PricingCommodityContract_Quant.ipynb

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        "# Load Libreries\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "from scipy import stats\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.dates as mdates\n",
        "from matplotlib import pyplot\n",
        "from scipy.stats import norm\n",
        "import datetime as dt"
      ]
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      "execution_count": 3,
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        "id": "Ezv6LGE919S8"
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      "source": [
        "# Import data\n",
        "Nat_gas_df = pd.read_csv(\"/content/Nat_Gas.csv\")"
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              "      Dates  Prices\n",
              "0  10/31/20    10.1\n",
              "1  11/30/20    10.3\n",
              "2  12/31/20    11.0\n",
              "3   1/31/21    10.9\n",
              "4   2/28/21    10.9"
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              "variable_name": "Nat_gas_df",
              "summary": "{\n  \"name\": \"Nat_gas_df\",\n  \"rows\": 48,\n  \"fields\": [\n    {\n      \"column\": \"Dates\",\n      \"properties\": {\n        \"dtype\": \"object\",\n        \"min\": \"1/31/21\",\n        \"max\": \"9/30/24\",\n        \"samples\": [\n          \"1/31/23\",\n          \"2/29/24\",\n          \"12/31/22\"\n        ],\n        \"num_unique_values\": 48,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    },\n    {\n      \"column\": \"Prices\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.7578973105463123,\n        \"min\": 9.84,\n        \"max\": 12.8,\n        \"samples\": [\n          11.2,\n          12.1,\n          10.1\n        ],\n        \"num_unique_values\": 25,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
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        "# Convert Month into Datetime\n",
        "Nat_gas_df['Dates']=pd.to_datetime(Nat_gas_df['Dates'])"
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              "       Dates  Prices\n",
              "0 2020-10-31    10.1\n",
              "1 2020-11-30    10.3\n",
              "2 2020-12-31    11.0\n",
              "3 2021-01-31    10.9\n",
              "4 2021-02-28    10.9"
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              "            Prices\n",
              "Dates             \n",
              "2020-10-31   10.10\n",
              "2020-11-30   10.30\n",
              "2020-12-31   11.00\n",
              "2021-01-31   10.90\n",
              "2021-02-28   10.90\n",
              "2021-03-31   10.90\n",
              "2021-04-30   10.40\n",
              "2021-05-31    9.84\n",
              "2021-06-30   10.00\n",
              "2021-07-31   10.10\n",
              "2021-08-31   10.30\n",
              "2021-09-30   10.20\n",
              "2021-10-31   10.10\n",
              "2021-11-30   11.20\n",
              "2021-12-31   11.40\n",
              "2022-01-31   11.50\n",
              "2022-02-28   11.80\n",
              "2022-03-31   11.50"
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              "    <tr>\n",
              "      <th>2022-02-28</th>\n",
              "      <td>11.80</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2022-03-31</th>\n",
              "      <td>11.50</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-5df6643d-3d78-4888-b2d1-0c279536dc41')\"\n",
              "            title=\"Convert this dataframe to an interactive table.\"\n",
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              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "    <script>\n",
              "      const buttonEl =\n",
              "        document.querySelector('#df-5df6643d-3d78-4888-b2d1-0c279536dc41 button.colab-df-convert');\n",
              "      buttonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "      async function convertToInteractive(key) {\n",
              "        const element = document.querySelector('#df-5df6643d-3d78-4888-b2d1-0c279536dc41');\n",
              "        const dataTable =\n",
              "          await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                    [key], {});\n",
              "        if (!dataTable) return;\n",
              "\n",
              "        const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "          '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "          + ' to learn more about interactive tables.';\n",
              "        element.innerHTML = '';\n",
              "        dataTable['output_type'] = 'display_data';\n",
              "        await google.colab.output.renderOutput(dataTable, element);\n",
              "        const docLink = document.createElement('div');\n",
              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-0b4c6f8b-0de5-454c-8ac1-c5ac9bd09ed1\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-0b4c6f8b-0de5-454c-8ac1-c5ac9bd09ed1')\"\n",
              "            title=\"Suggest charts\"\n",
              "            style=\"display:none;\">\n",
              "\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
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              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-0b4c6f8b-0de5-454c-8ac1-c5ac9bd09ed1 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "dataframe",
              "variable_name": "Nat_gas_df",
              "summary": "{\n  \"name\": \"Nat_gas_df\",\n  \"rows\": 48,\n  \"fields\": [\n    {\n      \"column\": \"Prices\",\n      \"properties\": {\n        \"dtype\": \"number\",\n        \"std\": 0.7578973105463123,\n        \"min\": 9.84,\n        \"max\": 12.8,\n        \"samples\": [\n          11.2,\n          12.1,\n          10.1\n        ],\n        \"num_unique_values\": 25,\n        \"semantic_type\": \"\",\n        \"description\": \"\"\n      }\n    }\n  ]\n}"
            }
