Asian Option Pricing (Monte-Carlo & Neural Networks).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9fa0a964-38f0-4384-a70c-142bb66216b4",
   "metadata": {},
   "source": [
    "# Fast price approximator to time dependent derivatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2843f3f3-3e19-4f87-9d50-a94454a90f81",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 2090,
    "lastExecutedAt": 1699390941127,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "import numpy as np\nimport matplotlib.pyplot as plt\nimport pandas as pd\n\nimport tensorflow as tf\nfrom tensorflow import keras\nfrom tensorflow.keras.layers import Dense, Dropout, Activation, LeakyReLU, ELU, ReLU\nfrom tensorflow.keras.optimizers import RMSprop\n\nfrom keras.models import Sequential\n\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score\nfrom sklearn.preprocessing import StandardScaler\n\nimport time"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "from tensorflow.keras.layers import Dense, Dropout, Activation, LeakyReLU, ELU, ReLU\n",
    "from tensorflow.keras.optimizers import RMSprop\n",
    "\n",
    "from keras.models import Sequential\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b581355-4611-46cc-9702-036786d156cd",
   "metadata": {},
   "source": [
    "## Monte-Carlo Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac81fddc-3262-45eb-9c44-749e63bb0d20",
   "metadata": {},
   "source": [
    "Here we create a function to estimate the price of an Arithmetic Asian Call Option.\n",
    "\n",
    "We start by simulating X paths for the underlying asset price under the equivalent martingale measure over 1 year with a daily time step, assuming that there are 22 business days in a month. Hence 22 × 12 = 264 business days in a year.\n",
    "\n",
    "We then calculate the payoff of each simulation and find the price $C_t$ of the option.\n",
    "\n",
    "$$ Payoffs = \\left[ \\frac{1}{n}\\sum_{i=1}^{n}{S_{t_i}} - K \\right]^+ $$\n",
    "\n",
    "$$ C_t = e^{-rt}\\mathbb{E}[Payoffs]$$\n",
    "\n",
    "assuming the underlying price process is GBM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f0a998f3-feea-4a4c-8a1f-3c34b8d941c4",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 53,
    "lastExecutedAt": 1699390941181,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "def generate_option_price(S0, K, r, sigma, maturity, n_paths, rng: np.random._generator.Generator):\n    \"\"\"\n    Function to generate data for asset prices and then calculate payoff and option price\n    \"\"\"\n\n    T = maturity / 264      # Maturity in year (264 days per year)\n    time_step = 1 / maturity\n    \n    logS = np.empty((maturity + 1, n_paths))  # Pre-allocation with an empty array\n    \n    logS[0,:] = np.log(S0)    # Initial log price\n    \n    m = r - .5 * sigma**2     # Expected log return\n    \n    # Geometric Brownian Motion:\n    for i in range(1, maturity + 1):\n        std_innov = rng.standard_normal(n_paths)\n        logS[i, :] = logS[i - 1, :] + m * time_step + sigma * np.sqrt(time_step) * std_innov\n        \n    Simulated_prices = np.exp(logS)\n    \n    # Calulcate payoffs\n    A = np.mean(Simulated_prices[1:,:], axis=0)\n    Payoffs = np.maximum(A - K, 0)\n     \n    # Calculate Asian option price\n    asian_option_price_mc = np.exp(-r * T) * np.mean(Payoffs)\n    \n    return asian_option_price_mc"
   },
   "outputs": [],
   "source": [
    "def generate_option_price(S0, K, r, sigma, maturity, n_paths, rng: np.random._generator.Generator):\n",
    "    \"\"\"\n",
    "    Function to generate data for asset prices and then calculate payoff and option price\n",
    "    \"\"\"\n",
    "\n",
    "    T = maturity / 264      # Maturity in year (264 days per year)\n",
    "    time_step = 1 / maturity\n",
    "    \n",
    "    logS = np.empty((maturity + 1, n_paths))  # Pre-allocation with an empty array\n",
    "    \n",
    "    logS[0,:] = np.log(S0)    # Initial log price\n",
    "    \n",
    "    m = r - .5 * sigma**2     # Expected log return\n",
    "    \n",
    "    # Geometric Brownian Motion:\n",
    "    for i in range(1, maturity + 1):\n",
    "        std_innov = rng.standard_normal(n_paths)\n",
    "        logS[i, :] = logS[i - 1, :] + m * time_step + sigma * np.sqrt(time_step) * std_innov\n",
    "        \n",
    "    Simulated_prices = np.exp(logS)\n",
    "    \n",
    "    # Calulcate payoffs\n",
    "    A = np.mean(Simulated_prices[1:,:], axis=0)\n",
    "    Payoffs = np.maximum(A - K, 0)\n",
    "     \n",
    "    # Calculate Asian option price\n",
