Pairs_trading_v5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "84fd97b8-26ea-40fd-8a2a-aa13fd538e86",
   "metadata": {},
   "source": [
    "# Pairs Trading Strategy\n",
    "\n",
    "Pairs trading is a classic example of a strategy based on mathematical analysis. The principle is as follows. Let's say you have a pair of securities X and Y that have some underlying economic link. An example might be two companies that manufacture the same product, or two companies in one supply chain. If we can model this economic link with a mathematical model, we can make trades on it. We'll start by constructing a toy example.\n",
    "\n",
    "Useful link: \n",
    "https://github.com/quantopian/research_public/blob/master/notebooks/lectures/Introduction_to_Pairs_Trading/notebook.ipynb\n",
    "https://github.com/quantopian/research_public/blob/master/notebooks/lectures/Integration_Cointegration_and_Stationarity/notebook.ipynb"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e517633-73f3-4f02-85da-231899e33590",
   "metadata": {},
   "source": [
    "## **** Utils Functions ****\n",
    "#### *Run this cell before the others, do not modify unless for specific needs*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e65c3460-67ac-41a6-a74b-e4dfb5f48fd0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: qstrader in c:\\users\\lucac\\anaconda3\\lib\\site-packages (0.2.7)\n",
      "Requirement already satisfied: seaborn>=0.13 in c:\\users\\lucac\\anaconda3\\lib\\site-packages (from qstrader) (0.13.2)\n",
      "Requirement already satisfied: matplotlib>=3.8 in c:\\users\\lucac\\anaconda3\\lib\\site-packages (from qstrader) (3.8.4)\n",
      "Requirement already satisfied: numpy>=1.26 in c:\\users\\lucac\\anaconda3\\lib\\site-packages (from qstrader) (1.26.4)\n",
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      "Requirement already satisfied: six>=1.5 in c:\\users\\lucac\\anaconda3\\lib\\site-packages (from python-dateutil>=2.7->matplotlib>=3.8->qstrader) (1.16.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install qstrader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "40d0230b-5727-4172-8843-bf45d0d75592",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: ib_insync in c:\\users\\lucac\\anaconda3\\lib\\site-packages (0.9.86)\n",
      "Requirement already satisfied: nest-asyncio in c:\\users\\lucac\\anaconda3\\lib\\site-packages (from ib_insync) (1.5.6)\n",
      "Requirement already satisfied: eventkit in c:\\users\\lucac\\anaconda3\\lib\\site-packages (from ib_insync) (1.0.3)\n",
      "Requirement already satisfied: numpy in c:\\users\\lucac\\anaconda3\\lib\\site-packages (from eventkit->ib_insync) (1.26.4)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install ib_insync"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "92e776e8-dcb8-4c74-a5ab-174a6b53e6f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import yfinance as yf\n",
    "import pandas as pd\n",
    "from statsmodels.tsa.stattools import coint\n",
    "import statsmodels\n",
    "import statsmodels.api as sm\n",
    "from statsmodels.regression.linear_model import OLS\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "from statsmodels.tsa.stattools import coint, adfuller\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize\n",
    "from datetime import datetime, timedelta\n",
    "import itertools\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80c471b7-3056-48b9-bce0-3814a7c3ca8c",
   "metadata": {},
   "source": [
    "## **** Asset Pairs and Data ****\n",
    "To conduct our analysis, we are using minute-by-minute price data from January 1, 2024, to May 31, 2024."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "059c2b18-f60a-4e22-b214-aefe122ea34a",
   "metadata": {},
   "outputs": [],
   "source": [
    "pairs = [\n",
    "    ('USDJPY=X', '^N225'),  # USD/JPY and Nikkei 225\n",
    "    ('USDCAD=X', 'CL=F'),   # USD/CAD and Crude Oil Futures\n",
    "    ('CL=F', 'USO'),        # Crude Oil Futures and United States Oil Fund\n",
    "    ('GC=F', 'SI=F'),       # Gold Futures and Silver Futures\n",
    "    ('AUDJPY=X', '^GSPC'),  # AUD/JPY and S&P 500\n",
    "    ('USDCHF=X', 'GC=F'),   # USD/CHF and Gold Futures\n",
    "    ('C', 'GS'),            # Citigroup and Goldman Sachs\n",
    "    ('AAPL', 'META')        # Apple and Meta Platforms (formerly Facebook)\n",
    "]\n",
    "\n",
    "# Define the start and end dates for downloading data\n",
    "start_date = '2024-01-01'\n",
    "end_date = '2024-05-31'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b54ea1ef-b48d-485a-9db3-97d21f128422",
   "metadata": {},
   "source": [
    "## **** Choosing Cointegrated Assets with ADF and CADF Tests ****\n",
    "Before implementing the strategy, it is crucial to select assets that exhibit\n",
    "cointegration with one another. To achieve this, we utilize two models: the\n",
    "Augmented Dickey-Fuller (ADF) test and the Cointegrated Augmented Dickey-\n",
    "Fuller (CADF) test, as detailed below:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52a2906c-0cc0-4a91-991b-60b0a405d746",
   "metadata": {},
   "source": [
    "### ADF test:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99bc70f7-2049-4252-8c78-53646e182249",
   "metadata": {},
   "source": [
    "The Augmented Dickey-Fuller (ADF) test is a statistical tool used to assess the stationarity of a time series. Stationarity is a key concept in time series analysis, indicating whether the statistical properties of the series, such as mean and variance, remain constant over time. Non-stationary series can display trends or seasonal patterns, potentially influencing the results of various time series models and analyses. We are conducting the ADF test on each asset to evaluate its stationarity, which is crucial for further analysis, including cointegration testing and the development of robust trading strategies. In this section, we will verify if each asset is non-stationary individually, as the concept of cointegration applies only to non-stationary time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "796e2b10-2090-4b5e-8046-a1c266d6cc9e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n",
