├── Option Pricing using Qiskit and Eikon Data API (Qiskit Runtime).ipynb
├── Option Pricing using Qiskit and Eikon Data API.ipynb
├── README.md
└── eikon.txt


/Option Pricing using Qiskit and Eikon Data API (Qiskit Runtime).ipynb:
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   1 | {
   2 |  "cells": [
   3 |   {
   4 |    "cell_type": "markdown",
   5 |    "id": "6b5d8ad0",
   6 |    "metadata": {},
   7 |    "source": [
   8 |     "## 1. Importing Packages"
   9 |    ]
  10 |   },
  11 |   {
  12 |    "cell_type": "code",
  13 |    "execution_count": 53,
  14 |    "id": "e36e6572",
  15 |    "metadata": {},
  16 |    "outputs": [
  17 |     {
  18 |      "data": {
  19 |       "text/html": [
  20 |        "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.18.1</td></tr><tr><td><code>qiskit-aer</code></td><td>0.8.2</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.6.0</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.18.3</td></tr><tr><td><code>qiskit-aqua</code></td><td>0.9.4</td></tr><tr><td><code>qiskit-finance</code></td><td>0.2.1</td></tr><tr><td><code>qiskit-optimization</code></td><td>0.2.2</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.8.8 (default, Apr 13 2021, 15:08:03) [MSC v.1916 64 bit (AMD64)]</td></tr><tr><td>OS</td><td>Windows</td></tr><tr><td>CPUs</td><td>4</td></tr><tr><td>Memory (Gb)</td><td>15.687431335449219</td></tr><tr><td colspan='2'>Wed Mar 02 07:51:31 2022 India Standard Time</td></tr></table>"
  21 |       ],
  22 |       "text/plain": [
  23 |        "<IPython.core.display.HTML object>"
  24 |       ]
  25 |      },
  26 |      "metadata": {},
  27 |      "output_type": "display_data"
  28 |     }
  29 |    ],
  30 |    "source": [
  31 |     "import warnings\n",
  32 |     "warnings.filterwarnings(\"ignore\")\n",
  33 |     "import qiskit.tools.jupyter\n",
  34 |     "%qiskit_version_table"
  35 |    ]
  36 |   },
  37 |   {
  38 |    "cell_type": "code",
  39 |    "execution_count": 2,
  40 |    "id": "2290c56d",
  41 |    "metadata": {},
  42 |    "outputs": [
  43 |     {
  44 |      "name": "stdout",
  45 |      "output_type": "stream",
  46 |      "text": [
  47 |       "Eikon version:  1.1.12\n"
  48 |      ]
  49 |     }
  50 |    ],
  51 |    "source": [
  52 |     "import eikon as ek\n",
  53 |     "print(\"Eikon version: \", ek.__version__)"
  54 |    ]
  55 |   },
  56 |   {
  57 |    "cell_type": "code",
  58 |    "execution_count": 54,
  59 |    "id": "23fff7a2",
  60 |    "metadata": {},
  61 |    "outputs": [],
  62 |    "source": [
  63 |     "import numpy as np\n",
  64 |     "import pandas as pd\n",
  65 |     "import datetime\n",
  66 |     "import matplotlib.pyplot as plt\n",
  67 |     "import seaborn as sns \n",
  68 |     "import qiskit\n",
  69 |     "from qiskit import Aer, QuantumCircuit\n",
  70 |     "from qiskit_finance.data_providers._base_data_provider import BaseDataProvider\n",
  71 |     "from qiskit.finance.applications.ising import portfolio\n",
  72 |     "from qiskit.circuit.library import TwoLocal\n",
  73 |     "from qiskit.aqua import QuantumInstance\n",
  74 |     "from qiskit.optimization.applications.ising.common import sample_most_likely\n",
  75 |     "from qiskit.aqua.algorithms import VQE, QAOA, NumPyMinimumEigensolver\n",
  76 |     "from qiskit.aqua.components.optimizers import COBYLA"
  77 |    ]
  78 |   },
  79 |   {
  80 |    "cell_type": "markdown",
  81 |    "id": "accf33ac",
  82 |    "metadata": {},
  83 |    "source": [
  84 |     "#### Setup token to run the experiment on a real device\n",
  85 |     "If you would like to run the experiment on a real device, you need to setup your account first. You can get your api token from [here](https://quantum-computing.ibm.com/)\n",
  86 |     "\n",
  87 |     "Note: If you do not store your token yet, use `IBMQ.save_account('MY_API_TOKEN')` to store it first."
  88 |    ]
  89 |   },
  90 |   {
  91 |    "cell_type": "code",
  92 |    "execution_count": 55,
  93 |    "id": "9741fc18",
  94 |    "metadata": {},
  95 |    "outputs": [],
  96 |    "source": [
  97 |     "from qiskit import IBMQ\n",
  98 |     "IBMQ.save_account('MY_API_TOKEN', overwrite=True)"
  99 |    ]
 100 |   },
 101 |   {
 102 |    "cell_type": "markdown",
 103 |    "id": "2936a100",
 104 |    "metadata": {},
 105 |    "source": [
 106 |     "#### Setup Eikon API\n",
 107 |     "I have saved my Eikon Data API key in a file for security reason and not displaying here in notebook."