    "    asian_option_price_mc = np.exp(-r * T) * np.mean(Payoffs)\n",
    "    \n",
    "    return asian_option_price_mc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5be026eb-d61f-437f-a6db-9c4bf9e0215b",
   "metadata": {},
   "source": [
    "With below codes we randomly generate 15000 values for our parameters, which are: asset prices at time 0, strikes, interest rates, volatilities and days to maturity. The range value for these parameters are set according to _Gan, lirong, Wang, Huamao and Yang, Zhaojun (2020)_. These parameters will play the role of independent variables (X) in our neural network model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4599c3fe-40c5-4bba-97e3-a411adb76a3b",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 48,
    "jupyter": {
     "outputs_hidden": false,
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    },
    "lastExecutedAt": 1699390941229,
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    "lastSuccessfullyExecutedCode": "num_samples = 15000\n\nnp.random.seed(123)\nS0 = np.random.uniform(10, 500, num_samples)  # Initial stock price, from 10 to 500 euros\n\nnp.random.seed(123)\nK = np.random.randint(S0*0.8, S0*1.2, num_samples)  # Strike price, picked among 80% and 120% initial stock price\n\nr_range = np.arange(0.01, 0.031, 0.001)  # Value range for Risk-free rate: 1% to 3%\nsigma_range = np.arange(0.05, 0.901, 0.005)  # Value range for Volatility: 5% to 90%\nmaturity_range = np.arange(22, 793, 22) # Value range for Maturity: 1 month to 3 years, 22 days per month\n\n# Choose randomly 15000 interest rates, volatilities and days to maturity in above value ranges\nnp.random.seed(123)\nr = np.random.choice(r_range, num_samples) \n\nnp.random.seed(123)\nsigma = np.random.choice(sigma_range, num_samples)\n\nnp.random.seed(123)\nmaturity = np.random.choice(maturity_range, num_samples)\n\ndata = {\n        'Initial Stock Prices': S0,\n        'Strikes': K,\n        'Risk-free Rates': r,\n        'Volatility': sigma,\n        'Maturity': maturity\n    }\n\ndf = pd.DataFrame(data)\ndf.head()",
    "outputsMetadata": {
     "0": {
      "height": 194,
      "type": "dataFrame"
     }
    }
   },
   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Initial Stock Prices</th>\n",
       "      <th>Strikes</th>\n",
       "      <th>Risk-free Rates</th>\n",
       "      <th>Volatility</th>\n",
       "      <th>Maturity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>351.269901</td>\n",
       "      <td>390</td>\n",
       "      <td>0.023</td>\n",
       "      <td>0.595</td>\n",
       "      <td>66</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>150.208274</td>\n",
       "      <td>122</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.680</td>\n",
       "      <td>638</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>121.157212</td>\n",
       "      <td>124</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.380</td>\n",
       "      <td>770</td>\n",
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       "      <th>3</th>\n",
       "      <td>280.144237</td>\n",
       "      <td>322</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.540</td>\n",
       "      <td>396</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>362.539795</td>\n",
       "      <td>307</td>\n",
       "      <td>0.027</td>\n",
       "      <td>0.135</td>\n",
       "      <td>440</td>\n",
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      "text/plain": [
       "   Initial Stock Prices  Strikes  Risk-free Rates  Volatility  Maturity\n",
       "0            351.269901      390            0.023       0.595        66\n",
       "1            150.208274      122            0.012       0.680       638\n",
       "2            121.157212      124            0.012       0.380       770\n",
       "3            280.144237      322            0.016       0.540       396\n",
       "4            362.539795      307            0.027       0.135       440"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_samples = 15000\n",
    "\n",
    "np.random.seed(123)\n",
    "S0 = np.random.uniform(10, 500, num_samples)  # Initial stock price, from 10 to 500 euros\n",
    "\n",
    "np.random.seed(123)\n",
    "K = np.random.randint(S0*0.8, S0*1.2, num_samples)  # Strike price, picked among 80% and 120% initial stock price\n",
    "\n",
    "r_range = np.arange(0.01, 0.031, 0.001)  # Value range for Risk-free rate: 1% to 3%\n",
    "sigma_range = np.arange(0.05, 0.901, 0.005)  # Value range for Volatility: 5% to 90%\n",