      "GS Test Statistic: -0.462, p-value: 0.899206. Critical Values: 1%: -3.439, 5%: -2.866, 10%: -2.569. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "AAPL Test Statistic: -1.260, p-value: 0.647475. Critical Values: 1%: -3.440, 5%: -2.866, 10%: -2.569. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "^GSPC Test Statistic: -1.842, p-value: 0.359589. Critical Values: 1%: -3.440, 5%: -2.866, 10%: -2.569. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "AUDJPY=X Test Statistic: -0.416, p-value: 0.907395. Critical Values: 1%: -3.433, 5%: -2.863, 10%: -2.567. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "C Test Statistic: -1.463, p-value: 0.551565. Critical Values: 1%: -3.439, 5%: -2.866, 10%: -2.569. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "USO Test Statistic: -1.929, p-value: 0.318476. Critical Values: 1%: -3.439, 5%: -2.866, 10%: -2.569. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "^N225 Test Statistic: -3.128, p-value: 0.024542. Critical Values: 1%: -3.441, 5%: -2.866, 10%: -2.569. The series is likely stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "USDJPY=X Test Statistic: -2.013, p-value: 0.280793. Critical Values: 1%: -3.433, 5%: -2.863, 10%: -2.567. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "GC=F Test Statistic: -0.450, p-value: 0.901496. Critical Values: 1%: -3.433, 5%: -2.863, 10%: -2.567. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "META Test Statistic: -2.445, p-value: 0.129547. Critical Values: 1%: -3.439, 5%: -2.866, 10%: -2.569. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "CL=F Test Statistic: -2.011, p-value: 0.281958. Critical Values: 1%: -3.433, 5%: -2.863, 10%: -2.567. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "USDCHF=X Test Statistic: -2.229, p-value: 0.195737. Critical Values: 1%: -3.433, 5%: -2.863, 10%: -2.567. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "USDCAD=X Test Statistic: -2.658, p-value: 0.081676. Critical Values: 1%: -3.433, 5%: -2.863, 10%: -2.567. The series is likely non-stationary.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "SI=F Test Statistic: 0.055, p-value: 0.962844. Critical Values: 1%: -3.433, 5%: -2.863, 10%: -2.567. The series is likely non-stationary.\n"
     ]
    }
   ],
   "source": [
    "# Function to perform the ADF test and print the results\n",
    "def adf_test(series, name):\n",
    "    series = series.dropna()\n",
    "    result = adfuller(series)\n",
    "    test_statistic = f'{result[0]:.3f}'\n",
    "    p_value = f'{result[1]:.6f}'  # Display p-value with higher precision\n",
    "    critical_values_str = ', '.join([f'{key}: {value:.3f}' for key, value in result[4].items()])\n",
    "\n",
    "    # Determine if the series is stationary\n",
    "    status = 'stationary' if result[1] < 0.05 else 'non-stationary'\n",
    "\n",
    "    # Print the result\n",
    "    print(f'{name} Test Statistic: {test_statistic}, p-value: {p_value}. Critical Values: {critical_values_str}. The series is likely {status}.')\n",
    "\n",
    "# Extract unique tickers from pairs\n",
    "unique_tickers = set(ticker for pair in pairs for ticker in pair)\n",
    "\n",
    "# Loop through each ticker and perform the ADF test\n",
    "for ticker in unique_tickers:\n",
    "    data = yf.download(ticker, start=start_date, end=end_date, interval='1h')['Adj Close']\n",
    "    adf_test(data, ticker)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd0fbadd-fb51-46fa-b91c-e16c21f05497",
   "metadata": {},
   "source": [
    "### CADF test:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8ef8637-effb-4010-8c82-440cb975da90",
   "metadata": {},
   "source": [
    "The Cointegrated Augmented Dickey-Fuller (CADF) test is a statistical method used to determine whether two or more time series are cointegrated, implying a long-term equilibrium relationship despite being non-stationary on their own. In time series analysis, identifying cointegration is crucial because it allows for the modeling of long-term relationships between non-stationary series that share a common stochastic drift. We are conducting the CADF test on each pair of assets to assess their cointegration, which is fundamental for further analysis, such as developing pairs trading strategies. In this section, we will verify if each pair of assets is cointegrated, as cointegration analysis applies specifically to non-stationary time series that move together over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "44c79a90-91b7-4e47-b3db-03061a4324bc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "======================================================\n",
      "Critical Values: 1%: -4.012, 5%: -3.399, 10%: -3.088\n",
      "======================================================\n",
      "USDJPY=X & ^N225 Test Statistic: -0.781, p-value: 0.937120. The series are likely not cointegrated.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "USDCAD=X & CL=F Test Statistic: -2.649, p-value: 0.218499. The series are likely not cointegrated.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "CL=F & USO Test Statistic: -1.067, p-value: 0.889417. The series are likely not cointegrated.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "GC=F & SI=F Test Statistic: -0.726, p-value: 0.943716. The series are likely not cointegrated.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "AUDJPY=X & ^GSPC Test Statistic: -0.619, p-value: 0.954711. The series are likely not cointegrated.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "USDCHF=X & GC=F Test Statistic: -3.895, p-value: 0.010068. The series are likely cointegrated.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "C & GS Test Statistic: -2.004, p-value: 0.526714. The series are likely not cointegrated.\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "AAPL & META Test Statistic: -1.736, p-value: 0.660073. The series are likely not cointegrated.\n"
     ]
    }
   ],
   "source": [
    "# Function to perform the CADF test and print the results\n",
    "def cadf_test(series1, series2, name1, name2):\n",
    "    series1 = series1.dropna()\n",
    "    series2 = series2.dropna()\n",
    "\n",
    "    # Ensure both series have the same length\n",
    "    if len(series1) != len(series2):\n",
    "        min_len = min(len(series1), len(series2))\n",
    "        series1 = series1[-min_len:]\n",
    "        series2 = series2[-min_len:]\n",
    "\n",
    "    score, p_value, critical_values = coint(series1, series2)\n",
    "    test_statistic = f'{score:.3f}'\n",
    "    p_value_formatted = f'{p_value:.6f}'\n",
    "\n",
    "    critical_values_str = ', '.join([f'{key}: {value:.3f}' for key, value in zip(['1%', '5%', '10%'], critical_values)])\n",
    "\n",
    "    # Print critical values only once at the start\n",
    "    if name1 == pairs[0][0] and name2 == pairs[0][1]:  # Assuming the first pair to print critical values\n",
    "        print('======================================================')\n",
    "        print(f'Critical Values: {critical_values_str}')\n",
    "        print('======================================================')\n",
    "\n",
    "    # Determine if the series are cointegrated\n",
    "    status = 'cointegrated' if p_value < 0.05 else 'not cointegrated'\n",
    "\n",
    "    # Print the result in one line\n",
    "    print(f'{name1} & {name2} Test Statistic: {test_statistic}, p-value: {p_value_formatted}. The series are likely {status}.')\n",
    "\n",
    "# Loop through each pair and perform the CADF test\n",
    "for name1, name2 in pairs:\n",
    "    # Download the data for each pair\n",
    "    data1 = yf.download(name1, start=start_date, end=end_date)['Adj Close']\n",
    "    data2 = yf.download(name2, start=start_date, end=end_date)['Adj Close']\n",
    "    cadf_test(data1, data2, name1, name2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8766c0ae-79ac-4cd5-80d9-c33689f51cef",
   "metadata": {},
   "source": [
