From 2c34f7d51bad680e872065dd38d18d02e552823d Mon Sep 17 00:00:00 2001
From: Akshat Sharma <111536616+Akshat111111@users.noreply.github.com>
Date: Mon, 11 Dec 2023 11:35:13 +0530
Subject: [PATCH 1/2] Delete notebooks/models/FINGBMPROCESS_generatePaths.ipynb

---
 .../models/FINGBMPROCESS_generatePaths.ipynb  | 429 ------------------
 1 file changed, 429 deletions(-)
 delete mode 100644 notebooks/models/FINGBMPROCESS_generatePaths.ipynb

diff --git a/notebooks/models/FINGBMPROCESS_generatePaths.ipynb b/notebooks/models/FINGBMPROCESS_generatePaths.ipynb
deleted file mode 100644
index ebd29ba0..00000000
--- a/notebooks/models/FINGBMPROCESS_generatePaths.ipynb
+++ /dev/null
@@ -1,429 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# MODEL GENERATION OF GBM RANDOM PATHS"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "In this notebook I show how you can generate random paths according to a GBM"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "####################################################################\n",
-      "# FINANCEPY BETA Version 0.33 - This build:  11 Nov 2023 at 07:07 #\n",
-      "#     This software is distributed FREE AND WITHOUT ANY WARRANTY   #\n",
-      "#  Report bugs as issues at https://github.com/domokane/FinancePy  #\n",
-      "####################################################################\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "from financepy.models.gbm_process_simulator import *"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "process = FinGBMProcess()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Single Asset"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "We can generate time series for a single asset over time."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "num_paths = 10000\n",
-    "num_time_steps = 2\n",
-    "t = 1.0\n",
-    "mu = 0.03\n",
-    "S=100.0\n",
-    "vol = 0.2\n",
-    "seed = 1912"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "x = get_paths(num_paths,num_time_steps,t,mu,S,vol,seed)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "This can be plotted"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(20000, 3)"
-      ]
-     },
-     "execution_count": 6,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "x.shape"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "The distribution at time zero is peaked at 100.0"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plt.hist(x[:,0], 100);"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "After a year there is a full lognormal distribution"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 640x480 with 1 Axes>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plt.hist(x[:,1], 100);"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Multiple Assets One Time"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "num_assets = 2\n",
-    "num_paths = 10000\n",
-    "num_time_steps = 2\n",
-    "t = 1.0\n",
-    "mus = 0.03 * np.ones(num_assets)\n",
-    "stock_prices = 100.0 * np.ones(num_assets)\n",
-    "volatilities = 0.2 * np.ones(num_assets)\n",
-    "rho = 0.9999\n",
-    "corr_matrix = np.array([[1.0, rho],[rho, 1.0]])\n",
-    "seed = 1912"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "x = get_assets(num_assets, num_paths, t,\n",
-    "                   mus, stock_prices, volatilities,\n",
-    "                   corr_matrix, seed)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(20000, 2)"
-      ]
-     },
-     "execution_count": 11,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "x.shape"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[177.55530639, 178.00024012],\n",
-       "       [ 98.01446156,  98.5703073 ],\n",
-       "       [122.594059  , 122.28616957],\n",
-       "       ...,\n",
-       "       [ 81.19405101,  81.2466739 ],\n",
-       "       [129.68390628, 129.74501396],\n",
-       "       [ 83.74783896,  83.33294683]])"
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "x"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## Multiple Assets and Times"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "num_assets = 2\n",
-    "num_paths = 10000\n",
-    "num_time_steps = 2\n",
-    "t = 1.0\n",
-    "mus = 0.03 * np.ones(num_assets)\n",
-    "stock_prices = 100.0 * np.ones(num_assets)\n",
-    "volatilities = 0.2 * np.ones(num_assets)\n",
-    "rho = 0.3\n",
-    "corr_matrix = np.array([[1.0, rho],[rho, 1.0]])\n",
-    "seed = 1912"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(array([0.03, 0.03]), array([100., 100.]), array([0.2, 0.2]))"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "mus, stock_prices, volatilities"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[1. , 0.3],\n",
