{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\"The" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multi-Risk Derivatives Portfolios" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The step from multi-risk derivatives instruments to multi-risk derivatives instrument portfolios is not a too large one. This part of the tutorial shows how to model an economy with three risk factors" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from dx import *\n", "from pylab import plt\n", "plt.style.use('seaborn')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Risk Factors" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This sub-section models the single risk factors. We start with definition of the risk-neutral discounting object." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# constant short rate\n", "r = constant_short_rate('r', 0.02)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Three risk factors** ares modeled:\n", "\n", "* geometric Brownian motion\n", "* jump diffusion\n", "* stochastic volatility process" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# market environments\n", "me_gbm = market_environment('gbm', dt.datetime(2015, 1, 1))\n", "me_jd = market_environment('jd', dt.datetime(2015, 1, 1))\n", "me_sv = market_environment('sv', dt.datetime(2015, 1, 1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assumptions for the `geometric_brownian_motion` object." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# geometric Brownian motion\n", "me_gbm.add_constant('initial_value', 36.)\n", "me_gbm.add_constant('volatility', 0.2) \n", "me_gbm.add_constant('currency', 'EUR')\n", "me_gbm.add_constant('model', 'gbm')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assumptions for the `jump_diffusion` object." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# jump diffusion\n", "me_jd.add_constant('initial_value', 36.)\n", "me_jd.add_constant('volatility', 0.2)\n", "me_jd.add_constant('lambda', 0.5)\n", " # probability for jump p.a.\n", "me_jd.add_constant('mu', -0.75)\n", " # expected jump size [%]\n", "me_jd.add_constant('delta', 0.1)\n", " # volatility of jump\n", "me_jd.add_constant('currency', 'EUR')\n", "me_jd.add_constant('model', 'jd')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assumptions for the `stochastic_volatility` object." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# stochastic volatility model\n", "me_sv.add_constant('initial_value', 36.)\n", "me_sv.add_constant('volatility', 0.2)\n", "me_sv.add_constant('vol_vol', 0.1)\n", "me_sv.add_constant('kappa', 2.5)\n", "me_sv.add_constant('theta', 0.4)\n", "me_sv.add_constant('rho', -0.5)\n", "me_sv.add_constant('currency', 'EUR')\n", "me_sv.add_constant('model', 'sv')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the unifying valuation assumption for the **valuation environment**." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# valuation environment\n", "val_env = market_environment('val_env', dt.datetime(2015, 1, 1))\n", "val_env.add_constant('paths', 10000)\n", "val_env.add_constant('frequency', 'W')\n", "val_env.add_curve('discount_curve', r)\n", "val_env.add_constant('starting_date', dt.datetime(2015, 1, 1))\n", "val_env.add_constant('final_date', dt.datetime(2015, 12, 31))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These are added to the single `market_environment` objects of the risk factors." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "# add valuation environment to market environments\n", "me_gbm.add_environment(val_env)\n", "me_jd.add_environment(val_env)\n", "me_sv.add_environment(val_env)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the **market model** with the risk factors and the correlations between them." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "risk_factors = {'gbm' : me_gbm, 'jd' : me_jd, 'sv' : me_sv}\n", "correlations = [['gbm', 'jd', 0.66], ['jd', 'sv', -0.75]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Derivatives" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this sub-section, we model the single derivatives instruments." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### American Put Option" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first derivative instrument is an **American put option**." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "gbm = geometric_brownian_motion('gbm_obj', me_gbm)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "me_put = market_environment('put', dt.datetime(2015, 1, 1))\n", "me_put.add_constant('maturity', dt.datetime(2015, 12, 31))\n", "me_put.add_constant('strike', 40.)\n", "me_put.add_constant('currency', 'EUR')\n", "me_put.add_environment(val_env)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "am_put = valuation_mcs_american_single('am_put', mar_env=me_put, underlying=gbm,\n", " payoff_func='np.maximum(strike - instrument_values, 0)')" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.012" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "am_put.present_value(fixed_seed=True, bf=5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### European Maximum Call on 2 Assets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The second derivative instrument is a **European maximum call option on two risk factors**." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "jd = jump_diffusion('jd_obj', me_jd)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "me_max_call = market_environment('put', dt.datetime(2015, 1, 1))\n", "me_max_call.add_constant('maturity', dt.datetime(2015, 9, 15))\n", "me_max_call.add_constant('currency', 'EUR')\n", "me_max_call.add_environment(val_env)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "payoff_call = \"np.maximum(np.maximum(maturity_value['gbm'], maturity_value['jd']) - 34., 0)\"" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "assets = {'gbm' : me_gbm, 'jd' : me_jd}\n", "asset_corr = [correlations[0]]" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[['gbm', 'jd', 0.66]]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "asset_corr" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "max_call = valuation_mcs_european_multi('max_call', me_max_call, assets, asset_corr,\n", " payoff_func=payoff_call)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.334" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max_call.present_value(fixed_seed=False)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.7596" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max_call.delta('jd')" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.2824" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "max_call.delta('gbm')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### American Minimum Put on 2 Assets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The third derivative instrument is an **American minimum put on two risk factors**." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "sv = stochastic_volatility('sv_obj', me_sv)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "me_min_put = market_environment('min_put', dt.datetime(2015, 1, 1))\n", "me_min_put.add_constant('maturity', dt.datetime(2015, 6, 17))\n", "me_min_put.add_constant('currency', 'EUR')\n", "me_min_put.add_environment(val_env)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "payoff_put = \"np.maximum(32. - np.minimum(instrument_values['jd'], instrument_values['sv']), 0)\"" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[['jd', 'sv', -0.75]]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "assets = {'jd' : me_jd, 'sv' : me_sv}\n", "asset_corr = [correlations[1]]\n", "asset_corr" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "min_put = valuation_mcs_american_multi(\n", " 'min_put', val_env=me_min_put, risk_factors=assets,\n", " correlations=asset_corr, payoff_func=payoff_put)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.296" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "min_put.present_value(fixed_seed=True)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.0981" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "min_put.delta('jd')" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-0.2102" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "min_put.delta('sv')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Portfolio" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compose a derivatives portfolio, `derivatives_position` objects are needed." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "am_put_pos = derivatives_position(\n", " name='am_put_pos',\n", " quantity=2,\n", " underlyings=['gbm'],\n", " mar_env=me_put,\n", " otype='American single',\n", " payoff_func='np.maximum(instrument_values - 36., 0)')" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "max_call_pos = derivatives_position(\n", " 'max_call_pos', 3, ['gbm', 'jd'],\n", " me_max_call, 'European multi',\n", " payoff_call)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "min_put_pos = derivatives_position(\n", " 'min_put_pos', 5, ['sv', 'jd'],\n", " me_min_put, 'American multi',\n", " payoff_put)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These objects are to be collected in `dictionary` objects." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "positions = {'am_put_pos' : am_put_pos, 'max_call_pos' : max_call_pos,\n", " 'min_put_pos' : min_put_pos}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All is together to instantiate the `derivatives_portfolio` class." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "port = derivatives_portfolio(name='portfolio',\n", " positions=positions,\n", " val_env=val_env,\n", " risk_factors=risk_factors,\n", " correlations=correlations)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us have a look at the major **portfolio statistics**." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Totals\n", " pos_value 51.769\n", "dtype: float64\n", "CPU times: user 1.42 s, sys: 124 ms, total: 1.55 s\n", "Wall time: 1.48 s\n" ] }, { "data": { "text/html": [ "
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positionnamequantityotyperisk_factsvaluecurrencypos_valuepos_deltapos_vega
