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Machine Learning for Finance | Dr. Yves J. Hilpisch | CQF Elective | London, 23. May 2017

Machine Learning for Finance

A CQF elective with Dr. Yves J. Hilpisch, The Python Quants GmbH

General resources:

Wifi

You can use the following wifi in this venue:

SSID Fitch Guest
PW   Ft1ch#2016#!

Abstract

This CQF elective is about machine learning and deep learning with Python applied to finance. It starts with techniques to retrieve financial data from open data sources and covers Python packages like NumPy, pandas, scikit-learn and TensorFlow. It provides the basis to further explore these recent developments in data science to improve traditional financial tasks such as the pricing of American options or the prediction of future stock market movements.

Among other, the elective covers:

  • Getting and working with financial time series data in Python
  • Using linear OLS regression to predict financial prices & returns
  • Using scikit-learn for machine learning with Python
  • Application to the pricing of American options by Monte Carlo simulation
  • Applying logistic regression to classification problems
  • Predicting stock market returns as a classification problem
  • Using TensorFlow for deep learning with Python
  • Using deep learning for predicting stock market returns

Overview slides under http://hilpisch.com/cqf_ml_elective.pdf

Python

Download and install Miniconda 3.6 from https://conda.io/miniconda.html

If you have either Miniconda or Anaconda installed there is not need to install anything new.

conda create -n elective python=3.6
(source) activate elective
conda install numpy pandas=0.19 scikit-learn matplotlib
conda install pandas-datareader pytables
conda install ipython jupyter
jupyter notebook

Installing TensorFlow: https://www.tensorflow.org/install/

Finance

Download the paper by Longstaff and Schwartz (2001) about the Least-Squares Monte Carlo algorithm to price American options from Paper about LSM algorithm

Basic Definitions

"You can think of deep learning, machine learning and artificial intelligence [AI] as a set of Russian dolls nested within each other, beginning with the smallest and working out. Deep learning is a subset of machine learning, which is a subset of AI. ... That is, all machine learning counts as AI, but not all AI counts as machine learning. For example, symbolic logic (rules engines, expert systems and knowledge graphs) as well as evolutionary algorithms and Baysian statistics could all be described as AI, and none of them are machine learning."

"Neural networks are a set of algorithms, modeled loosely after the human brain, that are designed to recognize patterns. They interpret sensory data through a kind of machine perception, labeling or clustering raw input. The patterns they recognize are numerical, contained in vectors, into which all real-world data, be it images, sound, text or time series, must be translated."

"Deep learning maps inputs to outputs. It finds correlations. It is known as a 'universal approximator', because it can learn to approximate the function f(x) = y between any input x and any output y, assuming they are related through correlation or causation at all. In the process of learning, a neural network finds the right f, or the correct manner of transforming x into y, whether that be f(x) = 3x + 12 or f(x) = 9x - 0.1."

"All classification tasks depend upon labeled datasets; that is, humans must transfer their knowledge to the dataset in order for a neural to learn the correlation between labels and data. This is known as supervised learning. ... Any labels that humans can generate, any outcomes you care about and which correlate to data, can be used to train a neural network."

Source: https://deeplearning4j.org

Machine Learning

Here some resources to get a first overview of basic machine learning concepts and logistic regression for classification:

Neural Networks

Here some resources to get a first overview of neural networks:

TensorFlow

Some resources to get started with Google's TensorFlow package for deep learning:

Data

Download a HDF5 database file, containing a single pandas DataFrame object with hitorical equites data, from http://hilpisch.com/equities.h5