-       "       [0.3, 1. ]])"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "corr_matrix"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "x = get_paths_assets(num_assets, num_paths, num_time_steps, t,\n",
-    "                   mus, stock_prices, volatilities,\n",
-    "                   corr_matrix, seed)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(20000, 3, 2)"
-      ]
-     },
-     "execution_count": 17,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "x.shape"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[[100.        , 100.        ],\n",
-       "        [ 98.38791532, 130.76293912],\n",
-       "        [113.39649611, 121.56624422]],\n",
-       "\n",
-       "       [[100.        , 100.        ],\n",
-       "        [122.73085817, 103.85874482],\n",
-       "        [ 94.80993213,  91.09672743]],\n",
-       "\n",
-       "       [[100.        , 100.        ],\n",
-       "        [ 92.99294116, 104.15982172],\n",
-       "        [101.33438841, 103.86885503]],\n",
-       "\n",
-       "       ...,\n",
-       "\n",
-       "       [[100.        , 100.        ],\n",
-       "        [ 84.43564014, 112.01112396],\n",
-       "        [ 80.53857693, 135.91115838]],\n",
-       "\n",
-       "       [[100.        , 100.        ],\n",
-       "        [110.01676438, 115.42047693],\n",
-       "        [115.22905479,  99.58218223]],\n",
-       "\n",
-       "       [[100.        , 100.        ],\n",
-       "        [116.01756008,  95.42216717],\n",
-       "        [114.06612186, 122.72885293]]])"
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "x"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "Copyright (c) 2019, Dominic O'Kane "
-   ]
-  }
- ],
- "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": "3.10.13"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}

From 4f9bef9e6dcb858440cdc095eb0a1ad7ad4c47b6 Mon Sep 17 00:00:00 2001
From: Akshat Sharma <111536616+Akshat111111@users.noreply.github.com>
Date: Mon, 11 Dec 2023 11:36:09 +0530
Subject: [PATCH 2/2] Add files via upload

---
 .../FINGBMPROCESS_generatePaths (2).ipynb     | 600 ++++++++++++++++++
 1 file changed, 600 insertions(+)
 create mode 100644 notebooks/models/FINGBMPROCESS_generatePaths (2).ipynb

diff --git a/notebooks/models/FINGBMPROCESS_generatePaths (2).ipynb b/notebooks/models/FINGBMPROCESS_generatePaths (2).ipynb
new file mode 100644
index 00000000..e12b645e
--- /dev/null
+++ b/notebooks/models/FINGBMPROCESS_generatePaths (2).ipynb	
@@ -0,0 +1,600 @@
+{
+  "nbformat": 4,
+  "nbformat_minor": 0,
+  "metadata": {
+    "colab": {
+      "provenance": []
+    },
+    "kernelspec": {
+      "name": "python3",
+      "display_name": "Python 3"
+    },
+    "language_info": {
+      "name": "python"
+    }
+  },
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# MODEL GENERATION OF GBM RANDOM PATHS\n",
+        "In this notebook I show how you can generate random paths according to a GBM"
+      ],
+      "metadata": {
+        "id": "ZfG37OKQdnda"
+      }
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "id": "gsfqtPCS_LEC"
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\n",
+        "import matplotlib.pyplot as plt"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "pip install financepy"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "urTtO08m_Ncm",
+        "outputId": "cf70ed1a-0191-4531-fd67-99f19c8d0603"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "Collecting financepy\n",
+            "  Downloading financepy-0.310-py3-none-any.whl (628 kB)\n",
+            "\u001b[?25l     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m0.0/628.6 kB\u001b[0m \u001b[31m?\u001b[0m eta \u001b[36m-:--:--\u001b[0m\r\u001b[2K     \u001b[91m━━━━━━━━━\u001b[0m\u001b[90m╺\u001b[0m\u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m143.4/628.6 kB\u001b[0m \u001b[31m4.4 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\r\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m628.6/628.6 kB\u001b[0m \u001b[31m9.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25hRequirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (from financepy) (1.23.5)\n",
+            "Requirement already satisfied: numba in /usr/local/lib/python3.10/dist-packages (from financepy) (0.58.1)\n",
+            "Requirement already satisfied: scipy in /usr/local/lib/python3.10/dist-packages (from financepy) (1.11.3)\n",
+            "Requirement already satisfied: llvmlite in /usr/local/lib/python3.10/dist-packages (from financepy) (0.41.1)\n",
+            "Requirement already satisfied: ipython in /usr/local/lib/python3.10/dist-packages (from financepy) (7.34.0)\n",