0am_put_posam_put_pos2American single[gbm]3.182EUR6.3641.218430.5422
1max_call_posmax_call_pos3European multi[gbm, jd]8.165EUR24.495{'gbm': 0.8646, 'jd': 2.2662}{'gbm': 14.9805, 'jd': 10.35}
2min_put_posmin_put_pos5American multi[sv, jd]4.182EUR20.910{'sv': -1.1675, 'jd': -0.6225}{'sv': 8.322, 'jd': 11.352}
\n", "
" ], "text/plain": [ " position name quantity otype risk_facts value \\\n", "0 am_put_pos am_put_pos 2 American single [gbm] 3.182 \n", "1 max_call_pos max_call_pos 3 European multi [gbm, jd] 8.165 \n", "2 min_put_pos min_put_pos 5 American multi [sv, jd] 4.182 \n", "\n", " currency pos_value pos_delta \\\n", "0 EUR 6.364 1.2184 \n", "1 EUR 24.495 {'gbm': 0.8646, 'jd': 2.2662} \n", "2 EUR 20.910 {'sv': -1.1675, 'jd': -0.6225} \n", "\n", " pos_vega \n", "0 30.5422 \n", "1 {'gbm': 14.9805, 'jd': 10.35} \n", "2 {'sv': 8.322, 'jd': 11.352} " ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%time stats = port.get_statistics()\n", "stats" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "51.769000000000005" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats['pos_value'].sum()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, a graphical look at **two selected, simulated paths** of the stochastic volatility risk factor and the jump diffusion risk factor, respectively." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [ "path_no = 1\n", "paths1 = port.underlying_objects['sv'].get_instrument_values()[:, path_no]\n", "paths2 = port.underlying_objects['jd'].get_instrument_values()[:, path_no]" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([36. , 36.34884124, 34.9130166 , 36.31001777, 34.85894675,\n", " 35.63213975, 39.0707393 , 44.35899961, 44.47413556, 43.13168786,\n", " 47.48647475, 46.27393881, 43.49655379, 47.23009583, 49.53908109,\n", " 43.71731937, 51.76008829, 52.58524036, 54.2573447 , 51.6460015 ,\n", " 44.28088435, 39.01540236, 32.91109921, 30.24790867, 29.61667412,\n", " 31.76473582, 27.30258542, 28.39127869, 28.23333544, 27.08972766,\n", " 27.32993764, 28.65926992, 26.9785575 , 31.8938528 , 34.58971037,\n", " 32.7699367 , 29.35365969, 28.66856698, 31.14196767, 31.37051847,\n", " 30.10832392, 33.11928276, 34.48108709, 32.97416103, 28.08648082,\n", " 26.52705819, 21.57771857, 20.42912064, 20.99231801, 19.23163105,\n", " 21.37234395, 20.80944619, 20.73301676, 20.79953889, 20.34822548,\n", " 18.69820953])" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "paths1" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([36. , 36.09036184, 37.30618631, 36.53472814, 36.79572901,\n", " 36.66944957, 35.56227649, 33.3644349 , 33.42674479, 34.22659123,\n", " 32.22562864, 33.05209641, 33.82798732, 33.20431052, 33.78753542,\n", " 36.17164509, 33.76072474, 33.00278459, 32.79744011, 33.50195594,\n", " 34.40874205, 34.57037634, 37.00098086, 37.7309694 , 38.32223737,\n", " 38.2477447 , 39.92233666, 39.6591103 , 39.43998269, 39.88306801,\n", " 40.35338195, 40.23418088, 41.48106905, 39.66194269, 39.32622142,\n", " 39.48978055, 40.67396363, 40.76122376, 40.00499204, 39.725126 ,\n", " 40.05448393, 39.06546207, 37.674332 , 38.48264394, 40.86222422,\n", " 41.3749628 , 44.02458974, 45.32751049, 44.704871 , 45.06224883,\n", " 43.38741804, 43.68855748, 44.75023229, 45.4285521 , 45.27511078,\n", " 45.68070094])" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "paths2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The resulting plot illustrates the strong **negative correlation**." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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6OcjIOHbMMGDrVpV337Vw3312mjZN4JJLEund28Fff6k8+KCPadO8sVnNuwjJ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\nAIJHd6Vs4GCCp5y2tbByrf6c/FN6YebmsvmDZURbtIwvkPJyGh3XFec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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "plt.figure(figsize=(10, 6))\n", "plt.plot(port.time_grid, paths1, 'r', label='sv')\n", "plt.plot(port.time_grid, paths2, 'b', label='jd')\n", "plt.gcf().autofmt_xdate()\n", "plt.legend(loc=0); plt.grid(True)\n", "# negatively correlated underlyings" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Copyright, License & Disclaimer**\n", "\n", "© Dr. Yves J. Hilpisch | The Python Quants GmbH\n", "\n", "DX Analytics (the \"dx library\" or \"dx package\") is licensed under the GNU Affero General\n", "Public License version 3 or later (see http://www.gnu.org/licenses/).\n", "\n", "DX Analytics comes with no representations or warranties, to the extent\n", "permitted by applicable law.\n", "\n", "http://tpq.io | [dx@tpq.io](mailto:team@tpq.io) |\n", "http://twitter.com/dyjh\n", "\n", "\"The
\n", "\n", "**Quant Platform** | http://pqp.io\n", "\n", "**Python for Finance Training** | http://training.tpq.io\n", "\n", "**Certificate in Computational Finance** | http://compfinance.tpq.io\n", "\n", "**Derivatives Analytics with Python (Wiley Finance)** |\n", "http://dawp.tpq.io\n", "\n", "**Python for Finance (2nd ed., O'Reilly)** |\n", "http://py4fi.tpq.io" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 1 }