 108 |    ]
 109 |   },
 110 |   {
 111 |    "cell_type": "code",
 112 |    "execution_count": 5,
 113 |    "id": "6556b57a",
 114 |    "metadata": {},
 115 |    "outputs": [],
 116 |    "source": [
 117 |     "eikon_key = open(\"eikon.txt\",\"r\")\n",
 118 |     "ek.set_app_key(str(eikon_key.read()))\n",
 119 |     "eikon_key.close()"
 120 |    ]
 121 |   },
 122 |   {
 123 |    "cell_type": "markdown",
 124 |    "id": "56c7c95b",
 125 |    "metadata": {},
 126 |    "source": [
 127 |     "## 2. Getting Data using Eikon API & Pre-Processing"
 128 |    ]
 129 |   },
 130 |   {
 131 |    "cell_type": "markdown",
 132 |    "id": "f1514ac0",
 133 |    "metadata": {},
 134 |    "source": [
 135 |     "#### Defining EikonDataProvider class for Loading Data as needed by Qiskit\n",
 136 |     "We will inherit BaseDataProvider from data provider module of Qiskit Finance to extend it's functionality of getting data from Eikon API in desired format and make use of existing functions."
 137 |    ]
 138 |   },
 139 |   {
 140 |    "cell_type": "code",
 141 |    "execution_count": 6,
 142 |    "id": "b1a2ab6d",
 143 |    "metadata": {},
 144 |    "outputs": [],
 145 |    "source": [
 146 |     "class EikonDataProvider(BaseDataProvider):\n",
 147 |     "    \"\"\"\n",
 148 |     "    The abstract base class for Eikon data_provider.\n",
 149 |     "    \"\"\"\n",
 150 |     "    def __init__(self, stocks_list, start_date, end_date):\n",
 151 |     "        '''\n",
 152 |     "        stocks -> List of interested assets\n",
 153 |     "        start -> start date to fetch historical data\n",
 154 |     "        end -> \n",
 155 |     "        '''\n",
 156 |     "        super().__init__()\n",
 157 |     "        self._stocks = stocks_list\n",
 158 |     "        self._start = start_date\n",
 159 |     "        self._end = end_date\n",
 160 |     "        self._data = []\n",
 161 |     "        self.stock_data = pd.DataFrame()\n",
 162 |     "        \n",
 163 |     "    def run(self):\n",
 164 |     "        self._data = []\n",
 165 |     "        stocks_notfound = []\n",
 166 |     "        stock_data = ek.get_timeseries(self._stocks,\n",
 167 |     "                  start_date=self._start, \n",
 168 |     "                  end_date=self._end, \n",
 169 |     "                  interval='daily',\n",
 170 |     "                  corax='adjusted')\n",
 171 |     "        for ticker in self._stocks:\n",
 172 |     "            stock_value = stock_data['CLOSE']\n",
 173 |     "            self.stock_data[ticker] = stock_data['CLOSE']\n",
 174 |     "            if stock_value.dropna().empty:\n",
 175 |     "                stocks_notfound.append(ticker)\n",
 176 |     "            self._data.append(stock_value)"
 177 |    ]
 178 |   },
 179 |   {
 180 |    "cell_type": "markdown",
 181 |    "id": "7720187f",
 182 |    "metadata": {},
 183 |    "source": [
 184 |     "### Initializing Required Parameters"
 185 |    ]
 186 |   },
 187 |   {
 188 |    "cell_type": "code",
 189 |    "execution_count": 7,
 190 |    "id": "879ed69a",
 191 |    "metadata": {},
 192 |    "outputs": [],
 193 |    "source": [
 194 |     "# List of stocks \n",
 195 |     "stock_list = ['FB.O']\n",
 196 |     "\n",
 197 |     "# Start Date\n",
 198 |     "start_date = datetime.datetime(2020,12,1)\n",
 199 |     "\n",
 200 |     "# End Date\n",
 201 |     "end_date = datetime.datetime(2021,12,1)\n",
 202 |     "\n",
 203 |     "# Set number of equities to the number of stocks\n",
 204 |     "num_assets = len(stock_list)\n",
 205 |     "\n",
 206 |     "# Set the risk factor\n",
 207 |     "risk_factor = 0.7\n",
 208 |     "\n",
 209 |     "# Set budget\n",
 210 |     "budget = 2\n",
 211 |     "\n",
 212 |     "# Scaling of budget penalty term will be dependant on the number of assets\n",
 213 |     "penalty = num_assets"
 214 |    ]
 215 |   },
 216 |   {
 217 |    "cell_type": "markdown",
 218 |    "id": "e8eb3840",
 219 |    "metadata": {},
 220 |    "source": [
 221 |     "### Getting data from Eikon API using EikonDataProvider class"
 222 |    ]
 223 |   },
 224 |   {
 225 |    "cell_type": "code",
 226 |    "execution_count": 8,
 227 |    "id": "cd003963",
 228 |    "metadata": {},
 229 |    "outputs": [],
 230 |    "source": [
 231 |     "data = EikonDataProvider(stocks_list = stock_list, start_date=start_date, end_date=end_date)\n",