    "maturity_range = np.arange(22, 793, 22) # Value range for Maturity: 1 month to 3 years, 22 days per month\n",
    "\n",
    "# Choose randomly 15000 interest rates, volatilities and days to maturity in above value ranges\n",
    "np.random.seed(123)\n",
    "r = np.random.choice(r_range, num_samples) \n",
    "\n",
    "np.random.seed(123)\n",
    "sigma = np.random.choice(sigma_range, num_samples)\n",
    "\n",
    "np.random.seed(123)\n",
    "maturity = np.random.choice(maturity_range, num_samples)\n",
    "\n",
    "data = {\n",
    "        'Initial Stock Prices': S0,\n",
    "        'Strikes': K,\n",
    "        'Risk-free Rates': r,\n",
    "        'Volatility': sigma,\n",
    "        'Maturity': maturity\n",
    "    }\n",
    "\n",
    "df = pd.DataFrame(data)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4273e3d-1b72-4c45-a33b-f3fb2c7e150c",
   "metadata": {},
   "source": [
    "Now we start to generate the prices of these Asian options using Monte Carlo method. For each option, we simulate 5000 scenarios and thus get 5000 payoffs. We then calculate the price based on these scenarios and get 1 price for each option. This will be our dependent variable (Y) in the neural network model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "08a351f6-4d76-4d0c-bcb3-d1764592aee7",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 656784,
    "lastExecutedAt": 1699391598013,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "np.random.seed(123)\nrng = np.random.default_rng(seed=123)\nn_paths = 5000\nprices = []\n\nstart_time_MC = time.time() #record time we need to simulate using Monte Carlo method\n\nfor i in range(df.shape[0]):\n    price = generate_option_price(df.iloc[i,0], df.iloc[i,1], df.iloc[i,2], df.iloc[i,3], df.iloc[i,4], n_paths, rng)\n    prices.append(price)\n    \nend_time_MC = time.time()"
   },
   "outputs": [],
   "source": [
    "np.random.seed(123)\n",
    "rng = np.random.default_rng(seed=123)\n",
    "n_paths = 5000\n",
    "prices = []\n",
    "\n",
    "start_time_MC = time.time() #record time we need to simulate using Monte Carlo method\n",
    "\n",
    "for i in range(df.shape[0]):\n",
    "    price = generate_option_price(df.iloc[i,0], df.iloc[i,1], df.iloc[i,2], df.iloc[i,3], df.iloc[i,4], n_paths, rng)\n",
    "    prices.append(price)\n",
    "    \n",
    "end_time_MC = time.time()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0491f4e9-5dd2-4a58-beb5-b904ccb89bae",
   "metadata": {},
   "source": [
    "We assign the independent variables and dependent variable to X and y respectively. We then scale X, and then divide the data into 3 parts: training set, validation set and testing set, with ratio 70/15/15."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "10030814-864f-4392-b12b-f354fadad761",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 44,
    "lastExecutedAt": 1699391598058,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "df['Option Prices'] = prices\nX, y = df[['Initial Stock Prices', 'Strikes', 'Risk-free Rates','Volatility', 'Maturity']], df[['Option Prices']]\n\nscaler = StandardScaler()\nX = scaler.fit_transform(X)\n\nX_train, X_temp, y_train, y_temp = train_test_split(X, y, test_size = 0.3, random_state = 42)\nX_val, X_test, y_val, y_test = train_test_split(X_temp, y_temp, test_size = 0.5, random_state = 42)"
   },
   "outputs": [],
   "source": [
    "df['Option Prices'] = prices\n",
    "X, y = df[['Initial Stock Prices', 'Strikes', 'Risk-free Rates','Volatility', 'Maturity']], df[['Option Prices']]\n",
    "\n",
    "scaler = StandardScaler()\n",
    "X = scaler.fit_transform(X)\n",
    "\n",
    "X_train, X_temp, y_train, y_temp = train_test_split(X, y, test_size = 0.3, random_state = 42)\n",
    "X_val, X_test, y_val, y_test = train_test_split(X_temp, y_temp, test_size = 0.5, random_state = 42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6d5e67d-6883-4c19-b7ec-7d28879d031a",
   "metadata": {},
   "source": [
    "## Building Neural Network"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "30dabbdb-ada1-4214-a919-726e208517f1",
   "metadata": {},
   "source": [
    "The optimal number of hidden layers being 4 is advocated by _Tugce Karatas, Amir Oskoui, Ali Hirsa (2019)_. This paper also proved that sigmoid and tanh are not suited for option pricing. Thus, 4 layers will be our choice for the Neural Networks."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0db1c4c-6f71-44d3-86dd-101ed1f03a0c",
   "metadata": {},
   "source": [