    "Most of the pairs tested do not show significant evidence of cointegration, with the exception of the USD/CHF and Gold Futures pair, which demonstrates a strong long-term equilibrium relationship. This result is important for the development of trading strategies based on cointegration, as only cointegrated pairs offer opportunities to exploit such stable relationships. Therefore, for most of the pairs analyzed, other trading methodologies may be more appropriate."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98802230-71f4-4dac-a476-ee9c82066145",
   "metadata": {},
   "source": [
    "# **** BACKTESTING ****\n",
    "In this section, we will explore a backtesting using optimal timing strategies for trading a mean-reverting price spread. We'll optimize the positions of the previously identified pairs to ensure the intraday portfolio value aligns closely with an Ornstein-Uhlenbeck (OU) process, using maximum likelihood estimation for the best fit.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7b685bf-b59c-41be-9c82-3f0af491495c",
   "metadata": {},
   "source": [
    "## Steps to Follow\n",
    "\n",
    "1. **Download Data**\n",
    "   - Download minute-level data for USD/CHF and GOLD from IBKR for the entire month of May.\n",
    "\n",
    "2. **Estimate Parameters**\n",
    "   - Estimate the parameters $\\mu$ , $\\theta$, $\\sigma$, $B$, and the optimal exit level $b$ as of May 31, 2024.\n",
    "\n",
    "3. **Conduct Backtesting**\n",
    "   - Conduct backtesting for the remaining days up to the current date to validate the strategy.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "cdce3e1a-ccf5-4db7-994f-9f97ecd1e8f5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error fetching data: strptime() argument 1 must be str, not Timestamp\n",
      "Error fetching data: strptime() argument 1 must be str, not Timestamp\n",
      "Optimized pair ratio B: 0.0744\n",
      "Optimized parameters: mu=0.1789, theta=-172.8241, sigma=0.0819\n",
      "Optimal exit level b: -172.4148\n",
      "Final portfolio value: $10000.00\n"
     ]
    }
   ],
   "source": [
    "import nest_asyncio\n",
    "from ib_insync import *\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy.optimize import minimize\n",
    "from scipy.integrate import quad\n",
    "import datetime as dt\n",
    "import time\n",
    "\n",
    "nest_asyncio.apply()\n",
    "\n",
    "# Connect to IBKR TWS or Gateway\n",
    "ib = IB()\n",
    "ib.connect('127.0.0.1', 7497, clientId=2)\n",
    "\n",
    "# Define the contracts for USD/CHF (Forex) and GC (Gold Futures)\n",
    "usdchf_contract = Forex('USDCHF')\n",
    "gc_contract = Future('GC', '202406', 'COMEX')\n",
    "\n",
    "# Function to fetch historical data\n",
    "def fetch_month_data(contract, start_date='20240501 00:00:00', end_date='20240531 23:59:59', bar_size='1 min'):\n",
    "    df_list = []\n",
    "    current_end_date = end_date\n",
    "\n",
    "    while True:\n",
    "        try:\n",
    "            bars = ib.reqHistoricalData(\n",
    "                contract,\n",
    "                endDateTime=current_end_date,\n",
    "                durationStr='1 D',  # Fetch 1 day of data at a time\n",
    "                barSizeSetting=bar_size,\n",
    "                whatToShow='MIDPOINT' if isinstance(contract, Forex) else 'TRADES',\n",
    "                useRTH=False,\n",
    "                formatDate=1\n",
    "            )\n",
    "            if not bars:\n",
    "                break\n",
    "            df = util.df(bars)\n",
    "            df_list.append(df)\n",
    "            current_end_date = df['date'].iloc[0]\n",
    "            time.sleep(10)\n",
    "            if dt.datetime.strptime(current_end_date, '%Y-%m-%d %H:%M:%S') <= dt.datetime.strptime(start_date, '%Y%m%d %H:%M:%S'):\n",
    "                break\n",
    "        except Exception as e:\n",
    "            print(f\"Error fetching data: {e}\")\n",
    "            break\n",
    "\n",
    "    return pd.concat(df_list) if df_list else None\n",
    "\n",
    "# Fetch data for USD/CHF and Gold\n",
    "usdchf_data = fetch_month_data(usdchf_contract)\n",
    "gc_data = fetch_month_data(gc_contract)\n",
    "\n",
    "# Disconnect from IBKR\n",
    "ib.disconnect()\n",
    "\n",
    "# Save data to CSV\n",
    "usdchf_data.to_csv('usdchf_may_2024_data.csv', index=False)\n",
    "gc_data.to_csv('gc_may_2024_data.csv', index=False)\n",
    "\n",
    "# Load data from CSV files\n",
    "usdchf_data = pd.read_csv('usdchf_may_2024_data.csv')\n",
    "gc_data = pd.read_csv('gc_may_2024_data.csv')\n",
    "\n",
    "# Convert the 'date' column to datetime and set as index\n",
    "usdchf_data['date'] = pd.to_datetime(usdchf_data['date'])\n",
    "gc_data['date'] = pd.to_datetime(gc_data['date'])\n",
    "usdchf_data.set_index('date', inplace=True)\n",
    "gc_data.set_index('date', inplace=True)\n",
    "\n",
    "# Resample to 1-hour intervals\n",
    "usdchf_resampled = usdchf_data.resample('1H').last().dropna()\n",
    "gc_resampled = gc_data.resample('1H').last().dropna()\n",
    "\n",
    "# Merge datasets\n",
    "merged_data = pd.merge(usdchf_resampled, gc_resampled, left_index=True, right_index=True, suffixes=('_usdchf', '_gc'))\n",
    "merged_data.dropna(inplace=True)\n",
    "\n",
    "# Extract price arrays\n",
    "usdchf_prices = merged_data['close_usdchf'].values\n",
    "gc_prices = merged_data['close_gc'].values\n",
    "\n",
    "# Function to construct portfolio\n",
    "def construct_portfolio(usdchf_prices, gc_prices, B):\n",
    "    return usdchf_prices - B * gc_prices\n",
    "\n",
    "# Function to optimize pair ratio\n",
    "def optimize_pair_ratio(usdchf_prices, gc_prices):\n",
    "    def negative_log_likelihood(B):\n",
    "        portfolio_values = construct_portfolio(usdchf_prices, gc_prices, B)\n",
    "        portfolio_values = (portfolio_values - np.mean(portfolio_values)) / np.std(portfolio_values)\n",
    "        _, theta, _ = optimize_ou_parameters(portfolio_values)\n",
    "        return -theta\n",
    "    result = minimize(negative_log_likelihood, 0.0, bounds=[(-2, 2)])\n",
    "    B_opt = result.x[0]\n",
    "    return B_opt\n",
    "\n",
    "# Function to optimize OU parameters\n",
    "def optimize_ou_parameters(portfolio_values):\n",
    "    def ou_log_likelihood(params, X):\n",
    "        mu, theta, sigma = params\n",
    "        n = len(X)\n",
    "        dt = 1\n",
    "        X_diff = np.diff(X)\n",
    "        X_prev = X[:-1]\n",
    "        likelihood = (\n",
    "            -n / 2 * np.log(2 * np.pi * sigma**2 * (1 - np.exp(-2 * mu * dt)) / (2 * mu))\n",
    "            - (X_diff - (theta - X_prev) * (1 - np.exp(-mu * dt)))**2\n",
    "            / (2 * sigma**2 * (1 - np.exp(-2 * mu * dt)) / (2 * mu))\n",
    "        )\n",
    "        return -np.sum(likelihood)\n",
    "    initial_params = [0.1, portfolio_values.mean(), portfolio_values.std()]\n",
    "    bounds = [(1e-6, None), (None, None), (1e-6, None)]\n",
    "    result = minimize(ou_log_likelihood, initial_params, args=(portfolio_values,), bounds=bounds)\n",