          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "Nat_gas_df.head(18)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fKZiAj2J19TB",
        "outputId": "f6d955d3-7583-4db4-ea09-7bd47e0fc9bd"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['2021-06-30', '2021-07-31', '2021-08-31']"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "inj_dates = ['2021-06-30','2021-07-31','2021-08-31'] # injection dates\n",
        "inj_dates"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "qx4NLS5w19TC"
      },
      "outputs": [],
      "source": [
        "#Nat_gas_df.loc[T]['Prices'][1]"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w9HnLQSt19TD",
        "outputId": "6bcb6824-c26c-442c-a8ab-fb51d118ef0c"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Dates\n",
              "2021-06-30    10.0\n",
              "2021-07-31    10.1\n",
              "2021-08-31    10.3\n",
              "Name: Prices, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "inj_prices = Nat_gas_df.loc[inj_dates]['Prices'] # Prices at time of injection\n",
        "inj_prices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LZvLfocS19TE",
        "outputId": "a9173e3e-a5d4-4616-e8d6-d1b83ce587de"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['2021-12-31', '2022-01-31', '2022-02-28']"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ],
      "source": [
        "wtdhr_dates = ['2021-12-31','2022-01-31','2022-02-28'] # Withdrawal  dates\n",
        "wtdhr_dates"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-8l5NEZa19TF",
        "outputId": "70fd9b57-e872-483f-aa6e-ce1bb25c06eb"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Dates\n",
              "2021-12-31    11.4\n",
              "2022-01-31    11.5\n",
              "2022-02-28    11.8\n",
              "Name: Prices, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ],
      "source": [
        "wtdhr_prices = Nat_gas_df.loc[wtdhr_dates]['Prices'] # Prices at time of Withdrawal\n",
        "wtdhr_prices"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "bbnUIjUo19TG"
      },
      "outputs": [],
      "source": [
        "# Costs\n",
        "\n",
        "injection_cost = 10000 #$\n",
        "withdrawal_cost = 10000 #$\n",
        "transp_cost = 50000 #$\n",
        "max_inventory = 1500000 #BTU total\n",
        "max_injection_rate_monthly = 500000 #BTU monthly\n",
        "max_withdrawal_rate_monthly = 500000 #BTU monthly\n",
        "storage_cost_monthly = 100000 #$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "npgXHC0y19TH",
        "outputId": "e4660e7f-8e2b-480b-9b0e-680a7c628ef3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "15200000.0"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ],
      "source": [
        "planned_injection = 0\n",
        "\n",
        "for i in range(0,len(inj_prices)):\n",
        "     planned_injection += inj_prices[i]*max_injection_rate_monthly\n",
        "\n",
        "planned_injection"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 14,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vPYjO9vV19TH",
        "outputId": "77a11ed4-ba32-4ab9-acc8-3d66a63eca69"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "17350000.0"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ],
      "source": [
        "planned_Withdrawal = 0\n",
        "\n",
        "for i in range(0,len(wtdhr_prices)):\n",
        "     planned_Withdrawal += wtdhr_prices[i]*max_withdrawal_rate_monthly\n",
        "\n",
        "planned_Withdrawal"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "uRpi9rZu19TI",
        "outputId": "e70ce4dc-dc06-4277-803f-df637054b363"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2150000.0"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ],
      "source": [
        "Margin = planned_Withdrawal - planned_injection\n",
        "Margin"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "28pqy7CF19TI",
        "outputId": "09fc9982-84e6-4d7e-e76e-8edf92a7c8e9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'2021-06-30'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 16
        }
      ],
      "source": [
        "inj_dates[0] # firt injection"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "id": "_2f4HfEJ19TJ",
        "outputId": "5b2fbc4d-d59d-4d97-a279-349a2855cb28"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'2022-02-28'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 17
        }
      ],
      "source": [
        "wtdhr_dates[-1] # last withdrawal"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Zva_H_Hk19TJ",
        "outputId": "32cf909e-5b97-479b-c1e2-82430f39459d"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ],
      "source": [
        "storage_time = len(pd.date_range(start=inj_dates[0], end=wtdhr_dates[-1], freq='M'))\n",
        "storage_time"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 19,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "t91FgupR19TK",
        "outputId": "7c3341fd-89a6-4178-8dee-b86ea92c99ea"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "900000"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ],
      "source": [
        "total_storage_cost = storage_time*storage_cost_monthly\n",
        "total_storage_cost"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "PwGXY8Oz19TL",
        "outputId": "822db5c8-153a-41f4-da51-d62ff9338fb3"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "890000.0"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ],
      "source": [
        "Net_margin = ( Margin - transp_cost*(len(wtdhr_dates)+len(inj_dates)) -\n",
        "                    total_storage_cost -\n",
        "                    injection_cost*len(inj_dates) -\n",
        "                     withdrawal_cost*len(wtdhr_dates) )\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "# Value of the contract\n",
        "Net_margin"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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