    "Regarding the activation functions, _Gan, lirong, Wang, Huamao and Yang, Zhaojun (2020)_, suggested `LeakyReLU, ELU, ReLU` and `ELU` for Asian options. _Tugce Karatas, Amir Oskoui, Ali Hirsa (2019)_, on the other hand,suggested 4 `LeakyReLU` layers give the best result. But we also want to try a potential candidate for option pricing: `ReLU`, which is similar to the shape of option payoffs. Thus, we will try 3 models and pick out the one with the best result: First model with `LeakyReLU, ELU, ReLU` and `ELU`, second model with 4 `LeakyReLU` layers and the third model with 4 `ReLU` layers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76153565-5c8c-4b0d-8571-c3c3614e1893",
   "metadata": {},
   "source": [
    "For each hidden layer, we add a `Dropout` rate 0.25 to avoid overfitting. The loss function will be Mean Squared Error, a popular metric for model evaluation. At this step, the number of epochs are 10, because we don't want to overfit (epoch too high) or underfit (epoch too low). Optimizer and number of neurons are chosen as suggested in _Gan, lirong, Wang, Huamao and Yang, Zhaojun (2020)_. But to test other possibilities for our model, we will change these 2 parameters later and pick out the best ones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5d91a686-cde2-4c28-a8fe-b4ca6e90c8a4",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 51,
    "jupyter": {
     "outputs_hidden": false,
     "source_hidden": false
    },
    "lastExecutedAt": 1699391598109,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "start_train_NN = time.time() #recording training time using Neural Networks\n\ndef neural_network(neurons, Act_func1, Act_func2, Act_func3, Act_func4, epochs):\n    \"\"\"\n    Function to build a neural network\n    \"\"\"\n    \n    model = Sequential()\n\n    model.add(Dense(neurons, input_dim=X_train.shape[1]))\n    model.add(Act_func1())\n    model.add(Dropout(0.25))\n\n    model.add(Dense(neurons))\n    model.add(Act_func2())\n    model.add(Dropout(0.25))\n\n    model.add(Dense(neurons))\n    model.add(Act_func3())\n    model.add(Dropout(0.25))\n\n    model.add(Dense(neurons))\n    model.add(Act_func4())\n    model.add(Dropout(0.25))\n\n    model.add(Dense(1))\n\n    model.compile(loss='mse',optimizer='rmsprop')\n\n    history = model.fit(X_train, y_train, batch_size=64, epochs=epochs, validation_split=0.1, verbose=0)\n    \n    return model",
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   },
   "outputs": [],
   "source": [
    "start_train_NN = time.time() #recording training time using Neural Networks\n",
    "\n",
    "def neural_network(neurons, Act_func1, Act_func2, Act_func3, Act_func4, epochs):\n",
    "    \"\"\"\n",
    "    Function to build a neural network\n",
    "    \"\"\"\n",
    "    \n",
    "    model = Sequential()\n",
    "\n",
    "    model.add(Dense(neurons, input_dim=X_train.shape[1]))\n",
    "    model.add(Act_func1())\n",
    "    model.add(Dropout(0.25))\n",
    "\n",
    "    model.add(Dense(neurons))\n",
    "    model.add(Act_func2())\n",
    "    model.add(Dropout(0.25))\n",
    "\n",
    "    model.add(Dense(neurons))\n",
    "    model.add(Act_func3())\n",
    "    model.add(Dropout(0.25))\n",
    "\n",
    "    model.add(Dense(neurons))\n",
    "    model.add(Act_func4())\n",
    "    model.add(Dropout(0.25))\n",
    "\n",
    "    model.add(Dense(1))\n",
    "\n",
    "    model.compile(loss='mse',optimizer='rmsprop')\n",
    "\n",
    "    history = model.fit(X_train, y_train, batch_size=64, epochs=epochs, validation_split=0.1, verbose=0)\n",
    "    \n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3a509bb7-d58d-4b8d-acd4-5882a4391071",
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    "executionCancelledAt": null,
    "executionTime": 48,
    "lastExecutedAt": 1699391598157,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "def check_accuracy(y_test,y_pred):\n    \"\"\"\n    Function to produce values for metrics to evaluate models\n    (Mean squared error, Root Mean squared error, Mean absolute error and R-Squared)\n    \"\"\"\n    y_test = np.array(y_test).flatten()\n    y_pred = np.array(y_pred).flatten()\n    mse = mean_squared_error(y_test, y_pred)\n    rmse = np.sqrt(mse)\n    mae = mean_absolute_error(y_test, y_pred)\n    r2 = r2_score(y_test, y_pred)\n    return [mse, rmse, mae, r2]"
   },
   "outputs": [],
   "source": [
    "def check_accuracy(y_test,y_pred):\n",
    "    \"\"\"\n",
    "    Function to produce values for metrics to evaluate models\n",
    "    (Mean squared error, Root Mean squared error, Mean absolute error and R-Squared)\n",