 232 |     "data.run()"
 233 |    ]
 234 |   },
 235 |   {
 236 |    "cell_type": "code",
 237 |    "execution_count": 9,
 238 |    "id": "6f69c082",
 239 |    "metadata": {},
 240 |    "outputs": [
 241 |     {
 242 |      "data": {
 243 |       "text/html": [
 244 |        "<div>\n",
 245 |        "<style scoped>\n",
 246 |        "    .dataframe tbody tr th:only-of-type {\n",
 247 |        "        vertical-align: middle;\n",
 248 |        "    }\n",
 249 |        "\n",
 250 |        "    .dataframe tbody tr th {\n",
 251 |        "        vertical-align: top;\n",
 252 |        "    }\n",
 253 |        "\n",
 254 |        "    .dataframe thead th {\n",
 255 |        "        text-align: right;\n",
 256 |        "    }\n",
 257 |        "</style>\n",
 258 |        "<table border=\"1\" class=\"dataframe\">\n",
 259 |        "  <thead>\n",
 260 |        "    <tr style=\"text-align: right;\">\n",
 261 |        "      <th></th>\n",
 262 |        "      <th>FB.O</th>\n",
 263 |        "    </tr>\n",
 264 |        "    <tr>\n",
 265 |        "      <th>Date</th>\n",
 266 |        "      <th></th>\n",
 267 |        "    </tr>\n",
 268 |        "  </thead>\n",
 269 |        "  <tbody>\n",
 270 |        "    <tr>\n",
 271 |        "      <th>2020-12-01</th>\n",
 272 |        "      <td>286.55</td>\n",
 273 |        "    </tr>\n",
 274 |        "    <tr>\n",
 275 |        "      <th>2020-12-02</th>\n",
 276 |        "      <td>287.52</td>\n",
 277 |        "    </tr>\n",
 278 |        "    <tr>\n",
 279 |        "      <th>2020-12-03</th>\n",
 280 |        "      <td>281.85</td>\n",
 281 |        "    </tr>\n",
 282 |        "    <tr>\n",
 283 |        "      <th>2020-12-04</th>\n",
 284 |        "      <td>279.7</td>\n",
 285 |        "    </tr>\n",
 286 |        "    <tr>\n",
 287 |        "      <th>2020-12-07</th>\n",
 288 |        "      <td>285.58</td>\n",
 289 |        "    </tr>\n",
 290 |        "  </tbody>\n",
 291 |        "</table>\n",
 292 |        "</div>"
 293 |       ],
 294 |       "text/plain": [
 295 |        "              FB.O\n",
 296 |        "Date              \n",
 297 |        "2020-12-01  286.55\n",
 298 |        "2020-12-02  287.52\n",
 299 |        "2020-12-03  281.85\n",
 300 |        "2020-12-04   279.7\n",
 301 |        "2020-12-07  285.58"
 302 |       ]
 303 |      },
 304 |      "execution_count": 9,
 305 |      "metadata": {},
 306 |      "output_type": "execute_result"
 307 |     }
 308 |    ],
 309 |    "source": [
 310 |     "# Top 5 rows of data \n",
 311 |     "df = data.stock_data\n",
 312 |     "df.head()"
 313 |    ]
 314 |   },
 315 |   {
 316 |    "cell_type": "code",
 317 |    "execution_count": 10,
 318 |    "id": "b57ce602",
 319 |    "metadata": {},
 320 |    "outputs": [
 321 |     {
 322 |      "data": {
 323 |       "text/html": [
 324 |        "<div>\n",
 325 |        "<style scoped>\n",
 326 |        "    .dataframe tbody tr th:only-of-type {\n",
 327 |        "        vertical-align: middle;\n",
 328 |        "    }\n",
 329 |        "\n",
 330 |        "    .dataframe tbody tr th {\n",
 331 |        "        vertical-align: top;\n",
 332 |        "    }\n",
 333 |        "\n",
 334 |        "    .dataframe thead th {\n",
 335 |        "        text-align: right;\n",
 336 |        "    }\n",
 337 |        "</style>\n",
 338 |        "<table border=\"1\" class=\"dataframe\">\n",
 339 |        "  <thead>\n",
 340 |        "    <tr style=\"text-align: right;\">\n",
 341 |        "      <th></th>\n",
 342 |        "      <th>FB.O</th>\n",
 343 |        "    </tr>\n",
 344 |        "  </thead>\n",
 345 |        "  <tbody>\n",
 346 |        "    <tr>\n",
 347 |        "      <th>count</th>\n",
 348 |        "      <td>253.000000</td>\n",
 349 |        "    </tr>\n",
 350 |        "    <tr>\n",
 351 |        "      <th>mean</th>\n",
 352 |        "      <td>316.401403</td>\n",
 353 |        "    </tr>\n",
 354 |        "    <tr>\n",
 355 |        "      <th>std</th>\n",
 356 |        "      <td>36.680760</td>\n",
 357 |        "    </tr>\n",
 358 |        "    <tr>\n",
 359 |        "      <th>min</th>\n",
 360 |        "      <td>245.640000</td>\n",
 361 |        "    </tr>\n",
 362 |        "    <tr>\n",
 363 |        "      <th>25%</th>\n",
 364 |        "      <td>278.010000</td>\n",
 365 |        "    </tr>\n",
 366 |        "    <tr>\n",
 367 |        "      <th>50%</th>\n",
