEII0dRpFA2j29/NkBbD+Hz3p/ySt5pn1vyBFEsqV7W8lqtaXUusMS7SYQohROjFscPheB0YAaw7YXMv4Cmn0/lVuIEJIYQ4/7SKSuepC54mEPSzKHsBs/Z/w4fb32XCzvFcl34T3eK60zu+L1a9NdKhCiGaqXB6jpcBXwMPnrCtN9DT4XA8BqwE/uB0Ov1hXEMIIcR5SKvRMTz1UoanXsr2YidTdn/G13u/5KusLwBoZU1nSIthjGo7GpveHuFohRDNiXK2J4cdDsdY4PGTNo9xOp2rHA7HMOAhp9N529Fjn6CyYN4DvANsdDqdb574Rrfbq+p02joKv/a0Wg2BQLDBr3u+kPyFTnIXHslf6Jpa7tx+N5vyN7Hi8HK2FmxhZc5KrDorvZJ6k2pNYUzmWBLMCQ0WT1PLX2Mj+Qud5C48x/Kn12tDWqrzrMXxmdRQHMc4nc6io/++ChjpdDrHnvie3NySiMzjExNjoaioPBKXPi9I/kInuQuP5C90TT1324u3MS1rKjuKnewt24tRY6RvYj/6JPQjPaoNJq0Jk9ZEC3MKBq2xzq/f1PMXaZK/0EnuwnMsf4mJtpCK4zqbrcLhcCjABofDcaHT6TwAXAKsqavzCyGEaF46Rnfij92fAWBf6V6m7P6MVXk/syh7QbXjEk1JjGxzK51jMjHrzGTY2uEP+nH5XBwqO8De0ix6xPckPapNw9+EEKLJqbPi2Ol0qg6H4z5gmsPhcANbgPfr6vxCCCGar/So1vzugj+hqir7y/aR6zmCJ+DB5S1m5v4ZvLPt+Ag+DRqCnPqVdJ+EflyaOoIEUyI94nvJFHJCiBqFNawiFDKsommS/IVOchceyV/omlPuctzZ7C3NosTrIqt0N2adBbveToIpkTRLK+Ye/I7ZB2ZVLUDSyprOTW1u5dLUEVUzYxxx56BRNMQbE1AUpVnlrz5I/kInuQtPuMMqpDgWtSL5C53kLjySv9BJ7qrzBDzsKdnNwbL9fJX1Bc7ibQAkmZLxBb0UegsBSDGn0sbWloEt+zMi6Tr0Gn3VOVRV5VD5QbSKljhjPHqNHkUJ6fP3vCftL3SSu/A0mjHHQgghRGNm0proHNOFzjFduCT1cjYXbmRt/hr2lmZh0lU+2GfWmlmVt5LtxdtYfmQJ7+rexaa3YdPbaR3Vmh2uHewt3VN1TqvOikFj4Nr0G7k5YxTeoI+skt3oNDo6x2RWK6yFEE2D9ByLWpH8hU5yFx7JX+gkd+HZUr6O73bOxh0op8RXwr7SvSSak7gk5XIURSHHnU1+RR4FFfmsyVuFXmPAF/RWvf/YbBqZsd3oGtudbrEX0CW2awTvqGFJ+wud5C480nMshBBC1IMLUy+ki6VHrY7dUexk5r4ZJJmT6RyTSbm/jHUFv1DmK2NDwTqW5iwGoGd8b+5zPETnmMz6DF0IEQYpjoUQQogwdYh28Hi3p6ptG9zioqp/F1QU8NOhuXy+awLjlt3PoOShPEJSLSgAABU/SURBVNz5t6RYUhs6VCHEWcg8NkIIIUQ9izPGcUvGbUwcNpUxHe9nbf5qHlhyD/MP/Rjp0IQQJ5HiWAghhGggFp2Vu9qP4YPBn9I6qg3PrXuWlzc8j9vvjnRoQoijpDgWQgghGlgLSwqvDXibO9rdw5wDs3ho6Rh2urZHOiwhBFIcCyGEEBGh0+gY63iQV/r/l3J/OQ8t+RWvbXoZX9AX6dCEaNbkgTwhhBAignrG9+b9wZ/wyY4PmbFvGmvyVtE/6UKubnUdGba2kQ5PiGZHimMhhBAiwmKMsTza9Xf0jO/NzP0zmLnva6ZlTaF3Ql9GZdxBn8R+kQ5RiGZDimMhhBCikRiaMpyhKcMp9hbxzb7pfLvva55a9RiDkodwffpI2trbY9PbyPUcwaK1EG2IkeWrhahjUhwLIYQQjUy0IYa72o9hVMYdTNr1CdOyplQtJGLQGPAeXYnPpreRYWtHhq0dXWO70dHeiQRTAmadJZLhC9GkSXEshBBCNFIGrYExHe/n1ozRbC3azK6SnWS7D9PO1o6KQAV7S7PYXbKL7w98x4y9X1W9b1DyEO53/Jr0qDaRC16IJkqKYyGEEKKRs+qt9Ensd9qxx4Ggn42FGzjiyWFvSRbf7vuaB5bcyy