    "    return result.x\n",
    "\n",
    "# Function to calculate optimal exit level\n",
    "def calculate_optimal_exit_level(theta, mu, sigma, c=0):\n",
    "    def F(x):\n",
    "        integral_result, _ = quad(\n",
    "            lambda u: (u**(2*mu/sigma**2 - 1)) * np.exp(np.sqrt(2*mu/sigma**2) * (theta - x) * u - u**2 / 2), \n",
    "            0, \n",
    "            np.inf\n",
    "        )\n",
    "        return integral_result\n",
    "    \n",
    "    def F_prime(x):\n",
    "        integral_result, _ = quad(\n",
    "            lambda u: (u**(2*mu/sigma**2 - 2)) * np.exp(np.sqrt(2*mu/sigma**2) * (theta - x) * u - u**2 / 2) \n",
    "            * (np.sqrt(2*mu/sigma**2) * (theta - x) - u), \n",
    "            0, \n",
    "            np.inf\n",
    "        )\n",
    "        return integral_result\n",
    "    \n",
    "    def objective(b):\n",
    "        return np.abs(F(b) - (b - c) * F_prime(b))\n",
    "    \n",
    "    result = minimize(objective, theta, bounds=[(theta - 5 * sigma, theta + 5 * sigma)])\n",
    "    return result.x[0]\n",
    "\n",
    "# Function to calculate signals for optimal exit model\n",
    "def calculate_optimal_exit_signals(portfolio_values, optimal_exit_level, window_size=30):\n",
    "    signals = []\n",
    "    for i in range(window_size, len(portfolio_values)):\n",
    "        current_value = portfolio_values[i]\n",
    "        moving_avg = np.mean(portfolio_values[i - window_size:i])\n",
    "        std_dev = np.std(portfolio_values[i - window_size:i])\n",
    "        if current_value < moving_avg - std_dev:\n",
    "            signals.append(1)\n",
    "        elif current_value > optimal_exit_level:\n",
    "            signals.append(-1)\n",
    "        else:\n",
    "            signals.append(0)\n",
    "    signals = [0] * window_size + signals\n",
    "    return np.array(signals)\n",
    "\n",
    "# Function to simulate trading strategy\n",
    "def simulate_optimal_exit_strategy(portfolio_values, signals, initial_cash=10000):\n",
    "    position = 0\n",
    "    cash = initial_cash\n",
    "    portfolio = []\n",
    "    min_length = min(len(signals), len(portfolio_values))\n",
    "    for i in range(min_length):\n",
    "        signal = signals[i]\n",
    "        current_value = portfolio_values[i]\n",
    "        if signal == 1 and position == 0:\n",
    "            position = 1\n",
    "            cash -= current_value\n",
    "        elif signal == -1 and position == 1:\n",
    "            position = 0\n",
    "            cash += current_value\n",
    "        portfolio_value = cash + (position * current_value)\n",
    "        portfolio.append(portfolio_value)\n",
    "    return np.array(portfolio)\n",
    "\n",
    "# Optimize pair ratio\n",
    "B_opt = optimize_pair_ratio(usdchf_prices, gc_prices)\n",
    "print(f\"Optimized pair ratio B: {B_opt:.4f}\")\n",
    "\n",
    "# Construct the portfolio\n",
    "portfolio_values = construct_portfolio(usdchf_prices, gc_prices, B_opt)\n",
    "\n",
    "# Optimize the OU parameters\n",
    "mu_opt, theta_opt, sigma_opt = optimize_ou_parameters(portfolio_values)\n",
    "print(f\"Optimized parameters: mu={mu_opt:.4f}, theta={theta_opt:.4f}, sigma={sigma_opt:.4f}\")\n",
    "\n",
    "# Calculate the optimal exit level\n",
    "optimal_exit_level = calculate_optimal_exit_level(theta_opt, mu_opt, sigma_opt)\n",
    "print(f\"Optimal exit level b: {optimal_exit_level:.4f}\")\n",
    "\n",
    "# Calculate the optimal exit signals\n",
    "optimal_exit_signals = calculate_optimal_exit_signals(portfolio_values, optimal_exit_level)\n",
    "\n",
    "# Simulate the optimal exit strategy\n",
    "portfolio_simulation = simulate_optimal_exit_strategy(portfolio_values, optimal_exit_signals)\n",
    "\n",
    "# Print the final portfolio value\n",
    "final_value = portfolio_simulation[-1]\n",
    "print(f\"Final portfolio value: ${final_value:.2f}\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae9f1a60-0318-4a5f-89a8-cff3baaf6de7",
   "metadata": {},
   "source": [
    "# **** LIVE TRADING ****"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af2a4967-fcd5-4e28-adb4-4f81089d2e81",
   "metadata": {},
   "source": [
    "## Steps to Follow\n",
    "\n",
    "1. **Download Data**\n",
    "   - Obtain minute-level data for USD/CHF and GOLD from Interactive Brokers (IBKR) for the past 30 days.\n",
    "\n",
    "2. **Estimate Parameters**\n",
    "   - Calculate the parameters $\\mu$, $\\theta$, $\\sigma$, $B$, and the optimal exit level $b$ using the most recent 30 days of data, as of today.\n",
    "\n",
    "3. **Connect to IBKR - real time data**\n",
    "   - Establish a connection to IBKR to access real-time market data.\n",
    "\n",
    "4. **Live trading execution**\n",
    "   - Initiate the trading algorithm to begin executing the strategy with live data.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa6bd77b-02f9-4bce-82e0-96914d4f4763",
   "metadata": {},
   "source": [
    "#### 1. Download Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c3a73b1f-34d4-4a5b-9a92-62f1d7299e4e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "reqHistoricalData: Timeout for Forex('USDCHF', exchange='IDEALPRO')\n",
      "Error 162, reqId 3: Messaggio di errore servizio dati di mercato storici:API historical data query cancelled: 3, contract: Forex('USDCHF', exchange='IDEALPRO')\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No historical data fetched for USD\n",
      "Historical data fetched for GC:\n",
      "                       date    open    high     low   close  volume  average  \\\n",
      "0 2024-05-07 09:30:00-04:00  2326.5  2326.8  2325.7  2326.1   303.0  2326.20   \n",
      "1 2024-05-07 09:31:00-04:00  2326.0  2326.1  2325.1  2325.2   242.0  2325.63   \n",
      "2 2024-05-07 09:32:00-04:00  2325.2  2327.1  2325.1  2326.8   501.0  2326.09   \n",
      "3 2024-05-07 09:33:00-04:00  2326.7  2327.9  2325.6  2327.5  1550.0  2327.04   \n",
      "4 2024-05-07 09:34:00-04:00  2327.3  2327.7  2327.0  2327.0   256.0  2327.33   \n",
      "\n",
      "   barCount  \n",
      "0       195  \n",
      "1       156  \n",
      "2       265  \n",
      "3       689  \n",
      "4       150  \n"
     ]
    }
   ],
   "source": [
    "# Import necessary libraries\n",
    "import nest_asyncio\n",
    "import asyncio\n",
    "from ib_insync import *\n",
    "\n",
    "# Import other useful libraries\n",
    "import pandas as pd\n",
    "\n",
    "# Allow nested event loops (needed for Jupyter Notebooks)\n",
    "nest_asyncio.apply()\n",
    "\n",
    "# Connect to IBKR TWS or Gateway\n",
    "ib = IB()\n",
    "ib.connect('127.0.0.1', 7497, clientId=2)\n",
    "\n",
    "# Define the contract for USD/CHF (Forex)\n",
    "usdchf_contract = Forex('USDCHF')\n",
    "\n",
    "# Define the contract for GC (Gold Futures)\n",
    "gc_contract = Future('GC', '202406', 'COMEX')  # Update '202406' with the relevant expiry date\n",
    "\n",
    "# Function to fetch historical data\n",