+            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.10/dist-packages (from financepy) (3.7.1)\n",
+            "Requirement already satisfied: pandas in /usr/local/lib/python3.10/dist-packages (from financepy) (1.5.3)\n",
+            "Requirement already satisfied: prettytable in /usr/local/lib/python3.10/dist-packages (from financepy) (3.9.0)\n",
+            "Requirement already satisfied: setuptools>=18.5 in /usr/local/lib/python3.10/dist-packages (from ipython->financepy) (67.7.2)\n",
+            "Collecting jedi>=0.16 (from ipython->financepy)\n",
+            "  Downloading jedi-0.19.1-py2.py3-none-any.whl (1.6 MB)\n",
+            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.6/1.6 MB\u001b[0m \u001b[31m61.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[?25hRequirement already satisfied: decorator in /usr/local/lib/python3.10/dist-packages (from ipython->financepy) (4.4.2)\n",
+            "Requirement already satisfied: pickleshare in /usr/local/lib/python3.10/dist-packages (from ipython->financepy) (0.7.5)\n",
+            "Requirement already satisfied: traitlets>=4.2 in /usr/local/lib/python3.10/dist-packages (from ipython->financepy) (5.7.1)\n",
+            "Requirement already satisfied: prompt-toolkit!=3.0.0,!=3.0.1,<3.1.0,>=2.0.0 in /usr/local/lib/python3.10/dist-packages (from ipython->financepy) (3.0.41)\n",
+            "Requirement already satisfied: pygments in /usr/local/lib/python3.10/dist-packages (from ipython->financepy) (2.16.1)\n",
+            "Requirement already satisfied: backcall in /usr/local/lib/python3.10/dist-packages (from ipython->financepy) (0.2.0)\n",
+            "Requirement already satisfied: matplotlib-inline in /usr/local/lib/python3.10/dist-packages (from ipython->financepy) (0.1.6)\n",
+            "Requirement already satisfied: pexpect>4.3 in /usr/local/lib/python3.10/dist-packages (from ipython->financepy) (4.8.0)\n",
+            "Requirement already satisfied: contourpy>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib->financepy) (1.2.0)\n",
+            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.10/dist-packages (from matplotlib->financepy) (0.12.1)\n",
+            "Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib->financepy) (4.44.3)\n",
+            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib->financepy) (1.4.5)\n",
+            "Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib->financepy) (23.2)\n",
+            "Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.10/dist-packages (from matplotlib->financepy) (9.4.0)\n",
+            "Requirement already satisfied: pyparsing>=2.3.1 in /usr/local/lib/python3.10/dist-packages (from matplotlib->financepy) (3.1.1)\n",
+            "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.10/dist-packages (from matplotlib->financepy) (2.8.2)\n",
+            "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.10/dist-packages (from pandas->financepy) (2023.3.post1)\n",
+            "Requirement already satisfied: wcwidth in /usr/local/lib/python3.10/dist-packages (from prettytable->financepy) (0.2.10)\n",
+            "Requirement already satisfied: parso<0.9.0,>=0.8.3 in /usr/local/lib/python3.10/dist-packages (from jedi>=0.16->ipython->financepy) (0.8.3)\n",
+            "Requirement already satisfied: ptyprocess>=0.5 in /usr/local/lib/python3.10/dist-packages (from pexpect>4.3->ipython->financepy) (0.7.0)\n",
+            "Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.7->matplotlib->financepy) (1.16.0)\n",
+            "Installing collected packages: jedi, financepy\n",
+            "Successfully installed financepy-0.310 jedi-0.19.1\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "from financepy.models.gbm_process_simulator import *"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "TJc1qkQW_dm-",
+        "outputId": "8ea2f690-c24e-40ff-ed83-b8ef135f53ee"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "####################################################################\n",
+            "# FINANCEPY BETA Version 0.310 - This build:  25 Aug 2023 at 16:17 #\n",
+            "#     This software is distributed FREE AND WITHOUT ANY WARRANTY   #\n",
+            "#  Report bugs as issues at https://github.com/domokane/FinancePy  #\n",
+            "####################################################################\n",
+            "\n"
+          ]
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "process = FinGBMProcess()"
+      ],
+      "metadata": {
+        "id": "ZUOMNLhK_iqB"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Single Asset\n",
+        "We can generate time series for a single asset over time."