    "    \"\"\"\n",
    "    y_test = np.array(y_test).flatten()\n",
    "    y_pred = np.array(y_pred).flatten()\n",
    "    mse = mean_squared_error(y_test, y_pred)\n",
    "    rmse = np.sqrt(mse)\n",
    "    mae = mean_absolute_error(y_test, y_pred)\n",
    "    r2 = r2_score(y_test, y_pred)\n",
    "    return [mse, rmse, mae, r2]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df122d80-0210-4b45-a938-ff1e758cd003",
   "metadata": {},
   "source": [
    "### Activation Function selection"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e355111-67ee-4912-8534-dbfc115d8a64",
   "metadata": {},
   "source": [
    "Now let's build our three models with aforementioned activation functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4d70ddcb-ec2e-44ec-8d4e-ee634e35a3d3",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 8616,
    "lastExecutedAt": 1699391606773,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "model1 = neural_network(120, LeakyReLU, ELU, ReLU, ELU, 10)\nmodel2 = neural_network(120, LeakyReLU, LeakyReLU, LeakyReLU, LeakyReLU, 10)\nmodel3 = neural_network(120, ReLU, ReLU, ReLU, ReLU, 10)",
    "outputsMetadata": {
     "0": {
      "height": 95,
      "type": "stream"
     }
    }
   },
   "outputs": [],
   "source": [
    "model1 = neural_network(120, LeakyReLU, ELU, ReLU, ELU, 10)\n",
    "model2 = neural_network(120, LeakyReLU, LeakyReLU, LeakyReLU, LeakyReLU, 10)\n",
    "model3 = neural_network(120, ReLU, ReLU, ReLU, ReLU, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "249b3bf7-2bc7-4e14-b096-87316d555be1",
   "metadata": {},
   "source": [
    "Now let's use validation data to choose the best model among above three"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "786a47ae-b54b-465b-8175-966b69e7e436",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 413,
    "lastExecutedAt": 1699391607187,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "y_val_model1 = model1.predict(X_val)\ny_val_model2 = model2.predict(X_val)\ny_val_model3 = model3.predict(X_val)",
    "outputsMetadata": {
     "0": {
      "height": 75,
      "type": "stream"
     }
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step\n"
     ]
    }
   ],
   "source": [
    "y_val_model1 = model1.predict(X_val)\n",
    "y_val_model2 = model2.predict(X_val)\n",
    "y_val_model3 = model3.predict(X_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "985b681f-92dd-4eaf-bf9f-59914003a7db",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 50,
    "lastExecutedAt": 1699391607237,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "y_val_pred = np.concatenate((y_val_model1, y_val_model2, y_val_model3), axis=1)"
   },
   "outputs": [],
   "source": [
    "y_val_pred = np.concatenate((y_val_model1, y_val_model2, y_val_model3), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c10595fa-dfc2-4e63-a403-18fe68b40804",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 53,
    "lastExecutedAt": 1699391607290,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "#Check accuracy among 3 models\ncheck_acc = []\nfor column in range(y_val_pred.shape[1]):\n    accuracy = check_accuracy(y_val, y_val_pred[:, column])\n    check_acc.append(accuracy)\n    \ndf = pd.DataFrame(check_acc, columns = ['MSE', 'RMSE', 'MAE', 'R2'], index = ['Model 1', 'Model 2', 'Model 3'])\ndf",
    "outputsMetadata": {
     "0": {
      "height": 145,
      "type": "dataFrame"
     }
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>MSE</th>\n",
       "      <th>RMSE</th>\n",
       "      <th>MAE</th>\n",
       "      <th>R2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Model 1</th>\n",
       "      <td>9.676030</td>\n",
       "      <td>3.110632</td>\n",
       "      <td>2.185134</td>\n",
       "      <td>0.986805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Model 2</th>\n",
       "      <td>4.663258</td>\n",
       "      <td>2.159458</td>\n",
       "      <td>1.648380</td>\n",
       "      <td>0.993641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Model 3</th>\n",
       "      <td>3.381441</td>\n",
       "      <td>1.838870</td>\n",
       "      <td>1.352239</td>\n",
       "      <td>0.995389</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              MSE      RMSE       MAE        R2\n",
       "Model 1  9.676030  3.110632  2.185134  0.986805\n",
       "Model 2  4.663258  2.159458  1.648380  0.993641\n",
       "Model 3  3.381441  1.838870  1.352239  0.995389"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Check accuracy among 3 models\n",