    "def fetch_historical_data(contract, duration='30 D', bar_size='1 min'):\n",
    "    \"\"\"Fetch historical data for a given contract.\"\"\"\n",
    "    bars = ib.reqHistoricalData(\n",
    "        contract,\n",
    "        endDateTime='',\n",
    "        durationStr=duration,\n",
    "        barSizeSetting=bar_size,\n",
    "        whatToShow='MIDPOINT' if isinstance(contract, Forex) else 'TRADES',\n",
    "        useRTH=True\n",
    "    )\n",
    "    if bars:\n",
    "        df = util.df(bars)\n",
    "        print(f\"Historical data fetched for {contract.symbol}:\")\n",
    "        print(df.head())\n",
    "        return df\n",
    "    else:\n",
    "        print(f\"No historical data fetched for {contract.symbol}\")\n",
    "        return None\n",
    "\n",
    "# Fetch and display data for USD/CHF\n",
    "usdchf_data = fetch_historical_data(usdchf_contract, duration='30 D', bar_size='1 min')\n",
    "\n",
    "# Fetch and display data for Gold Futures\n",
    "gc_data = fetch_historical_data(gc_contract, duration='30 D', bar_size='1 min')\n",
    "\n",
    "# Disconnect from IBKR\n",
    "ib.disconnect()\n",
    "\n",
    "# Save the data to CSV for further analysis\n",
    "if usdchf_data is not None:\n",
    "    usdchf_data.to_csv('usdchf_data.csv', index=False)\n",
    "if gc_data is not None:\n",
    "    gc_data.to_csv('gc_data.csv', index=False)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "10e0d4f0-7cf9-48b9-a643-f376377b26aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data\n",
    "usdchf_data = pd.read_csv('usdchf_data.csv')\n",
    "gc_data = pd.read_csv('gc_data.csv')\n",
    "\n",
    "# Merge data on datetime\n",
    "usdchf_data['date'] = pd.to_datetime(usdchf_data['date'])\n",
    "gc_data['date'] = pd.to_datetime(gc_data['date'])\n",
    "\n",
    "# Resample to 1-hour bars and merge\n",
    "usdchf_data.set_index('date', inplace=True)\n",
    "gc_data.set_index('date', inplace=True)\n",
    "usdchf_resampled = usdchf_data.resample('1H').last().dropna()\n",
    "gc_resampled = gc_data.resample('1H').last().dropna()\n",
    "\n",
    "# Align the data\n",
    "merged_data = pd.merge(usdchf_resampled, gc_resampled, left_index=True, right_index=True, suffixes=('_usdchf', '_gc'))\n",
    "merged_data.dropna(inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "250b8760-76b9-4417-b587-ea3104f64e93",
   "metadata": {},
   "source": [
    "#### 2. Estimate parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2cdc9fb3-4e00-421a-9a94-caf6677ee654",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Construct the portfolio\n",
    "def construct_portfolio(usdchf_prices, gc_prices, B):\n",
    "    \"\"\"Construct the portfolio value.\"\"\"\n",
    "    return usdchf_prices - B * gc_prices\n",
    "\n",
    "\n",
    "# Define the OU log-likelihood function\n",
    "def ou_log_likelihood(params, X):\n",
    "    mu, theta, sigma = params\n",
    "    n = len(X)\n",
    "    dt = 1  # Assuming data is resampled to hourly\n",
    "    X_diff = np.diff(X)\n",
    "    X_prev = X[:-1]\n",
    "    likelihood = (\n",
    "        -n / 2 * np.log(2 * np.pi * sigma**2 * (1 - np.exp(-2 * mu * dt)) / (2 * mu))\n",
    "        - (X_diff - (theta - X_prev) * (1 - np.exp(-mu * dt)))**2\n",
    "        / (2 * sigma**2 * (1 - np.exp(-2 * mu * dt)) / (2 * mu))\n",
    "    )\n",
    "    return -np.sum(likelihood)\n",
    "\n",
    "# Optimize parameters for OU process\n",
    "def optimize_ou_parameters(portfolio_values):\n",
    "    \"\"\"Optimize the parameters for the OU process.\"\"\"\n",
    "    initial_params = [0.1, portfolio_values.mean(), portfolio_values.std()]\n",
    "    bounds = [(1e-6, None), (None, None), (1e-6, None)]\n",
    "    result = minimize(ou_log_likelihood, initial_params, args=(portfolio_values,), bounds=bounds)\n",
    "    mu_opt, theta_opt, sigma_opt = result.x\n",
    "    print(f\"Optimized parameters: mu={mu_opt:.4f}, theta={theta_opt:.4f}, sigma={sigma_opt:.4f}\")\n",
    "    return mu_opt, theta_opt, sigma_opt\n",
    "\n",
    "# Function to optimize the pair ratio\n",
    "def optimize_pair_ratio(usdchf_prices, gc_prices):\n",
    "    \"\"\"Optimize the pair ratio B.\"\"\"\n",
    "    def negative_log_likelihood(B):\n",
    "        portfolio_values = construct_portfolio(usdchf_prices, gc_prices, B)\n",
    "        portfolio_values = np.array(portfolio_values)\n",
    "        portfolio_values = (portfolio_values - np.mean(portfolio_values)) / np.std(portfolio_values)\n",
    "        _, theta, _ = optimize_ou_parameters(portfolio_values)\n",
    "        return -theta  # We want to maximize mean-reversion (i.e., mean is closer to zero)\n",
    "\n",
    "    result = minimize(negative_log_likelihood, 0.0, bounds=[(-2, 2)])  # Adjust bounds as necessary\n",
    "    B_opt = result.x[0]\n",
    "    print(f\"Optimized pair ratio B: {B_opt:.4f}\")\n",
    "    return B_opt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "3a637bb0-70aa-4715-a6a4-6a35b8eefad4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimized parameters: mu=0.0480, theta=-0.5134, sigma=0.0466\n",
      "Optimized parameters: mu=0.0480, theta=-0.5133, sigma=0.0466\n",
      "Optimized parameters: mu=0.1602, theta=0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1522, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=-0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=-0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=-0.1528, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=-0.1528, sigma=0.0613\n",
      "Optimized parameters: mu=0.1604, theta=-0.1563, sigma=0.0613\n",
      "Optimized parameters: mu=0.1604, theta=-0.1563, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1524, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1524, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=-0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=-0.1527, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=-0.1528, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=-0.1528, sigma=0.0613\n",
      "Optimized parameters: mu=0.1604, theta=-0.1563, sigma=0.0613\n",
      "Optimized parameters: mu=0.1604, theta=-0.1563, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1524, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1524, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1525, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized parameters: mu=0.1602, theta=0.1526, sigma=0.0613\n",
      "Optimized pair ratio B: 0.2553\n",
      "Optimized parameters: mu=0.1602, theta=-590.8839, sigma=0.3190\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.16019019869433226, -590.8838873628364, 0.3189628780197693)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Run the optimization\n",
    "usdchf_prices = merged_data['close_usdchf'].values\n",
    "gc_prices = merged_data['close_gc'].values\n",
    "\n",
    "# Optimize pair ratio\n",
    "B_opt = optimize_pair_ratio(usdchf_prices, gc_prices)\n",
    "\n",
    "# Construct portfolio with optimized pair ratio\n",