 368 |        "      <td>324.630000</td>\n",
 369 |        "    </tr>\n",
 370 |        "    <tr>\n",
 371 |        "      <th>75%</th>\n",
 372 |        "      <td>343.180000</td>\n",
 373 |        "    </tr>\n",
 374 |        "    <tr>\n",
 375 |        "      <th>max</th>\n",
 376 |        "      <td>382.180000</td>\n",
 377 |        "    </tr>\n",
 378 |        "  </tbody>\n",
 379 |        "</table>\n",
 380 |        "</div>"
 381 |       ],
 382 |       "text/plain": [
 383 |        "             FB.O\n",
 384 |        "count  253.000000\n",
 385 |        "mean   316.401403\n",
 386 |        "std     36.680760\n",
 387 |        "min    245.640000\n",
 388 |        "25%    278.010000\n",
 389 |        "50%    324.630000\n",
 390 |        "75%    343.180000\n",
 391 |        "max    382.180000"
 392 |       ]
 393 |      },
 394 |      "execution_count": 10,
 395 |      "metadata": {},
 396 |      "output_type": "execute_result"
 397 |     }
 398 |    ],
 399 |    "source": [
 400 |     "df.describe()"
 401 |    ]
 402 |   },
 403 |   {
 404 |    "cell_type": "code",
 405 |    "execution_count": 11,
 406 |    "id": "f6bc70ce",
 407 |    "metadata": {},
 408 |    "outputs": [
 409 |     {
 410 |      "data": {
 411 |       "image/png": 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\n",
 412 |       "text/plain": [
 413 |        "<Figure size 1080x576 with 1 Axes>"
 414 |       ]
 415 |      },
 416 |      "metadata": {
 417 |       "needs_background": "light"
 418 |      },
 419 |      "output_type": "display_data"
 420 |     }
 421 |    ],
 422 |    "source": [
 423 |     "# Closing Price History\n",
 424 |     "fig, ax = plt.subplots(figsize=(15, 8))\n",
 425 |     "ax.plot(df)\n",
 426 |     "plt.title('Close Price History')\n",
 427 |     "plt.xlabel('Date',fontsize =20)\n",
 428 |     "plt.ylabel('Price in USD',fontsize = 20)\n",
 429 |     "ax.legend(df.columns.values)\n",
 430 |     "plt.show()"
 431 |    ]
 432 |   },
 433 |   {
 434 |    "cell_type": "markdown",
 435 |    "id": "2431bf79",
 436 |    "metadata": {},
 437 |    "source": [
 438 |     "For the purposes of this article we are going to direct our attention towards the Qiskit Finance application module by IBM, more specifically we are going to look at the quantum computing approach for pricing European Call options. In the Qiskit tutorial we can look at the gradual construction of a circuit specific for European Call."
 439 |    ]
 440 |   },
 441 |   {
 442 |    "cell_type": "code",
 443 |    "execution_count": 12,
 444 |    "id": "9794b56b",
 445 |    "metadata": {},
 446 |    "outputs": [
 447 |     {
 448 |      "data": {
 449 |       "text/html": [
 450 |        "<div>\n",
 451 |        "<style scoped>\n",
 452 |        "    .dataframe tbody tr th:only-of-type {\n",
 453 |        "        vertical-align: middle;\n",
 454 |        "    }\n",
 455 |        "\n",
 456 |        "    .dataframe tbody tr th {\n",
 457 |        "        vertical-align: top;\n",
 458 |        "    }\n",
 459 |        "\n",
 460 |        "    .dataframe thead th {\n",
 461 |        "        text-align: right;\n",
 462 |        "    }\n",
 463 |        "</style>\n",
 464 |        "<table border=\"1\" class=\"dataframe\">\n",
 465 |        "  <thead>\n",
 466 |        "    <tr style=\"text-align: right;\">\n",
 467 |        "      <th></th>\n",
 468 |        "      <th>FB.O</th>\n",
 469 |        "    </tr>\n",
 470 |        "    <tr>\n",
 471 |        "      <th>Date</th>\n",
 472 |        "      <th></th>\n",
 473 |        "    </tr>\n",
 474 |        "  </thead>\n",
 475 |        "  <tbody>\n",
 476 |        "    <tr>\n",
 477 |        "      <th>2021-11-24</th>\n",
 478 |        "      <td>341.06</td>\n",
 479 |        "    </tr>\n",
 480 |        "    <tr>\n",
 481 |        "      <th>2021-11-26</th>\n",
 482 |        "      <td>333.12</td>\n",
 483 |        "    </tr>\n",
 484 |        "    <tr>\n",
 485 |        "      <th>2021-11-29</th>\n",
 486 |        "      <td>338.03</td>\n",
 487 |        "    </tr>\n",
 488 |        "    <tr>\n",
 489 |        "      <th>2021-11-30</th>\n",
 490 |        "      <td>324.46</td>\n",
 491 |        "    </tr>\n",
 492 |        "    <tr>\n",
 493 |        "      <th>2021-12-01</th>\n",
 494 |        "      <td>310.6</td>\n",
 495 |        "    </tr>\n",
 496 |        "  </tbody>\n",
 497 |        "</table>\n",