0Zt3FTm1uJNcY1cMRCNF1SHAshhBBNnFajo0d8r6rXIzNu5c0tr/HZrk/5KmsqI9vcyh3t78GkNUUwSiGaBpnnWAghhDjPxBnjebbnc3w09DMGJg1i0q5PuOWn63hq5WM4i7aiqmqkQxSi0ZLiWAghhDhPpUe15pmef+c//d9ieMolbC3awq+XjeXuhaOYvX8m3oA30iEK0ehIcSyEEEKc57rH9+SJbn/gs+Ff8njXp7DorLy88Xlun38jb215nXxP3mnfG1SDHCw7IIW0aDZkzLEQQgjRTNj0dq5Nv4FrWl3PL/mrmZ41la/3fsms/d+QGdOVNGtLks0t0GsMHCo/yNr8NeS4s/EE3ETpbHSJzURVVbrEdmVI8jDa2ttF+paEqHNSHAshhBDNjKIo9E7oS++EvhwsO8Dk3RPZ6drOj4e+p9xfDoBJa6ZrbDd6J/Ql3dqaLUWb2F68DY2iZcKO8Xyy40Mc0Z3ok9CPa9NvJMmcHOG7EqJuSHEshBBCNGNp1pY82e2PVa+z3YcxaIzEGGLQKMdHX17X+saqfxd7i5h9YBbLc5bw+a6JfL57Ej3jetHCksIFcT0YnnJpg96DEHVJaegnVnNzSyLyiGxMjIWiovJIXPq8IPkLneQuPJK/0EnuwiP5q51s92G+3fs1P+cu43D5YdyBchzRnXi016N0NHWrVmCL2pG2F55j+UtMtIW0troUx6JWJH+hk9yFR/IXOsldeCR/584f9LMwex5vbnmNYm8RLS2tuLfjfQxtMRydRr6sri1pe+EJtziWP+eEEEIIUSd0Gh2XpF7OF8On8/yFL4Ci8I91f+H2+Tcxdffn+IP+SIcoxFlJcSyEEEKIOmXQGrmizZWMHzKR5/u8TJuoDN7e9gYPLrmXTQUbIh2eEGckxbEQQggh6oVOo2NA0iBe7v86z/X+F2X+Mn674iFe2fgC2e7DkQ5PiBrJACAhhBBC1LtByUPpFd+HT3aM58usL/hu/7ekmFPpk9CPC5OH0C9xAIoS0hBRIepUSMWxw+GIBiYCdsAAPOF0Opc7HI4BwOuAH5jrdDr/VmeRCiGEEKJJM+ssPNT5Ea5udR2r8lbwS95qfjo8l2/3f02qJY3ucT0JqkFsehvd43vSP/FCeZBPNLhQW9wTwE9Op/M1h8PhAD4HegHvACOB3cAsh8PRy+l0/lI3oQohhBDifNAqKp1WUenc1OZW/EE/Pxycw8LseSzNWYxW0VDqL+PLrC9IMafyRLc/0Duhb6RDFs1IqMXxf4CKE87hcTgcdsDodDp3ATgcju+BSwApjoUQQghRI51Gx5WtruHKVtdUbfMFfazMXc672/7H71c+yrXpN3Jly6sxak2kWVpi0BoiGLE43511nmOHwzEWePykzWOcTucqh8PRApgNPAbsAr5yOp39j77vV0Bbp9P5fye+0e32qjqdtq7irzWtVkMgEGzw654vJH+hk9yFR/IXOsldeCR/4amL/Hn8Hv634S0mbZuISmW9YtQa6RDTgSRLMknmJByxDoamDSXWFIcv4EOn0TX5scvS9sJzLH96vbZhFwFxOBzdgMnA75xO5+yjPccrnE5nl6P7HwX0TqfzlRPfJ4uANE2Sv9BJ7sIj+Qud5C48kr/w1GX+DpYdYE/JLioCFWwr3sqekl3kV+SR6zlCub8cDRra2zuyp3QXJq2JDFs7EoyJOGI60y9xAOnW1k2qYJa2F55wFwEJ9YG8LsBUYJTT6VwP4HQ6XQ6Hw+twONpROeZ4BCAP5AkhhBAiLGnWlqRZWwJwSdrlVdtVVWWnaztLcxazoWAdF6dchl6jZ6drBxsL1zPv8A+8vfW/6BQdMcZY4o3xZMZ2o2d8H3rG98Kis0bqlkQjFuqY4xcAE/B65fN4FDudzuuBh4BJgJbK2Sp+rpMohRBCCCFOoigKHaIddIh21Lg/132EpTmLyfUcodBbQI47m1n7vmFa1lR0io7M2G70iu9Dh+iOxBnjSTa3wK6PblK9zKLuhVQcHy2Ea9q+AhgQVkRCCCGEEHUg0ZzEDW1GVtvmDXjZXLSRVbkrWJ23io93fFA1nhmgdVQGV7W8hitbXUuUPqqhQxaNgEweKIQQQohmw6A10DO+Nz3je/MAUOwt5mDZfvIr8jlUfpDF2fN5e9sbfLb7U6KP9iL3iOvFpWkjaGFOId6UEOlbEPVMimMhhBBCNFvRhmiiDdFVr0e1Hc3mwo18sfszAPyqn5n7ZzBj3zQAkkzJtLd3IMPWlutajyTRlBiRuEX9keJYCCGEEOIEmbHd+HvvF6peHyo/SFbJHg6WH2Bb0RZ2l+xk+ZGlfL5rIpelXcE9HcfSwpwSwYhFXZLiWAghhBDiDFItaaRa0qptO1h2gBl7v2LGvunMO/wDg5OH0jO+D5elXYFRa4xQpKIuaCIdgBBCCCFEU5NmbcnDXR5l4kVTuKLlNWwoWM+/N73IXQtvZea+r/EH/ZEOUYRIimMhhBBCiBAlmpN4vOvvmXLxDP7d/02STEn8e9NL3LPoNibsGM+Bsv2RDlGcIxlWIYQQQggRJkVR6BHfizcGvsfyI0uZsuczPtnxIR/v+IAUcyrd4rozLOUSesb3lmEXjZwUx0IIIYQQdURRFC5MHsyFyYPJdR9hQfY8thRuYmnOYuYenI1eYyAzpiu3t7uT3gn90CjyJX5jI8WxEEIIIUQ9SDQncUvGbZAB3kAF6wrWsjJ3OYuyF/CHVU8Qb0ygd0JfusR0JT2qNe3s7bHp7ZEOu9mT4lgIIYQQop4ZtEb6JQ6gX+IAHnA8zLIjS1h4eD7Ljyxh7sHZAOgUHRcmD2Fcr4dJJO0sZxT1RYpjIYQQQogGZNAaGZZyCcNSLkFVVY54cthfuo9VeSuYc2AWt88eRZeYrrQwp9A/cSDJ5hakWtOIM8ZHOvRmQYpjIYQQQogIURSFZHMLks0t6JPYjzva3cuMQ1NYcmApq/J+5sdD3wOVvcrd43rSOTaTEl8JR9w5eIMVoEKfxP70SehLW1t7FEWJ7A2dBxRVVRv0grm5JQ17waNiYiwUFZVH4tLnBclf6CR34ZH8hU5yFx7J3/+3d+dBUpRnHMe/s7Mse3Asx3IKkhB9gogLrIUYkKwEg0EpjEkqhEKDR6ImEY0mWhotkiqTmEo0XomWlhQqGlKoBCKKiCICyqEcnnkQRBERORTkxl02f3QvNsMsx+w6M+z8PlVU9fTbzTz71Ns9T3e/3V0/yl/qanNXXVPNqs9XsmXvZyzauIBXNy5kzY4PaJbfnHZF7ciLxana9wXvb18NQNvCMk5t249hxw2nZ6teOVso1+avrKx5SgnQmWMRERGRLBSPxTmxpQHQr6w/ADU1NQcVvRt3bWDxpoUs3riQuevnMGPtdLqWHE/PVr3Ij+VTmF9Ij9KenFZ2OkX5xWn/O441Ko5FREREjhHJzgaXFbVjWJfhDOsynF1Vu5i17llmr5vFgg3z2UcNu6t2MXn1JJrkFVDeujcFeQVUtO1H12bHUxgvpCheTMfiThTlF2XgL8o+Ko5FREREGomi/CKGdz2P4V3P2z+vuqaaNz97nRfXPc+yT5ewt3ovL2+Yd8B6TfIKOKvTUK7oMZaSJiXpDjurqDgWERERacTisTjlrftQ3rrP/nnrdn7Ept0b2V29m51VO1m2+TWeWjOVhRtfYWD7QZS36cPJrU6hbWFZBiPPDBXHIiIiIjmmU3FnOhV/+Szlyo6DGdJpKBNXPcTMj2Ywdc2TALRp2pafdB/NiK7nE8/LjbIxN/5KERERETmkk1ufwq2tb6N6XxUrPnfe2fIW8z+Zyz1v38GU9x9nzAmXckaHSgriBZkO9Sul4lhERERE9ovn5dOjtCc9Snvy/eN/xMsb5vLQu+P54/LfE1seo19Zf87qfDYD2g+iabxppsNtcCqORURERCSpWCzGgPaD6N9uALPXzWLF1v8xZ/1sblk2juL8YgZ1OJNzu4zgpFYnZzrUBqPiWEREREQOKR6LM6TzUIZ0HsrlPa5k+adLmbn2GeZ8PJsZa6fTs1Uv+rSpoHfrvpS37n1Mj08+diMXERERkbTLi+XRp00FfdpUMLbntUz5YDLz1r/EY6seYeLKCZTkl9Ct+dfp1uxrnNDC+HbHwbQsaJnpsI+YimMRERERSUlRfhGjul/IqO4XsuOLHSzetJDlm5ewevt7zF3/ItM/nMbOqh2M7D4606EeMRXHIiIiIlJvJU1KqOw4mMqOg4HgVdef7FpPu6L2GY7s6Kg4FhEREZEGF4vF6FDcMdNhHLW8