    "portfolio_values = construct_portfolio(usdchf_prices, gc_prices, B_opt)\n",
    "\n",
    "# Optimize OU parameters for the constructed portfolio\n",
    "optimize_ou_parameters(portfolio_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6a637965-59b0-4cea-858b-097949afa2ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimized parameters: mu=0.1602, theta=-590.8839, sigma=0.3190\n",
      "Optimal exit level b: -589.2891\n"
     ]
    }
   ],
   "source": [
    "import scipy.integrate as integrate\n",
    "\n",
    "# Function to calculate the optimal exit level\n",
    "def calculate_optimal_exit_level(theta, mu, sigma, c=0):\n",
    "    \"\"\"Calculate the optimal exit level b.\"\"\"\n",
    "    def F(x):\n",
    "        integral_result, _ = integrate.quad(\n",
    "            lambda u: (u**(2*mu/sigma**2 - 1)) * np.exp(np.sqrt(2*mu/sigma**2) * (theta - x) * u - u**2 / 2), \n",
    "            0, \n",
    "            np.inf\n",
    "        )\n",
    "        return integral_result\n",
    "    \n",
    "    def F_prime(x):\n",
    "        integral_result, _ = integrate.quad(\n",
    "            lambda u: (u**(2*mu/sigma**2 - 2)) * np.exp(np.sqrt(2*mu/sigma**2) * (theta - x) * u - u**2 / 2) \n",
    "            * (np.sqrt(2*mu/sigma**2) * (theta - x) - u), \n",
    "            0, \n",
    "            np.inf\n",
    "        )\n",
    "        return integral_result\n",
    "    \n",
    "    def objective(b):\n",
    "        return np.abs(F(b) - (b - c) * F_prime(b))\n",
    "    \n",
    "    result = minimize(objective, theta, bounds=[(theta - 5 * sigma, theta + 5 * sigma)])\n",
    "    b_opt = result.x[0]\n",
    "    print(f\"Optimal exit level b: {b_opt:.4f}\")\n",
    "    return b_opt\n",
    "\n",
    "# Calculate the optimal exit level\n",
    "mu_opt, theta_opt, sigma_opt = optimize_ou_parameters(portfolio_values)\n",
    "optimal_exit_level = calculate_optimal_exit_level(theta_opt, mu_opt, sigma_opt)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7b0a20a-ae78-46cc-a409-86d95701cfae",
   "metadata": {},
   "source": [
    "Now we calclate the optimal exit model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "3047d12e-134b-4da1-928a-f36cc122930f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Function to calculate signals for optimal exit model\n",
    "def calculate_optimal_exit_signals(portfolio_values, optimal_exit_level, window_size=30):\n",
    "    \"\"\"Calculate signals for the optimal exit model.\"\"\"\n",
    "    signals = []\n",
    "    for i in range(window_size, len(portfolio_values)):\n",
    "        current_value = portfolio_values[i]\n",
    "        moving_avg = np.mean(portfolio_values[i - window_size:i])\n",
    "        std_dev = np.std(portfolio_values[i - window_size:i])\n",
    "\n",
    "        # Entry signal: enter when portfolio value is below the lower band\n",
    "        if current_value < moving_avg - std_dev:\n",
    "            signals.append(1)  # Buy signal\n",
    "        # Exit signal: exit when portfolio value is above the optimal exit level\n",
    "        elif current_value > optimal_exit_level:\n",
    "            signals.append(-1)  # Sell signal\n",
    "        else:\n",
    "            signals.append(0)  # Hold\n",
    "\n",
    "    return np.array(signals)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8689f1b7-0937-4ac8-8739-c17bead8e75e",
   "metadata": {},
   "source": [
    "#### 3. Connect to IBKR - real time data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "805ef2a0-39b7-40dd-bbff-9c4e7016c73a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import nest_asyncio\n",
    "from ib_insync import IB, Forex, Future, util\n",
    "import pandas as pd\n",
    "import numpy a\n",
    "from scipy.optimize import minimize\n",
    "import scipy.integrate as integrate\n",
    "import time\n",
    "\n",
    "# Allow nested event loops (needed for Jupyter Notebooks)\n",
    "nest_asyncio.apply()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ecd5a8f-e94d-43d3-a4cd-cca55198772b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to connect to IBKR\n",
    "def connect_ibkr(ib, host='127.0.0.1', port=7497, client_id=2):\n",
    "    \"\"\"Connect to IBKR TWS or Gateway.\"\"\"\n",
    "    if not ib.isConnected():\n",
    "        ib.connect(host, port, clientId=client_id)\n",
    "    else:\n",
    "        print(\"Already connected to IBKR.\")\n",
    "    return ib\n",
    "\n",
    "# Connect to IBKR TWS or Gateway\n",
    "ib = IB()\n",
    "ib = connect_ibkr(ib)\n",
    "\n",
    "# Check connection status\n",
    "if not ib.isConnected():\n",
    "    print(\"Not connected to IBKR. Exiting...\")\n",
    "    exit()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35d93bbe-b8cc-4e32-a0b5-70aeae30083a",
   "metadata": {},
   "source": [
    "Contract definition:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "edb84bf3-a5dc-49fd-89d5-69daba6484ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the contracts\n",
    "usdchf_contract = Forex('USDCHF')\n",
    "gc_contract = Future('GC', '202406', 'COMEX')  # Update '202406' with the relevant expiry date\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "432c736b-5d73-43b1-9d0e-d1886dbf258b",
   "metadata": {},
   "source": [
    "Fetching Real-Time Data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "e8e707ac-d02f-4d98-97d4-6c67be609cb0",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "ename": "ConnectionError",
     "evalue": "Not connected",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mConnectionError\u001b[0m                           Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[39], line 17\u001b[0m\n\u001b[0;32m     14\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m bars\n\u001b[0;32m     16\u001b[0m \u001b[38;5;66;03m# Fetch initial data\u001b[39;00m\n\u001b[1;32m---> 17\u001b[0m usdchf_bars \u001b[38;5;241m=\u001b[39m \u001b[43mfetch_realtime_data\u001b[49m\u001b[43m(\u001b[49m\u001b[43musdchf_contract\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     18\u001b[0m gc_bars \u001b[38;5;241m=\u001b[39m fetch_realtime_data(gc_contract)\n",