 498 |        "</div>"
 499 |       ],
 500 |       "text/plain": [
 501 |        "              FB.O\n",
 502 |        "Date              \n",
 503 |        "2021-11-24  341.06\n",
 504 |        "2021-11-26  333.12\n",
 505 |        "2021-11-29  338.03\n",
 506 |        "2021-11-30  324.46\n",
 507 |        "2021-12-01   310.6"
 508 |       ]
 509 |      },
 510 |      "execution_count": 12,
 511 |      "metadata": {},
 512 |      "output_type": "execute_result"
 513 |     }
 514 |    ],
 515 |    "source": [
 516 |     "df.tail()"
 517 |    ]
 518 |   },
 519 |   {
 520 |    "cell_type": "code",
 521 |    "execution_count": 13,
 522 |    "id": "999df20a",
 523 |    "metadata": {},
 524 |    "outputs": [],
 525 |    "source": [
 526 |     "strike_price = 315   # agreed upon strike price\n",
 527 |     "T = 40 / 253         # 40 days to maturity\n",
 528 |     "\n",
 529 |     "S = 310.6              # initial spot price\n",
 530 |     "# vol = 0.4            # volatility of 40%\n",
 531 |     "vol = df['FB.O'].pct_change().std()\n",
 532 |     "r = 0.05             # annual interest rate of 4%\n",
 533 |     "\n",
 534 |     "# resulting parameters for log-normal distribution\n",
 535 |     "mu = ((r - 0.5 * vol**2) * T + np.log(S))\n",
 536 |     "sigma = vol * np.sqrt(T)\n",
 537 |     "mean = np.exp(mu + sigma**2/2)\n",
 538 |     "variance = (np.exp(sigma**2) - 1) * np.exp(2*mu + sigma**2)\n",
 539 |     "stddev = np.sqrt(variance)\n",
 540 |     "\n",
 541 |     "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n",
 542 |     "low  = np.maximum(0, mean - 3*stddev)\n",
 543 |     "high = mean + 3*stddev"
 544 |    ]
 545 |   },
 546 |   {
 547 |    "cell_type": "code",
 548 |    "execution_count": 14,
 549 |    "id": "868cc1ea",
 550 |    "metadata": {},
 551 |    "outputs": [
 552 |     {
 553 |      "data": {
 554 |       "text/plain": [
 555 |        "306.2211877059792"
 556 |       ]
 557 |      },
 558 |      "execution_count": 14,
 559 |      "metadata": {},
 560 |      "output_type": "execute_result"
 561 |     }
 562 |    ],
 563 |    "source": [
 564 |     "low"
 565 |    ]
 566 |   },
 567 |   {
 568 |    "cell_type": "code",
 569 |    "execution_count": 15,
 570 |    "id": "3f5bf264",
 571 |    "metadata": {},
 572 |    "outputs": [
 573 |     {
 574 |      "data": {
 575 |       "text/plain": [
 576 |        "319.90894524815974"
 577 |       ]
 578 |      },
 579 |      "execution_count": 15,
 580 |      "metadata": {},
 581 |      "output_type": "execute_result"
 582 |     }
 583 |    ],
 584 |    "source": [
 585 |     "high"
 586 |    ]
 587 |   },
 588 |   {
 589 |    "cell_type": "code",
 590 |    "execution_count": 16,
 591 |    "id": "19d514fa",
 592 |    "metadata": {},
 593 |    "outputs": [],
 594 |    "source": [
 595 |     "import numpy as np\n",
 596 |     "from qiskit.algorithms import AmplitudeEstimation\n",
 597 |     "from qiskit_finance.circuit.library import EuropeanCallPricingObjective  # F\n",
 598 |     "from qiskit.circuit.library import LogNormalDistribution, NormalDistribution\n",
 599 |     "from qiskit_finance.applications import EuropeanCallPricing\n",
 600 |     "from qiskit_finance.applications.estimation import EuropeanCallDelta\n",
 601 |     "from qiskit import Aer\n",
 602 |     "from qiskit.algorithms import IterativeAmplitudeEstimation"
 603 |    ]
 604 |   },
 605 |   {
 606 |    "cell_type": "code",
 607 |    "execution_count": 17,
 608 |    "id": "bd68b69f",
 609 |    "metadata": {},
 610 |    "outputs": [
 611 |     {
 612 |      "data": {
 613 |       "text/plain": [
 614 |        "[<IBMQSimulator('ibmq_qasm_simulator') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 615 |        " <IBMQBackend('ibmq_armonk') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 616 |        " <IBMQBackend('ibmq_santiago') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 617 |        " <IBMQBackend('ibmq_bogota') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 618 |        " <IBMQBackend('ibmq_lima') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 619 |        " <IBMQBackend('ibmq_belem') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 620 |        " <IBMQBackend('ibmq_quito') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 621 |        " <IBMQSimulator('simulator_statevector') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 622 |        " <IBMQSimulator('simulator_mps') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 623 |        " <IBMQSimulator('simulator_extended_stabilizer') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 624 |        " <IBMQSimulator('simulator_stabilizer') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