    "check_acc = []\n",
    "for column in range(y_val_pred.shape[1]):\n",
    "    accuracy = check_accuracy(y_val, y_val_pred[:, column])\n",
    "    check_acc.append(accuracy)\n",
    "    \n",
    "df = pd.DataFrame(check_acc, columns = ['MSE', 'RMSE', 'MAE', 'R2'], index = ['Model 1', 'Model 2', 'Model 3'])\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75779afd-7a38-407e-8cc0-04131abae44e",
   "metadata": {},
   "source": [
    "### Number of Neurons selection"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb1469f3-a354-46e2-8f75-39afb8a9786b",
   "metadata": {},
   "source": [
    "In this step, we will see how many neurons we should use for our model. We will try a value range from 40 to 300 (with the step of 20)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "74be9c7c-95c6-4a1d-82bc-3cdb4052982e",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 49330,
    "jupyter": {
     "outputs_hidden": true,
     "source_hidden": false
    },
    "lastExecutedAt": 1699391656620,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "neuron = np.arange(40,301,20)\nloss = []\nfor i in neuron:\n    model3_epoch = neural_network(i, ReLU, ReLU, ReLU, ReLU, 10)\n    y_val_pre = model3_epoch.predict(X_val)\n    model_val_loss = model3_epoch.evaluate(X_val, y_val)\n    loss.append(model_val_loss)",
    "outputsMetadata": {
     "0": {
      "height": 524,
      "type": "stream"
     }
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 16.5237\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 8.6132\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 4.2925\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 5.7601\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 3.1527\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 16.4426\n",
      "71/71 [==============================] - 0s 3ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 3.6100\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 4.1781\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 9.8267\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 26.3022\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 4.1555\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 3ms/step - loss: 4.2627\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 2ms/step - loss: 5.9330\n",
      "71/71 [==============================] - 0s 2ms/step\n",
      "71/71 [==============================] - 0s 3ms/step - loss: 7.1042\n"
     ]
    }
   ],
   "source": [
    "neuron = np.arange(40,301,20)\n",
    "loss = []\n",
    "for i in neuron:\n",
    "    model3_epoch = neural_network(i, ReLU, ReLU, ReLU, ReLU, 10)\n",
    "    y_val_pre = model3_epoch.predict(X_val)\n",
    "    model_val_loss = model3_epoch.evaluate(X_val, y_val)\n",
    "    loss.append(model_val_loss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "bf461479-6f1f-4227-a2b6-afb7ebb4db7e",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 217,
    "lastExecutedAt": 1699391656837,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "plt.figure(figsize=(10,6))\nplt.plot(neuron, loss, '-')\nplt.title('Validation Loss over 40-300 neurons')\nplt.xlabel('Loss on Validation set')\nplt.ylabel('Number of neurons')\nplt.show()"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10,6))\n",
    "plt.plot(neuron, loss, '-')\n",
    "plt.title('Validation Loss over 40-300 neurons')\n",
    "plt.xlabel('Loss on Validation set')\n",
    "plt.ylabel('Number of neurons')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec865c16-1f0f-4fc9-bdfc-e611ab223d59",
   "metadata": {},
   "source": [
    "### Number of Epochs selection"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6c3940f-c407-40c5-b8dc-b315704b5412",
   "metadata": {},
   "source": [
    "In this step, we will use the chosen activation functions and number of neurons to build a neural network with 500 epochs, and see how many epochs we should use to avoid overfitting and still get a reasonable loss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "11947507-e8ef-4555-8dc0-aa5a50b95515",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 108028,
    "lastExecutedAt": 1699391764865,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "neurons = 120\nmodel = Sequential()\n\nmodel.add(Dense(neurons, input_dim=X_train.shape[1]))\nmodel.add(ReLU())\nmodel.add(Dropout(0.25))\n\nmodel.add(Dense(neurons))\nmodel.add(ReLU())\nmodel.add(Dropout(0.25))\n\nmodel.add(Dense(neurons))\nmodel.add(ReLU())\nmodel.add(Dropout(0.25))\n\nmodel.add(Dense(neurons))\nmodel.add(ReLU())\nmodel.add(Dropout(0.25))\n\nmodel.add(Dense(1))\n\nmodel.compile(loss='mse',optimizer='rmsprop')\n\nhistory = model.fit(X_train, y_train, batch_size=64, epochs=500, validation_split=0.1, verbose=0)"