      "Cell \u001b[1;32mIn[39], line 4\u001b[0m, in \u001b[0;36mfetch_realtime_data\u001b[1;34m(contract, duration, bar_size)\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mfetch_realtime_data\u001b[39m(contract, duration\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m10 D\u001b[39m\u001b[38;5;124m'\u001b[39m, bar_size\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m1 hour\u001b[39m\u001b[38;5;124m'\u001b[39m):\n\u001b[0;32m      3\u001b[0m     \u001b[38;5;124;03m\"\"\"Fetch real-time data for a given contract.\"\"\"\u001b[39;00m\n\u001b[1;32m----> 4\u001b[0m     bars \u001b[38;5;241m=\u001b[39m \u001b[43mib\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreqHistoricalData\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m      5\u001b[0m \u001b[43m        \u001b[49m\u001b[43mcontract\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      6\u001b[0m \u001b[43m        \u001b[49m\u001b[43mendDateTime\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[0;32m      7\u001b[0m \u001b[43m        \u001b[49m\u001b[43mdurationStr\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mduration\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      8\u001b[0m \u001b[43m        \u001b[49m\u001b[43mbarSizeSetting\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mbar_size\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m      9\u001b[0m \u001b[43m        \u001b[49m\u001b[43mwhatToShow\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mMIDPOINT\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mif\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;28;43misinstance\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mcontract\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mForex\u001b[49m\u001b[43m)\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01melse\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mTRADES\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[0;32m     10\u001b[0m \u001b[43m        \u001b[49m\u001b[43museRTH\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m,\u001b[49m\n\u001b[0;32m     11\u001b[0m \u001b[43m        \u001b[49m\u001b[43mformatDate\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[0;32m     12\u001b[0m \u001b[43m        \u001b[49m\u001b[43mkeepUpToDate\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\n\u001b[0;32m     13\u001b[0m \u001b[43m    \u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m     14\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m bars\n",
      "File \u001b[1;32m~\\anaconda3\\lib\\site-packages\\ib_insync\\ib.py:1070\u001b[0m, in \u001b[0;36mIB.reqHistoricalData\u001b[1;34m(self, contract, endDateTime, durationStr, barSizeSetting, whatToShow, useRTH, formatDate, keepUpToDate, chartOptions, timeout)\u001b[0m\n\u001b[0;32m   1021\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mreqHistoricalData\u001b[39m(\n\u001b[0;32m   1022\u001b[0m         \u001b[38;5;28mself\u001b[39m, contract: Contract,\n\u001b[0;32m   1023\u001b[0m         endDateTime: Union[datetime\u001b[38;5;241m.\u001b[39mdatetime, datetime\u001b[38;5;241m.\u001b[39mdate, \u001b[38;5;28mstr\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m],\n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m   1026\u001b[0m         chartOptions: List[TagValue] \u001b[38;5;241m=\u001b[39m [], timeout: \u001b[38;5;28mfloat\u001b[39m \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m60\u001b[39m) \\\n\u001b[0;32m   1027\u001b[0m         \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m BarDataList:\n\u001b[0;32m   1028\u001b[0m     \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[0;32m   1029\u001b[0m \u001b[38;5;124;03m    Request historical bar data.\u001b[39;00m\n\u001b[0;32m   1030\u001b[0m \n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m   1068\u001b[0m \u001b[38;5;124;03m            indefinitely.\u001b[39;00m\n\u001b[0;32m   1069\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[1;32m-> 1070\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_run\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m   1071\u001b[0m \u001b[43m        \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreqHistoricalDataAsync\u001b[49m\u001b[43m(\u001b[49m\n\u001b[0;32m   1072\u001b[0m \u001b[43m            \u001b[49m\u001b[43mcontract\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mendDateTime\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mdurationStr\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mbarSizeSetting\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwhatToShow\u001b[49m\u001b[43m,\u001b[49m\n\u001b[0;32m   1073\u001b[0m \u001b[43m            \u001b[49m\u001b[43museRTH\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mformatDate\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mkeepUpToDate\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mchartOptions\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtimeout\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[1;32m~\\anaconda3\\lib\\site-packages\\ib_insync\\ib.py:318\u001b[0m, in \u001b[0;36mIB._run\u001b[1;34m(self, *awaitables)\u001b[0m\n\u001b[0;32m    317\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21m_run\u001b[39m(\u001b[38;5;28mself\u001b[39m, \u001b[38;5;241m*\u001b[39mawaitables: Awaitable):\n\u001b[1;32m--> 318\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mutil\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mawaitables\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtimeout\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mRequestTimeout\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[1;32m~\\anaconda3\\lib\\site-packages\\ib_insync\\util.py:341\u001b[0m, in \u001b[0;36mrun\u001b[1;34m(timeout, *awaitables)\u001b[0m\n\u001b[0;32m    339\u001b[0m globalErrorEvent\u001b[38;5;241m.\u001b[39mconnect(onError)\n\u001b[0;32m    340\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m--> 341\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mloop\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun_until_complete\u001b[49m\u001b[43m(\u001b[49m\u001b[43mtask\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m    342\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m asyncio\u001b[38;5;241m.\u001b[39mCancelledError \u001b[38;5;28;01mas\u001b[39;00m e:\n\u001b[0;32m    343\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m globalErrorEvent\u001b[38;5;241m.\u001b[39mvalue() \u001b[38;5;129;01mor\u001b[39;00m e\n",
      "File \u001b[1;32m~\\anaconda3\\lib\\site-packages\\nest_asyncio.py:90\u001b[0m, in \u001b[0;36m_patch_loop.<locals>.run_until_complete\u001b[1;34m(self, future)\u001b[0m\n\u001b[0;32m     87\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m f\u001b[38;5;241m.\u001b[39mdone():\n\u001b[0;32m     88\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mRuntimeError\u001b[39;00m(\n\u001b[0;32m     89\u001b[0m         \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mEvent loop stopped before Future completed.\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m---> 90\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mf\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mresult\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[1;32m~\\anaconda3\\lib\\asyncio\\futures.py:201\u001b[0m, in \u001b[0;36mFuture.result\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    199\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m__log_traceback \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n\u001b[0;32m    200\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_exception \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m--> 201\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_exception\u001b[38;5;241m.\u001b[39mwith_traceback(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_exception_tb)\n\u001b[0;32m    202\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_result\n",