+      ],
+      "metadata": {
+        "id": "5DDyJkQp_mkr"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "num_paths = 10000\n",
+        "num_time_steps = 2\n",
+        "t = 1.0\n",
+        "mu = 0.03\n",
+        "S=100.0\n",
+        "vol = 0.2\n",
+        "seed = 1912\n"
+      ],
+      "metadata": {
+        "id": "BEAchrII_qj_"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "x = get_paths(num_paths,num_time_steps,t,mu,S,vol,seed)"
+      ],
+      "metadata": {
+        "id": "S2ap4QVK_wol"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "This can be plotted"
+      ],
+      "metadata": {
+        "id": "Bt_CP_APeDDg"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "x.shape"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "loEtojyt_0k7",
+        "outputId": "51bec9a5-76fa-49d5-f9bf-611543f17257"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(20000, 3)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 8
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "The distribution at time zero is peaked at 100.0"
+      ],
+      "metadata": {
+        "id": "lx-W9yGfeI9c"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "plt.hist(x[:,0], 100);"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 430
+        },
+        "id": "0tvFRim6_2DS",
+        "outputId": "ded0d4a2-7fe9-4ba6-dc92-bd4d96e575ef"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 640x480 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {}
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "After a year there is a full lognormal distribution"
+      ],
+      "metadata": {
+        "id": "Nyt1vVUJ_9rf"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "plt.hist(x[:,1], 100);"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 430
+        },
+        "id": "n1Le4DW-_95E",
+        "outputId": "a472ef45-9b50-4889-bbc4-2298a028b5fa"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 640x480 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {}
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Multiple Assets One Time"
+      ],
+      "metadata": {
+        "id": "XULMMo9lAM_-"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "num_assets = 2\n",
+        "num_paths = 10000\n",
+        "num_time_steps = 2\n",
+        "t = 1.0\n",
+        "mus = 0.03 * np.ones(num_assets)\n",
+        "stock_prices = 100.0 * np.ones(num_assets)\n",
+        "volatilities = 0.2 * np.ones(num_assets)\n",
+        "rho = 0.9999\n",
+        "corr_matrix = np.array([[1.0, rho],[rho, 1.0]])\n",
+        "seed = 1912\n",
+        "\n",
+        "x = get_assets(num_assets, num_paths, t,\n",
+        "                   mus, stock_prices, volatilities,\n",
+        "                   corr_matrix, seed)"
+      ],
+      "metadata": {
+        "id": "x-p2F4EUAPMJ"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "x.shape"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "qx_lsnDnAdWJ",
+        "outputId": "13694ddc-5258-4c88-9796-3362e5fbdf47"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(20000, 2)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 12
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "x"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "mVk3rfxiAhGQ",
+        "outputId": "f2dcd9d7-f438-4793-a598-47706a40b4a7"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[177.55530639, 178.00024012],\n",
+              "       [ 98.01446156,  98.5703073 ],\n",
+              "       [122.594059  , 122.28616957],\n",
+              "       ...,\n",
+              "       [ 81.19405101,  81.2466739 ],\n",
+              "       [129.68390628, 129.74501396],\n",
+              "       [ 83.74783896,  83.33294683]])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 13
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "plt.hist(x[:,1], 100);"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 430
+        },
+        "id": "PKX84noEAkBT",
+        "outputId": "f283e0eb-65ed-4e18-e96a-bdf4dc178a76"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 640x480 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {}
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "# Multiple Assets and Times"
+      ],
+      "metadata": {
+        "id": "vhw5QBDFAu8M"
+      }
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "num_assets = 2\n",