   },
   "outputs": [],
   "source": [
    "neurons = 120\n",
    "model = Sequential()\n",
    "\n",
    "model.add(Dense(neurons, input_dim=X_train.shape[1]))\n",
    "model.add(ReLU())\n",
    "model.add(Dropout(0.25))\n",
    "\n",
    "model.add(Dense(neurons))\n",
    "model.add(ReLU())\n",
    "model.add(Dropout(0.25))\n",
    "\n",
    "model.add(Dense(neurons))\n",
    "model.add(ReLU())\n",
    "model.add(Dropout(0.25))\n",
    "\n",
    "model.add(Dense(neurons))\n",
    "model.add(ReLU())\n",
    "model.add(Dropout(0.25))\n",
    "\n",
    "model.add(Dense(1))\n",
    "\n",
    "model.compile(loss='mse',optimizer='rmsprop')\n",
    "\n",
    "history = model.fit(X_train, y_train, batch_size=64, epochs=500, validation_split=0.1, verbose=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2dbb801a-5b9e-47cf-8b01-cda45b215d7e",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 233,
    "lastExecutedAt": 1699391765099,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "#Visualize the loss over numbers of epochs\nhistory_df = pd.DataFrame(history.history)\n\nplt.figure(figsize=(10, 6))\nplt.plot(history_df['loss'], label='Training Loss')\nplt.plot(history_df['val_loss'], label='Validation Loss')\nplt.xlabel('Epoch')\nplt.ylabel('Loss (MSE)')\nplt.legend()\nplt.title('Training and Validation Loss Over Epochs')\nx_ticks = range(0, len(history_df), 20)\nplt.xticks(x_ticks)\nplt.show()\n\nend_train_NN = time.time() #done training our Neural Networks model"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Visualize the loss over numbers of epochs\n",
    "history_df = pd.DataFrame(history.history)\n",
    "\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(history_df['loss'], label='Training Loss')\n",
    "plt.plot(history_df['val_loss'], label='Validation Loss')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel('Loss (MSE)')\n",
    "plt.legend()\n",
    "plt.title('Training and Validation Loss Over Epochs')\n",
    "x_ticks = range(0, len(history_df), 20)\n",
    "plt.xticks(x_ticks)\n",
    "plt.show()\n",
    "\n",
    "end_train_NN = time.time() #done training our Neural Networks model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7a236b12-1d9c-451a-b9f3-255337805c16",
   "metadata": {},
   "source": [
    "### Final Model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8089cc55-af64-480b-99b1-58a4386e23be",
   "metadata": {},
   "source": [
    "To sum up, our final model will contain:\n",
    "- 4 layers of `ReLU` activation function\n",
    "- 120 neurons for each layer\n",
    "- 20 epochs\n",
    "Let's see how our model works on testing data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ac9da717-766d-4d6a-9cca-d63806b1d937",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 4856,
    "lastExecutedAt": 1699391769955,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "final_model = neural_network(120, ReLU, ReLU, ReLU, ReLU, 20)"
   },
   "outputs": [],
   "source": [
    "final_model = neural_network(120, ReLU, ReLU, ReLU, ReLU, 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "1760613c-cce4-4c8e-a435-4a85ff3861b6",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 137,
    "lastExecutedAt": 1699391770093,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "y_pred = final_model.predict(X_test)",
    "outputsMetadata": {
     "0": {
      "height": 36,
      "type": "stream"
     }
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "71/71 [==============================] - 0s 2ms/step\n"
     ]
    }
   ],
   "source": [
    "y_pred = final_model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0a8b2abe-7209-4632-a393-f1d6a1d023d2",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 49,
    "lastExecutedAt": 1699391770142,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "final_accuracy = check_accuracy(y_test,y_pred)\nprint('Accuracy checking for final model:')\nprint(f\"Mean Squared Error: {final_accuracy[0]:.2f}\")\nprint(f\"Root Mean Squared Error: {final_accuracy[1]:.2f}\")\nprint(f\"Mean Absolute Error: {final_accuracy[2]:.2f}\")\nprint(f\"R-squared: {final_accuracy[3]: .4f}\")",
    "outputsMetadata": {
     "0": {
      "height": 114,
      "type": "stream"
     }
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy checking for final model:\n",
      "Mean Squared Error: 5.45\n",
      "Root Mean Squared Error: 2.33\n",