      "File \u001b[1;32m~\\anaconda3\\lib\\asyncio\\tasks.py:232\u001b[0m, in \u001b[0;36mTask.__step\u001b[1;34m(***failed resolving arguments***)\u001b[0m\n\u001b[0;32m    228\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m    229\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m exc \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m    230\u001b[0m         \u001b[38;5;66;03m# We use the `send` method directly, because coroutines\u001b[39;00m\n\u001b[0;32m    231\u001b[0m         \u001b[38;5;66;03m# don't have `__iter__` and `__next__` methods.\u001b[39;00m\n\u001b[1;32m--> 232\u001b[0m         result \u001b[38;5;241m=\u001b[39m \u001b[43mcoro\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msend\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43;01mNone\u001b[39;49;00m\u001b[43m)\u001b[49m\n\u001b[0;32m    233\u001b[0m     \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m    234\u001b[0m         result \u001b[38;5;241m=\u001b[39m coro\u001b[38;5;241m.\u001b[39mthrow(exc)\n",
      "File \u001b[1;32m~\\anaconda3\\lib\\site-packages\\ib_insync\\ib.py:1965\u001b[0m, in \u001b[0;36mIB.reqHistoricalDataAsync\u001b[1;34m(self, contract, endDateTime, durationStr, barSizeSetting, whatToShow, useRTH, formatDate, keepUpToDate, chartOptions, timeout)\u001b[0m\n\u001b[0;32m   1957\u001b[0m \u001b[38;5;28;01masync\u001b[39;00m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mreqHistoricalDataAsync\u001b[39m(\n\u001b[0;32m   1958\u001b[0m         \u001b[38;5;28mself\u001b[39m, contract: Contract,\n\u001b[0;32m   1959\u001b[0m         endDateTime: Union[datetime\u001b[38;5;241m.\u001b[39mdatetime, datetime\u001b[38;5;241m.\u001b[39mdate, \u001b[38;5;28mstr\u001b[39m, \u001b[38;5;28;01mNone\u001b[39;00m],\n\u001b[1;32m   (...)\u001b[0m\n\u001b[0;32m   1963\u001b[0m         chartOptions: List[TagValue] \u001b[38;5;241m=\u001b[39m [], timeout: \u001b[38;5;28mfloat\u001b[39m \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m60\u001b[39m) \\\n\u001b[0;32m   1964\u001b[0m         \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m BarDataList:\n\u001b[1;32m-> 1965\u001b[0m     reqId \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mclient\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mgetReqId\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[0;32m   1966\u001b[0m     bars \u001b[38;5;241m=\u001b[39m BarDataList()\n\u001b[0;32m   1967\u001b[0m     bars\u001b[38;5;241m.\u001b[39mreqId \u001b[38;5;241m=\u001b[39m reqId\n",
      "File \u001b[1;32m~\\anaconda3\\lib\\site-packages\\ib_insync\\client.py:160\u001b[0m, in \u001b[0;36mClient.getReqId\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    158\u001b[0m \u001b[38;5;124;03m\"\"\"Get new request ID.\"\"\"\u001b[39;00m\n\u001b[0;32m    159\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39misReady():\n\u001b[1;32m--> 160\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mConnectionError\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mNot connected\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m    161\u001b[0m newId \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_reqIdSeq\n\u001b[0;32m    162\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_reqIdSeq \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n",
      "\u001b[1;31mConnectionError\u001b[0m: Not connected"
     ]
    }
   ],
   "source": [
    "# Function to fetch real-time data\n",
    "def fetch_realtime_data(contract, duration='10 D', bar_size='1 hour'):\n",
    "    \"\"\"Fetch real-time data for a given contract.\"\"\"\n",
    "    bars = ib.reqHistoricalData(\n",
    "        contract,\n",
    "        endDateTime='',\n",
    "        durationStr=duration,\n",
    "        barSizeSetting=bar_size,\n",
    "        whatToShow='MIDPOINT' if isinstance(contract, Forex) else 'TRADES',\n",
    "        useRTH=True,\n",
    "        formatDate=1,\n",
    "        keepUpToDate=True\n",
    "    )\n",
    "    return bars\n",
    "\n",
    "# Fetch initial data\n",
    "usdchf_bars = fetch_realtime_data(usdchf_contract)\n",
    "gc_bars = fetch_realtime_data(gc_contract)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b967b527-44c8-4bcd-9b9f-4fdb9febdc67",
   "metadata": {},
   "source": [
    "Order Placement:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "41a88a2c-86c1-4c10-ba2e-3318f4fc1b53",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to place order on IBKR\n",
    "def place_order(contract, action, quantity):\n",
    "    \"\"\"Place an order with IBKR.\"\"\"\n",
    "    order = MarketOrder(action, quantity)\n",
    "    trade = ib.placeOrder(contract, order)\n",
    "    return trade\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7166adff-dcf2-4f48-a3ff-19fd3bf361db",
   "metadata": {},
   "source": [
    "#### 4. Live trading execution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a4c587cd-8906-4da4-8533-e457e90c41f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize variables for live trading\n",
    "B_opt = None\n",
    "optimal_exit_level = None\n",
    "current_position = 0  # 0: no position, 1: long position\n",
    "\n",
    "# Function to update portfolio and execute strategy\n",
    "def execute_live_strategy():\n",
    "    global B_opt, optimal_exit_level, current_position\n",
    "\n",
    "    # Update data\n",
    "    usdchf_prices = np.array([bar.close for bar in usdchf_bars])\n",
    "    gc_prices = np.array([bar.close for bar in gc_bars])\n",
    "\n",
    "    if len(usdchf_prices) < 30 or len(gc_prices) < 30:\n",
    "        print(\"Not enough data to compute strategy. Waiting for more data.\")\n",
    "        return\n",
    "\n",
    "    # Optimize pair ratio\n",
    "    B_opt = optimize_pair_ratio(usdchf_prices, gc_prices)\n",
    "\n",
    "    # Construct portfolio\n",
    "    portfolio_values = construct_portfolio(usdchf_prices, gc_prices, B_opt)\n",
    "\n",
    "    # Optimize OU parameters\n",
    "    mu_opt, theta_opt, sigma_opt = optimize_ou_parameters(portfolio_values)\n",
    "\n",
    "    # Calculate optimal exit level\n",
    "    optimal_exit_level = calculate_optimal_exit_level(theta_opt, mu_opt, sigma_opt)\n",
    "\n",
    "    # Generate trading signals\n",
    "    signals = calculate_optimal_exit_signals(portfolio_values, optimal_exit_level)\n",
    "\n",
    "    # Execute trading strategy\n",
    "    last_signal = signals[-1]\n",
    "    if last_signal == 1 and current_position == 0:  # Buy signal and no current position\n",
    "        print(\"Placing buy\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c9a1289-d213-47c8-b409-f1314a61c59c",
   "metadata": {},
   "source": [
    "#### *References *\n",
    "Hull, J.C. (2017) Option, Futures, and Other Derivatives (Pearson), 9th edition\n",
    "\n",
    "Leung T., Xin L. (2015) Optimal Mean Reversion Trading with Transaction Costs and Stop-Loss Exit\n",
    "\n",
    "Lee D., Leung T. (2020) On the E cacy of Optimized Exit Rule for Mean Reversion Trading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5d2348b7-879b-4965-82a2-2949efd8a9ad",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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