+        "num_paths = 10000\n",
+        "num_time_steps = 2\n",
+        "t = 1.0\n",
+        "mus = 0.03 * np.ones(num_assets)\n",
+        "stock_prices = 100.0 * np.ones(num_assets)\n",
+        "volatilities = 0.2 * np.ones(num_assets)\n",
+        "rho = 0.3\n",
+        "corr_matrix = np.array([[1.0, rho],[rho, 1.0]])\n",
+        "seed = 1912\n",
+        "\n",
+        "mus, stock_prices, volatilities"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "2PyyrnhpAxpf",
+        "outputId": "07e82ec4-8655-4eeb-eaa9-541854c05497"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(array([0.03, 0.03]), array([100., 100.]), array([0.2, 0.2]))"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 15
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "corr_matrix"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "WO9CyIY_A6_H",
+        "outputId": "2b79227f-f4ef-4143-ba3a-5f916bf8f2dc"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[1. , 0.3],\n",
+              "       [0.3, 1. ]])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 16
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "x = get_paths_assets(num_assets, num_paths, num_time_steps, t,\n",
+        "                   mus, stock_prices, volatilities,\n",
+        "                   corr_matrix, seed)"
+      ],
+      "metadata": {
+        "id": "v9suCxxCA8KZ"
+      },
+      "execution_count": null,
+      "outputs": []
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "x.shape"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "xcQV2Wg0A-2A",
+        "outputId": "786404ab-06f9-4661-b95c-3597501fe72e"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "(20000, 3, 2)"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 18
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "x"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        },
+        "id": "irWrRvidBCAq",
+        "outputId": "1ec19942-e95f-4df1-9b9e-45f24048f3e4"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "execute_result",
+          "data": {
+            "text/plain": [
+              "array([[[100.        , 100.        ],\n",
+              "        [ 98.38791532, 130.76293912],\n",
+              "        [113.39649611, 121.56624422]],\n",
+              "\n",
+              "       [[100.        , 100.        ],\n",
+              "        [122.73085817, 103.85874482],\n",
+              "        [ 94.80993213,  91.09672743]],\n",
+              "\n",
+              "       [[100.        , 100.        ],\n",
+              "        [ 92.99294116, 104.15982172],\n",
+              "        [101.33438841, 103.86885503]],\n",
+              "\n",
+              "       ...,\n",
+              "\n",
+              "       [[100.        , 100.        ],\n",
+              "        [ 84.43564014, 112.01112396],\n",
+              "        [ 80.53857693, 135.91115838]],\n",
+              "\n",
+              "       [[100.        , 100.        ],\n",
+              "        [110.01676438, 115.42047693],\n",
+              "        [115.22905479,  99.58218223]],\n",
+              "\n",
+              "       [[100.        , 100.        ],\n",
+              "        [116.01756008,  95.42216717],\n",
+              "        [114.06612186, 122.72885293]]])"
+            ]
+          },
+          "metadata": {},
+          "execution_count": 19
+        }
+      ]
+    },
+    {
+      "cell_type": "code",
+      "source": [
+        "plt.hist(x[:,1], 100);"
+      ],
+      "metadata": {
+        "colab": {
+          "base_uri": "https://localhost:8080/",
+          "height": 430
+        },
+        "id": "D60XzHqTBMET",
+        "outputId": "5d4ba1bc-f921-453c-e499-fccdbe2f95f8"
+      },
+      "execution_count": null,
+      "outputs": [
+        {
+          "output_type": "display_data",
+          "data": {
+            "text/plain": [
+              "<Figure size 640x480 with 1 Axes>"
+            ],
+            "image/png": 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\n"
+          },
+          "metadata": {}
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "source": [
+        "Copyright (c) 2019, Dominic O'Kane"
+      ],
+      "metadata": {
+        "id": "p0d_FHNIeZYU"
+      }
+    }
+  ]
+}
\ No newline at end of file