      "Mean Absolute Error: 1.60\n",
      "R-squared:  0.9929\n"
     ]
    }
   ],
   "source": [
    "final_accuracy = check_accuracy(y_test,y_pred)\n",
    "print('Accuracy checking for final model:')\n",
    "print(f\"Mean Squared Error: {final_accuracy[0]:.2f}\")\n",
    "print(f\"Root Mean Squared Error: {final_accuracy[1]:.2f}\")\n",
    "print(f\"Mean Absolute Error: {final_accuracy[2]:.2f}\")\n",
    "print(f\"R-squared: {final_accuracy[3]: .4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f048cf52-703b-4a3c-a9fa-5b005433044e",
   "metadata": {},
   "source": [
    "The model produces good result with small errors and high R-squared value. Conclusion: the accuracy between our Neural Network model and Monte Carlo method is really high."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d590ad8-f5e7-41d2-86d2-91f18effb612",
   "metadata": {},
   "source": [
    "To see it better, let's visualize the out-of-sample comparison between Neural Network and Monte Carlo methods in predicting option prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6eba5805-c386-4999-af7f-3f8a9a3f0fe5",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 143,
    "lastExecutedAt": 1699391770285,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "#Visualize\nplt.figure(figsize = (6,6))\nplt.plot(y_test, y_pred, '.')\nplt.title('OOS Comparison - 4 ReLU, 120 neurons, epochs')\nplt.xlabel('Monte Carlo Prices')\nplt.ylabel('Neural Networks Prices')\nplt.show()"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Visualize\n",
    "plt.figure(figsize = (6,6))\n",
    "plt.plot(y_test, y_pred, '.')\n",
    "plt.title('OOS Comparison - 4 ReLU, 120 neurons, epochs')\n",
    "plt.xlabel('Monte Carlo Prices')\n",
    "plt.ylabel('Neural Networks Prices')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21149f7f-e660-4946-8ea5-56fd5d113f4d",
   "metadata": {},
   "source": [
    "## Evaluate the model on the Testing Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf1620ad-11f1-4dea-b21a-762eb0420d64",
   "metadata": {},
   "source": [
    "### Compare speed of two methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b1c649e1-ea7d-49bf-9a1b-d1a8b8b5f604",
   "metadata": {
    "executionCancelledAt": null,
    "executionTime": 48,
    "lastExecutedAt": 1699391770333,
    "lastScheduledRunId": null,
    "lastSuccessfullyExecutedCode": "#we roughly estimate time for simulate prices for tesing set using Monte Carlo method\n#roughly 1/5 time of simulating the whole data set\n\ntraining_MC = (end_time_MC - start_time_MC)*0.85\ntesting_MC = (end_time_MC - start_time_MC)*0.15\ntraining_NN = end_train_NN - start_train_NN\n\nprint(f'Runtime on Training and Validation data set using Monte Carlo is: {training_MC: .2f}')\nprint(f'Runtime to traing the Neural Network model is: {training_NN: .2f}')\nprint('------------------------------------------------------------------------')\nprint(f'Runtime on Testing data set using Monte Carlo is: {testing_MC: .2f}')",
    "outputsMetadata": {
     "0": {
      "height": 95,
      "type": "stream"
     }
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Runtime on Training and Validation data set using Monte Carlo is:  863.05\n",
      "Runtime to traing the Neural Network model is:  530.14\n",
      "------------------------------------------------------------------------\n",
      "Runtime on Testing data set using Monte Carlo is:  152.30\n"
     ]
    }
   ],
   "source": [
    "#we roughly estimate time for simulate prices for tesing set using Monte Carlo method\n",
    "#roughly 1/5 time of simulating the whole data set\n",
    "\n",
    "training_MC = (end_time_MC - start_time_MC)*0.85\n",
    "testing_MC = (end_time_MC - start_time_MC)*0.15\n",
    "training_NN = end_train_NN - start_train_NN\n",
    "\n",
    "print(f'Runtime on Training and Validation data set using Monte Carlo is: {training_MC: .2f}')\n",
    "print(f'Runtime to traing the Neural Network model is: {training_NN: .2f}')\n",
    "print('------------------------------------------------------------------------')\n",
    "print(f'Runtime on Testing data set using Monte Carlo is: {testing_MC: .2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2c5642b-6143-4dbb-b2a5-3176116315ee",
   "metadata": {},
   "source": [
    "### Compare Accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c63b61d0-d4c1-432b-b34d-ca6f666b6295",
   "metadata": {},
   "source": [
    "As above"
   ]
  }
 ],
 "metadata": {
  "editor": "DataCamp Workspace",
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}