 625 |        " <IBMQBackend('ibmq_manila') from IBMQ(hub='ibm-q', group='open', project='main')>]"
 626 |       ]
 627 |      },
 628 |      "execution_count": 17,
 629 |      "metadata": {},
 630 |      "output_type": "execute_result"
 631 |     }
 632 |    ],
 633 |    "source": [
 634 |     "provider = IBMQ.load_account() \n",
 635 |     "provider.backends()"
 636 |    ]
 637 |   },
 638 |   {
 639 |    "cell_type": "code",
 640 |    "execution_count": 56,
 641 |    "id": "c9f9ccb5",
 642 |    "metadata": {},
 643 |    "outputs": [],
 644 |    "source": [
 645 |     "backend = provider.get_backend(\"ibmq_lima\")\n",
 646 |     "sim = QuantumInstance(backend=backend, shots=1000)"
 647 |    ]
 648 |   },
 649 |   {
 650 |    "cell_type": "markdown",
 651 |    "id": "b4633b14",
 652 |    "metadata": {},
 653 |    "source": [
 654 |     "#### Due to limitation in number of publicly available qubits of IBMQ systems, we will be using 2 qubits to test it on real quantum computer. "
 655 |    ]
 656 |   },
 657 |   {
 658 |    "cell_type": "code",
 659 |    "execution_count": 19,
 660 |    "id": "6b9998fd",
 661 |    "metadata": {},
 662 |    "outputs": [],
 663 |    "source": [
 664 |     "# number of qubits to represent the uncertainty\n",
 665 |     "num_uncertainty_qubits = 2"
 666 |    ]
 667 |   },
 668 |   {
 669 |    "cell_type": "markdown",
 670 |    "id": "9f552acf",
 671 |    "metadata": {},
 672 |    "source": [
 673 |     "## 3. Log Normal Distribution\n",
 674 |     "\n",
 675 |     "### Call Option"
 676 |    ]
 677 |   },
 678 |   {
 679 |    "cell_type": "code",
 680 |    "execution_count": 20,
 681 |    "id": "c5b8ef3e",
 682 |    "metadata": {},
 683 |    "outputs": [],
 684 |    "source": [
 685 |     "distribution = LogNormalDistribution(num_uncertainty_qubits, mu=mu, sigma=sigma**2, bounds=(low, high))"
 686 |    ]
 687 |   },
 688 |   {
 689 |    "cell_type": "code",
 690 |    "execution_count": 21,
 691 |    "id": "0a3fb1c5",
 692 |    "metadata": {},
 693 |    "outputs": [],
 694 |    "source": [
 695 |     "european_call_pricing = EuropeanCallPricing(num_state_qubits=num_uncertainty_qubits,\n",
 696 |     "                                            strike_price=strike_price,\n",
 697 |     "                                            rescaling_factor=0.25,  # approximation constant for payoff function\n",
 698 |     "                                            bounds=(low, high),\n",
 699 |     "                                            uncertainty_model=distribution)"
 700 |    ]
 701 |   },
 702 |   {
 703 |    "cell_type": "code",
 704 |    "execution_count": 22,
 705 |    "id": "d838b580",
 706 |    "metadata": {},
 707 |    "outputs": [],
 708 |    "source": [
 709 |     "problem = european_call_pricing.to_estimation_problem()"
 710 |    ]
 711 |   },
 712 |   {
 713 |    "cell_type": "code",
 714 |    "execution_count": 23,
 715 |    "id": "f5790232",
 716 |    "metadata": {},
 717 |    "outputs": [
 718 |     {
 719 |      "data": {
 720 |       "image/png": 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\n",
 721 |       "text/plain": [
 722 |        "<Figure size 206.997x325.08 with 1 Axes>"
 723 |       ]
 724 |      },
 725 |      "metadata": {},
 726 |      "output_type": "display_data"
 727 |     }
 728 |    ],
 729 |    "source": [
 730 |     "problem.state_preparation.draw('mpl', style='iqx')\n",
 731 |     "plt.show()"
 732 |    ]
 733 |   },
 734 |   {
 735 |    "cell_type": "markdown",
 736 |    "id": "4767d59d",
 737 |    "metadata": {},
 738 |    "source": [
 739 |     "In this diagram, we see implementation of the Log-normal distribution on the first layer and Linear Amplitude Estimation function on the second layer. In both European call and European put implementations a central algorithm is Iterative Amplitude Estimation. Crucially, this implementation does not rely on Quantum Phase Estimation, instead it bases only on select Grover iterations. Essentially, we are interested in the probability of measuring ∣1⟩ in the last qubit."