TAcgIiIiIpItVByLiIiIiIRUHIuIiIiIhFIac2xmLYGJQAugALjG3V8xs/OBvwIfhouOc/c5DRKpiIiIiMhXLNUb8q4Bnnf3O8zMgH8BfcN/17n7Ew0VoIiIiIhIuqRaHP8d2BP5P3aH0xVAHzO7GlgEXO/uVdEVmzVrSn5+PMWvTV08nkdpaXHav7exUP5Sp9zVj/KXOuWufpS/+lH+Uqfc1U9983fY4tjMLgF+nTD7IndfbGYdCIZXXB3Ofw74D7AauA+4HLgnuuL27XvIhNLSYrZs2ZmR724MlL/UKXf1o/ylTrmrH+WvfpS/1Cl39VObv7Ky5imtH6upqUlpRTPrBUwCfuPuz4TzSt19Szg9DPiBu1+S0heIiIiIiKRZSk+rMLOTgMnAqEhhHANeN7PjwsW+A7zWIFGKiIiIiKRBSmeOzWwqUA68H87a6u4jzOy7wC3ALuBtYKy7f9FAsYqIiIiIfKVSHlYhIiIiItLY6CUgIiIiIiKhVB/llrXMLA/4J8Gwjz3Ape6+MtL+M+AyoAq4xd2fykigWcjMmgDjgW5AU4L8TIu0XwNcAmwMZ13m7p7uOLOZmS0FtoYfV7v7RZE29b06mNkYYEz4sRDoDXSI3OB7FzAA2BYuM8LdtyKY2WnAX9y90sy+AUwAaoA3gV+6+77IskUETxhqR5DLn7r7xoP/19yQkLvewN1ANcFvx4Xu/knC8nVu37koIX99gf8C74bN97r7vyPLqu8lSMjfJKBD2NQNWODuIyPLxoC1fJnfV9z9hnTGmw2S1SkEw3gn0ID7vUZXHAPnAYXufrqZ9QduA0YAhI+eGwucSvADPM/MnnP3zDxfLvuMBja7+wVm1gZYCkyLtPcl+MHQjZZJmFkhgLtXJmlT3zsEd59AsHPDzP4BjK8tjEN9gaHuvin90WUvM7sOuADYEc66HbjJ3V80s/sI9n1TIqtcAbzh7r83s5HATcBV6Yw5WyTJ3Z3Ale6+zMwuA64neOFV7fJ1bt+5KEn++gK3u/ttdayivheRmL/aQtjMWgGzOfgRut2BJe4+PJ1xZqFkdcoyGni/1xiHVQwEZgC4+wKCYqRWP2C+u+8JzzqtBE5Jf4hZazJwc+RzVUJ7BXCDmc0zs5w7Yj0C5UCxmc00sxfCg7Na6ntHwMxOBXq6+/2ReXnACcD9ZjbfzC7OWIDZZxVwfuRzBTAnnH4GGJKw/P79Yx3tuSQxdyPdfVk4HX25Va1Dbd+5KFnfO8fMXjKzB80s8QGz6nsHSsxfrT8Ad7v7xwnzK4DOZjbbzJ4O306ci5LVKQ2+32uMxXELvrzsBVBtZvl1tG0DWqYrsGzn7tvdfVu4U3uc4OgqahLBi10GAwPN7Nx0x5jldgJ/A4YS5OlR9b2jdiPBj0NUCcHl7tHA2cAvzEwHFoC7PwFEnwgUc/fau6yT9bFoP8zpPpiYu9pixMy+BfyK4E2wUYfavnNOkr63CPituw8C3gPGJayivheRJH+YWTuCx+BOSLLKx8Cf3f1M4E8EwwRyTh11SoPv9xpjcfw5ED1izYu8wjqxrTkQvXSb88ysC8ElnUfc/bHI/Bhwh7tvcve9wHSgT4bCzFYrgInuXuPuK4DNQMewTX3vMMysFPimu89OaNoJ3OnuO919G/ACwVk8Odi+yHSyPhbth+qDCczsxwRvdz0nyZjEQ23fAlMiQ+6mcPDvg/re4f0QeMzdq5O0vQpMBXD3eQRnkWPpDC5bJKlTGny/1xiL4/nAMIDwstcbkbZFwBlmVmhmLYEeBIO3BTCz9sBM4Hp3H5/Q3AJ408yahRvkYPSSl0QXE4xxx8w6EeSs9tKY+t7hDQJmJZl/IsEY7Xh4M8ZAYElaIzt2LDWzynD6e8DchPb9+8c62nOWmY0mOGNc6e7vJVnkUNu3wLNm1i+cTvYSMPW9wxtCcNk/mXHA1QBmVg6siZwtzRl11CkNvt9rjJeEpgBnmdnLQAy4KHzKwkp3nxbe9T6X4MDgd+6eOK4sl90ItAJuNrPaMT0PACXufr+Z3UhwtLYHeN7dn85QnNnqQWCCmc0juGv2YmCsmanvHRkjuBwbfDhwu30UWEBwGfJhd38rQzFmu2uBB8ysAHiH4LIjZjYTOBe4F3go7KN7gVGZCjSbmFkcuAtYAzwZDuec4+7jzOxhgku3B23fkauSEtz0dI+Z7QXWAz8H9b2jdMA+EA7I363ARDM7h2Cc7Zi0R5cdktUpVwF3NeR+Ty8BEREREREJNcZhFSIiIiIiKVFxLCIiIiISUnEsIiIiIhJScSwiIiIiElJxLCIiIiISUnEsIiIiIhJScSwiIiIiEvo/N1GJatKKYZoAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "HH = [0.1, 0.5, 0.9]\n", "deltaT = (rv1.index.max() - rv1.index.min()).days / 252.\n", "nbTimes = len(rv1.index)\n", "\n", "plt.figure(figsize=(12,4))\n", "for H in HH:\n", " times, fbm = fbmmatrix(deltaT, nbTimes, H)\n", " plt.plot(times, fbm, label=\"H = %.1f\" %H)\n", "\n", "plt.title(\"Fractional Brownian paths\", fontsize=13)\n", "plt.legend(loc=2)\n", "plt.grid(True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "source": [ "###Representations of fBm\n", "\n", "There are infinitely many possible representations of fBm in terms of Brownian motion. For example, w\n", "\n", "\n", "

\n", "Mandelbrot-Van Ness

\n", "
\n", "
\n", "
\n", "\n", "$$\n", "W^H_t ={C_H}\\,\\left\\{\\int_{-\\infty}^{t} (t-s)^{H-\\frac{1}{2}}dW_s - \\int_{-\\infty}^{0} (-s)^{H-\\frac{1}{2}}dW_s\\right\\}.\n", "$$\n", "
\n", "\n", "
\n", "\n", "
\n", "\n", "where the choice\n", "\n", "$$\n", "C_H = \\sqrt{ \\frac{2\\,H\\,\\Gamma(3/2-H)}{\\Gamma(H+1/2)\\,\\Gamma(2-2\\,H)}}\n", "$$\n", "\n", "ensures that\n", "\n", "$$\n", "\\mathbb{E}\\left[W^H_t W^H_s\\right] = \\frac{1}{2}\\,\\left\\{t^{2 H} + s^{2 H} - |t-s|^{2 H}\\right\\}.\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": { "zanadu": {} }, "source": [ "# Forecasting" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "source": [ "import scipy.special as scsp" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "slideshow": { "slide_type": "fragment" }, "zanadu": { "is_abstract": false, "is_hidden": false } }, "outputs": [], "source": [ "def c_tilde(h):\n", " return scsp.gamma(1.5-h) / (scsp.gamma(h+0.5) * scsp.gamma(2.-2.*h))\n", "\n", "def forecast_XTS(rvdata, h, date, nLags, delta, nu):\n", " nLagsRa = np.arange(nLags)\n", " cf = 1./((nLagsRa+0.5) ** (h+0.5) * (nLagsRa+0.5+delta))\n", " ldata = rvdata.truncate(after=date)\n", " ldata = np.log(ldata.iloc[-nLags:])\n", " ldata['cf'] = np.fliplr([cf])[0]\n", " ldata = ldata.dropna()\n", " fcst = (ldata.iloc[:, 0] * ldata['cf']).sum() / sum(ldata['cf']) ## Riemann sum approximation\n", " return np.exp(fcst + 2.