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src=\"http://hilpisch.com/tpq_logo.png\" width=350px align=\"right\">"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Stock Market Prediction"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"&copy; Dr. Yves J. Hilpisch\n",
"\n",
"The Python Quants GmbH"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"from pylab import plt\n",
"plt.style.use('seaborn')\n",
"%matplotlib inline\n",
"from pandas_datareader import data as web"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Getting Historical Data"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"data = pd.DataFrame(web.DataReader('AMZN', data_source='google')['Close'])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data.columns = ['prices']"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'pandas.core.frame.DataFrame'>\n",
"DatetimeIndex: 1858 entries, 2010-01-04 to 2017-05-22\n",
"Data columns (total 1 columns):\n",
"prices 1858 non-null float64\n",
"dtypes: float64(1)\n",
"memory usage: 29.0 KB\n"
]
}
],
"source": [
"data.info()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# !conda install -y pandas-datareader"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# !conda install -y pandas=0.19"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'0.19.2'"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pd.__version__"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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j1t8Jz4MYMVIK3xVkiYiIyIAdrW7m8dW7Y7Y9vno3znAfrHlTctiyt9Le11O2Kbpbw7Ga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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10af72668>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data.plot(figsize=(10, 6));"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data['returns'] = np.log(data / data.shift(1))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prices</th>\n",
" <th>returns</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Date</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2010-01-04</th>\n",
" <td>133.90</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-05</th>\n",
" <td>134.69</td>\n",
" <td>0.005883</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-06</th>\n",
" <td>132.25</td>\n",
" <td>-0.018282</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-07</th>\n",
" <td>130.00</td>\n",
" <td>-0.017160</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-08</th>\n",
" <td>133.52</td>\n",
" <td>0.026717</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" prices returns\n",
"Date \n",
"2010-01-04 133.90 NaN\n",
"2010-01-05 134.69 0.005883\n",
"2010-01-06 132.25 -0.018282\n",
"2010-01-07 130.00 -0.017160\n",
"2010-01-08 133.52 0.026717"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.head()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"lags = 5"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"cols = []"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"for lag in range(1, lags+1):\n",
" col = 'ret_%d' % lag\n",
" data[col] = data['returns'].shift(lag)\n",
" cols.append(col)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prices</th>\n",
" <th>returns</th>\n",
" <th>ret_1</th>\n",
" <th>ret_2</th>\n",
" <th>ret_3</th>\n",
" <th>ret_4</th>\n",
" <th>ret_5</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Date</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2010-01-04</th>\n",
" <td>133.90</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-05</th>\n",
" <td>134.69</td>\n",
" <td>0.005883</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-06</th>\n",
" <td>132.25</td>\n",
" <td>-0.018282</td>\n",
" <td>0.005883</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-07</th>\n",
" <td>130.00</td>\n",
" <td>-0.017160</td>\n",
" <td>-0.018282</td>\n",
" <td>0.005883</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-08</th>\n",
" <td>133.52</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" <td>-0.018282</td>\n",
" <td>0.005883</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-11</th>\n",
" <td>130.31</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" <td>-0.018282</td>\n",
" <td>0.005883</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-12</th>\n",
" <td>127.35</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" <td>-0.018282</td>\n",
" <td>0.005883</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-13</th>\n",
" <td>129.11</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" <td>-0.018282</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-14</th>\n",
" <td>127.35</td>\n",
" <td>-0.013726</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-15</th>\n",
" <td>127.14</td>\n",
" <td>-0.001650</td>\n",