 740 |    ]
 741 |   },
 742 |   {
 743 |    "cell_type": "code",
 744 |    "execution_count": 24,
 745 |    "id": "25281eee",
 746 |    "metadata": {},
 747 |    "outputs": [],
 748 |    "source": [
 749 |     "epsilon = 0.01  # determines final accuracy\n",
 750 |     "alpha = 0.05  # determines how certain we are of the result\n",
 751 |     "\n",
 752 |     "ae = IterativeAmplitudeEstimation(epsilon, alpha=alpha, quantum_instance=sim)"
 753 |    ]
 754 |   },
 755 |   {
 756 |    "cell_type": "code",
 757 |    "execution_count": 57,
 758 |    "id": "ccc01f92",
 759 |    "metadata": {},
 760 |    "outputs": [],
 761 |    "source": [
 762 |     "result = ae.estimate(problem)"
 763 |    ]
 764 |   },
 765 |   {
 766 |    "cell_type": "code",
 767 |    "execution_count": 26,
 768 |    "id": "40315560",
 769 |    "metadata": {},
 770 |    "outputs": [
 771 |     {
 772 |      "name": "stdout",
 773 |      "output_type": "stream",
 774 |      "text": [
 775 |       "Esimated value: \t2.5420\n",
 776 |       "Confidence interval: \t[2.4652, 2.6188]\n"
 777 |      ]
 778 |     }
 779 |    ],
 780 |    "source": [
 781 |     "conf_int_result = np.array(result.confidence_interval_processed)\n",
 782 |     "print(\"Esimated value: \\t%.4f\" % european_call_pricing.interpret(result))\n",
 783 |     "print(\"Confidence interval: \\t[%.4f, %.4f]\" % tuple(conf_int_result))"
 784 |    ]
 785 |   },
 786 |   {
 787 |    "cell_type": "code",
 788 |    "execution_count": 49,
 789 |    "id": "d2481ffb",
 790 |    "metadata": {},
 791 |    "outputs": [
 792 |     {
 793 |      "data": {
 794 |       "image/png": 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\n",
 795 |       "text/plain": [
 796 |        "<Figure size 432x288 with 1 Axes>"
 797 |       ]
 798 |      },
 799 |      "metadata": {
 800 |       "needs_background": "light"
 801 |      },
 802 |      "output_type": "display_data"
 803 |     }
 804 |    ],
 805 |    "source": [
 806 |     "x = distribution.values\n",
 807 |     "y = distribution.probabilities\n",
 808 |     "plt.figure(figsize=(6,4))\n",
 809 |     "plt.bar(x, y, width=2)\n",
 810 |     "plt.xticks(x, size=12, rotation=45)\n",
 811 |     "plt.yticks(size=12)\n",
 812 |     "plt.xlabel('Spot Price at Maturity $S_T$ (\\$)', size=15)\n",
 813 |     "plt.ylabel('Probability ($\\%$)', size=15)\n",
 814 |     "plt.show()"
 815 |    ]
 816 |   },
 817 |   {
 818 |    "cell_type": "code",
 819 |    "execution_count": 50,
 820 |    "id": "0c2a2fe8",
 821 |    "metadata": {},
 822 |    "outputs": [
 823 |     {
 824 |      "data": {
 825 |       "image/png": 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\n",
 826 |       "text/plain": [
 827 |        "<Figure size 432x288 with 1 Axes>"
 828 |       ]
 829 |      },
 830 |      "metadata": {
 831 |       "needs_background": "light"
 832 |      },
 833 |      "output_type": "display_data"
 834 |     }
 835 |    ],
 836 |    "source": [
 837 |     "# plot exact payoff function (evaluated on the grid of the uncertainty model)\n",
 838 |     "x = distribution.values\n",
 839 |     "y = np.maximum(0, x - strike_price)\n",
 840 |     "plt.figure(figsize=(6,4))\n",
 841 |     "plt.plot(x, y, \"ro-\")\n",
 842 |     "plt.title(\"Payoff Function\", size=15)\n",
 843 |     "plt.xlabel(\"Spot Price\", size=15)\n",
 844 |     "plt.ylabel(\"Payoff\", size=15)\n",
 845 |     "plt.xticks(x, size=12, rotation=45)\n",
 846 |     "plt.yticks(size=12)\n",
 847 |     "plt.show()"
 848 |    ]
 849 |   },
 850 |   {
 851 |    "cell_type": "code",
 852 |    "execution_count": 29,
 853 |    "id": "d4905eab",
 854 |    "metadata": {},
 855 |    "outputs": [
 856 |     {
 857 |      "name": "stdout",
 858 |      "output_type": "stream",
 859 |      "text": [
 860 |       "exact expected value:\t0.2159\n",
 861 |       "exact delta value:   \t0.4970\n"
 862 |      ]
 863 |     }
 864 |    ],
 865 |    "source": [
 866 |     "# evaluate exact expected value (normalized to the [0, 1] interval)\n",
 867 |     "exact_value = np.dot(distribution.probabilities, y)\n",
 868 |     "exact_delta = sum(distribution.probabilities[x >= strike_price])\n",
 869 |     "print(\"exact expected value:\\t%.4f\" % exact_value)\n",
 870 |     "print(\"exact delta value:   \\t%.4f\" % exact_delta)"
 871 |    ]
 872 |   },
 873 |   {
 874 |    "cell_type": "markdown",
 875 |    "id": "f049f27a",
 876 |    "metadata": {},
 877 |    "source": [
 878 |     "### Evaluate Delta\n",
 879 |     "\n",
 880 |     "The Delta is a bit simpler to evaluate than the expected payoff. Similarly to the expected payoff, we use a comparator circuit and an ancilla qubit to identify the cases. However, since we are only interested in the probability of this condition being true, we can directly use this ancilla qubit as the objective qubit in amplitude estimation without any further approximation."