*nu**2. *c_tilde(h)*delta**(2.*h))" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "zanadu": { "code_type": "" } }, "outputs": [], "source": [ "idCol = 0\n", "rvdata = pd.DataFrame(rv1[rv1.columns[idCol]])\n", "nu = Coefdf[\"nu\"][idCol] # Vol of vol estimate for index idCol\n", "h = Coefdf[\"H\"][idCol] # H estimate for index idCol\n", "delta = 1\n", "nLags = 600\n", "dates = rvdata.iloc[nLags:-delta].index\n", "rv_predict = [forecast_XTS(rvdata, h=h, date=d, nLags=nLags, delta=delta, nu=nu) for d in dates]\n", "rv_actual = rvdata.iloc[nLags+delta:].values" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "## Plot the annualised volatilities\n", "xx = [d.date() for d in rvdata.index[nLags+delta:]]\n", "N = 2000\n", "xxx = xx[:N]\n", "\n", "plt.figure(figsize=(14, 4))\n", "vol_actual = np.sqrt(np.multiply(rv_actual,252.))\n", "vol_predict = np.sqrt(np.multiply(rv_predict,252.))\n", "plt.plot(xxx, vol_actual[:N], \"b\", label=\"Actual vol\")\n", "plt.plot(xxx, vol_predict[:N], \"r\", label=\"Predicted vol\")\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "zanadu": { "code_type": "", "is_hidden": true } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "## Plot the log variances\n", "xx = [d.date() for d in rvdata.index[nLags+delta:]]\n", "N = 2000\n", "xxx = xx[:N]\n", "\n", "plt.figure(figsize=(14, 4))\n", "vol_actual = np.log(rv_actual)\n", "vol_predict = np.log(rv_predict)\n", "plt.plot(xxx, vol_actual[:N], \"b\", label=\"Actual vol\")\n", "plt.plot(xxx, vol_predict[:N], \"r\", label=\"Predicted vol\")\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" }, "zanadu": { "authors": [ "Antoine Jacquier" ], "bibliography_data": {}, "category": "1", "clearance": "Internal", "group_name": "ImperialMScMathFin", "md5": "ae137a5e30d3e2b7cb6c1a11764cb3fc", "notebook_id": "AFA86C74-8F9E-4AAC-9D43-AFB48C0094D9", "python_name": null, "reviewer_id": "B81D4EC4-269D-42B3-9975-85BC42EE5712", "status": "Approved" } }, "nbformat": 4, "nbformat_minor": 1 }