" <td>-0.013726</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" prices returns ret_1 ret_2 ret_3 ret_4 ret_5\n",
"Date \n",
"2010-01-04 133.90 NaN NaN NaN NaN NaN NaN\n",
"2010-01-05 134.69 0.005883 NaN NaN NaN NaN NaN\n",
"2010-01-06 132.25 -0.018282 0.005883 NaN NaN NaN NaN\n",
"2010-01-07 130.00 -0.017160 -0.018282 0.005883 NaN NaN NaN\n",
"2010-01-08 133.52 0.026717 -0.017160 -0.018282 0.005883 NaN NaN\n",
"2010-01-11 130.31 -0.024335 0.026717 -0.017160 -0.018282 0.005883 NaN\n",
"2010-01-12 127.35 -0.022977 -0.024335 0.026717 -0.017160 -0.018282 0.005883\n",
"2010-01-13 129.11 0.013726 -0.022977 -0.024335 0.026717 -0.017160 -0.018282\n",
"2010-01-14 127.35 -0.013726 0.013726 -0.022977 -0.024335 0.026717 -0.017160\n",
"2010-01-15 127.14 -0.001650 -0.013726 0.013726 -0.022977 -0.024335 0.026717"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.head(10)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data.dropna(inplace=True)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prices</th>\n",
" <th>returns</th>\n",
" <th>ret_1</th>\n",
" <th>ret_2</th>\n",
" <th>ret_3</th>\n",
" <th>ret_4</th>\n",
" <th>ret_5</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Date</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2010-01-12</th>\n",
" <td>127.35</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" <td>-0.018282</td>\n",
" <td>0.005883</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-13</th>\n",
" <td>129.11</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" <td>-0.018282</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-14</th>\n",
" <td>127.35</td>\n",
" <td>-0.013726</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-15</th>\n",
" <td>127.14</td>\n",
" <td>-0.001650</td>\n",
" <td>-0.013726</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-19</th>\n",
" <td>127.61</td>\n",
" <td>0.003690</td>\n",
" <td>-0.001650</td>\n",
" <td>-0.013726</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" prices returns ret_1 ret_2 ret_3 ret_4 ret_5\n",
"Date \n",
"2010-01-12 127.35 -0.022977 -0.024335 0.026717 -0.017160 -0.018282 0.005883\n",
"2010-01-13 129.11 0.013726 -0.022977 -0.024335 0.026717 -0.017160 -0.018282\n",
"2010-01-14 127.35 -0.013726 0.013726 -0.022977 -0.024335 0.026717 -0.017160\n",
"2010-01-15 127.14 -0.001650 -0.013726 0.013726 -0.022977 -0.024335 0.026717\n",
"2010-01-19 127.61 0.003690 -0.001650 -0.013726 0.013726 -0.022977 -0.024335"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## OLS Regression"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"reg = np.linalg.lstsq(data[cols].values, np.sign(data['returns'].values))[0]"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1.16886579, -0.96206944, -0.05028051, -1.33774549, 0.81681303])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"reg"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"pred = np.sign(np.dot(data[cols].values, reg))"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1., 1., -1., ..., -1., 1., -1.])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pred"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-1., 1., -1., ..., 1., 1., 1.])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.sign(data['returns'].values)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data['ols_pred'] = pred"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"c = np.sign(data['returns'] * data['ols_pred'])"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
" 1.0 941\n",
"-1.0 906\n",
" 0.0 5\n",
"dtype: int64"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c.value_counts()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.50809935205183587"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"c.value_counts()[1] / (c.value_counts().sum())"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data['ols_returns'] = data['returns'] * data['ols_pred']"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Ma2634t1NZfB4V7O1ddqx82gTAOA3P5iPwuzoVrlWKQKDpLx0HQAgMzkeFy4f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\nSJAkhBBCCOGGBElCCCGEEG78P5JmcSKGpe47AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b91f9e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data[['returns', 'ols_returns']].cumsum().apply(np.exp).plot(figsize=(10, 6));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Logistic Regression"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn import linear_model"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"lm = linear_model.LogisticRegression(C = 1e6)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"LogisticRegression(C=1000000.0, class_weight=None, dual=False,\n",
" fit_intercept=True, intercept_scaling=1, max_iter=100,\n",
" multi_class='ovr', n_jobs=1, penalty='l2', random_state=None,\n",