 881 |    ]
 882 |   },
 883 |   {
 884 |    "cell_type": "code",
 885 |    "execution_count": 30,
 886 |    "id": "3dc75abf",
 887 |    "metadata": {},
 888 |    "outputs": [],
 889 |    "source": [
 890 |     "european_call_delta = EuropeanCallDelta(\n",
 891 |     "    num_state_qubits=num_uncertainty_qubits,\n",
 892 |     "    strike_price=strike_price,\n",
 893 |     "    bounds=(low, high),\n",
 894 |     "    uncertainty_model=distribution,\n",
 895 |     ")"
 896 |    ]
 897 |   },
 898 |   {
 899 |    "cell_type": "code",
 900 |    "execution_count": 31,
 901 |    "id": "369d9b9c",
 902 |    "metadata": {},
 903 |    "outputs": [
 904 |     {
 905 |      "data": {
 906 |       "image/png": 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\n",
 907 |       "text/plain": [
 908 |        "<Figure size 186.314x264.88 with 1 Axes>"
 909 |       ]
 910 |      },
 911 |      "metadata": {},
 912 |      "output_type": "display_data"
 913 |     }
 914 |    ],
 915 |    "source": [
 916 |     "european_call_delta._objective.decompose().draw('mpl', style='iqx')\n",
 917 |     "plt.show()"
 918 |    ]
 919 |   },
 920 |   {
 921 |    "cell_type": "code",
 922 |    "execution_count": 32,
 923 |    "id": "66498857",
 924 |    "metadata": {},
 925 |    "outputs": [
 926 |     {
 927 |      "data": {
 928 |       "image/png": 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\n",
 929 |       "text/plain": [
 930 |        "<Figure size 206.997x264.88 with 1 Axes>"
 931 |       ]
 932 |      },
 933 |      "metadata": {},
 934 |      "output_type": "display_data"
 935 |     }
 936 |    ],
 937 |    "source": [
 938 |     "european_call_delta_circ = QuantumCircuit(european_call_delta._objective.num_qubits)\n",
 939 |     "european_call_delta_circ.append(distribution, range(num_uncertainty_qubits))\n",
 940 |     "european_call_delta_circ.append(\n",
 941 |     "    european_call_delta._objective, range(european_call_delta._objective.num_qubits)\n",
 942 |     ")\n",
 943 |     "\n",
 944 |     "european_call_delta_circ.draw('mpl', style='iqx')\n",
 945 |     "plt.show()"
 946 |    ]
 947 |   },
 948 |   {
 949 |    "cell_type": "code",
 950 |    "execution_count": 33,
 951 |    "id": "1c213222",
 952 |    "metadata": {},
 953 |    "outputs": [],
 954 |    "source": [
 955 |     "# set target precision and confidence level\n",
 956 |     "epsilon = 0.01\n",
 957 |     "alpha = 0.05\n",
 958 |     "\n",
 959 |     "problem = european_call_delta.to_estimation_problem()\n",
 960 |     "\n",
 961 |     "# construct amplitude estimation\n",
 962 |     "ae_delta = IterativeAmplitudeEstimation(epsilon, alpha=alpha, quantum_instance=sim)"
 963 |    ]
 964 |   },
 965 |   {
 966 |    "cell_type": "code",
 967 |    "execution_count": 34,
 968 |    "id": "47bdf592",
 969 |    "metadata": {},
 970 |    "outputs": [],
 971 |    "source": [
 972 |     "result_delta = ae_delta.estimate(problem)"
 973 |    ]
 974 |   },
 975 |   {
 976 |    "cell_type": "code",
 977 |    "execution_count": 35,
 978 |    "id": "12001519",
 979 |    "metadata": {},
 980 |    "outputs": [
 981 |     {
 982 |      "name": "stdout",
 983 |      "output_type": "stream",
 984 |      "text": [
 985 |       "Exact delta:    \t0.4970\n",
 986 |       "Esimated value: \t0.5023\n",
 987 |       "Confidence interval: \t[0.4976, 0.5071]\n"
 988 |      ]
 989 |     }
 990 |    ],
 991 |    "source": [
 992 |     "conf_int = np.array(result_delta.confidence_interval_processed)\n",
 993 |     "print(\"Exact delta:    \\t%.4f\" % exact_delta)\n",
 994 |     "print(\"Esimated value: \\t%.4f\" % european_call_delta.interpret(result_delta))\n",
 995 |     "print(\"Confidence interval: \\t[%.4f, %.4f]\" % tuple(conf_int))"
 996 |    ]
 997 |   }
 998 |  ],
 999 |  "metadata": {
1000 |   "kernelspec": {
1001 |    "display_name": "Python 3 (ipykernel)",
1002 |    "language": "python",
1003 |    "name": "python3"
1004 |   },
1005 |   "language_info": {
1006 |    "codemirror_mode": {
1007 |     "name": "ipython",
1008 |     "version": 3
1009 |    },
1010 |    "file_extension": ".py",
1011 |    "mimetype": "text/x-python",
1012 |    "name": "python",
1013 |    "nbconvert_exporter": "python",
1014 |    "pygments_lexer": "ipython3",
1015 |    "version": "3.8.8"
1016 |   }
1017 |  },
1018 |  "nbformat": 4,
1019 |  "nbformat_minor": 5
1020 | }
1021 | 


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/README.md:
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1 | # [Option Pricing using Qiskit and Eikon Data API](https://developers.refinitiv.com/en/article-catalog/article/option-pricing-using-qiskit-and-eikon-data-api)
2 | 
3 | In the previous article, we talked about applications of Quantum computing in Finance and saw how it can be used in Portfolio Optimization. In this article, we introduce options as financial instruments. We are going to propose the prevailing quantum approach in pricing European Options.
4 | 
5 | 
6 | 


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/eikon.txt:
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1 | Paste Eikon Data API Key here
2 | 


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