" solver='liblinear', tol=0.0001, verbose=0, warm_start=False)"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"lm.fit(data[cols], np.sign(data['returns']))"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data['log_pred'] = lm.predict(data[cols])"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prices</th>\n",
" <th>returns</th>\n",
" <th>ret_1</th>\n",
" <th>ret_2</th>\n",
" <th>ret_3</th>\n",
" <th>ret_4</th>\n",
" <th>ret_5</th>\n",
" <th>ols_pred</th>\n",
" <th>ols_returns</th>\n",
" <th>log_pred</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Date</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2010-01-12</th>\n",
" <td>127.35</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" <td>-0.018282</td>\n",
" <td>0.005883</td>\n",
" <td>1.0</td>\n",
" <td>-0.022977</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-13</th>\n",
" <td>129.11</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" <td>-0.018282</td>\n",
" <td>1.0</td>\n",
" <td>0.013726</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-14</th>\n",
" <td>127.35</td>\n",
" <td>-0.013726</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>-0.017160</td>\n",
" <td>-1.0</td>\n",
" <td>0.013726</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-15</th>\n",
" <td>127.14</td>\n",
" <td>-0.001650</td>\n",
" <td>-0.013726</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>0.026717</td>\n",
" <td>1.0</td>\n",
" <td>-0.001650</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2010-01-19</th>\n",
" <td>127.61</td>\n",
" <td>0.003690</td>\n",
" <td>-0.001650</td>\n",
" <td>-0.013726</td>\n",
" <td>0.013726</td>\n",
" <td>-0.022977</td>\n",
" <td>-0.024335</td>\n",
" <td>1.0</td>\n",
" <td>0.003690</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" prices returns ret_1 ret_2 ret_3 ret_4 \\\n",
"Date \n",
"2010-01-12 127.35 -0.022977 -0.024335 0.026717 -0.017160 -0.018282 \n",
"2010-01-13 129.11 0.013726 -0.022977 -0.024335 0.026717 -0.017160 \n",
"2010-01-14 127.35 -0.013726 0.013726 -0.022977 -0.024335 0.026717 \n",
"2010-01-15 127.14 -0.001650 -0.013726 0.013726 -0.022977 -0.024335 \n",
"2010-01-19 127.61 0.003690 -0.001650 -0.013726 0.013726 -0.022977 \n",
"\n",
" ret_5 ols_pred ols_returns log_pred \n",
"Date \n",
"2010-01-12 0.005883 1.0 -0.022977 1.0 \n",
"2010-01-13 -0.018282 1.0 0.013726 1.0 \n",
"2010-01-14 -0.017160 -1.0 0.013726 1.0 \n",
"2010-01-15 0.026717 1.0 -0.001650 1.0 \n",
"2010-01-19 -0.024335 1.0 0.003690 1.0 "
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.head()"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data['log_returns'] = data['returns'] * data['log_pred']"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
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kLDm6z3skSBJCCCH6YHd5Meq1HDkzN6b7DJ0Ts99fvQ9Lgp4zjioJfDfQOUkt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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11100dcf8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data[['returns', 'ols_returns', 'log_returns']].cumsum(\n",
" ).apply(np.exp).plot(figsize=(10, 6));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Deep Neural Network"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import tensorflow as tf"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"tf.logging.set_verbosity(tf.logging.ERROR)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"mean = data['returns'].mean()"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"std = data['returns'].std()"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.00108427123518 0.0199275076794\n"
]
}
],
"source": [
"print(mean, std)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"fc = tf.contrib.layers.real_valued_column('returns', dimension=lags)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"fcb = [tf.contrib.layers.bucketized_column(fc,\n",
" boundaries=[-0.0005, 0.0001, 0.0005])]"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"model = tf.contrib.learn.DNNClassifier(hidden_units=[50, 50],\n",
" feature_columns=fcb)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def get_data():\n",
" fc = {'returns': tf.constant(data[cols].values)}\n",
" la = tf.constant((data['returns'] > 0).astype(int).values,\n",
" shape=[len(data), 1])\n",
" return fc, la"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"DNNClassifier(params={'head': <tensorflow.contrib.learn.python.learn.estimators.head._BinaryLogisticHead object at 0x1195dfeb8>, 'hidden_units': [50, 50], 'feature_columns': (_BucketizedColumn(source_column=_RealValuedColumn(column_name='returns', dimension=5, default_value=None, dtype=tf.float32, normalizer=None), boundaries=(-0.0005, 0.0001, 0.0005)),), 'optimizer': None, 'activation_fn': <function relu at 0x11803e378>, 'dropout': None, 'gradient_clip_norm': None, 'embedding_lr_multipliers': None, 'input_layer_min_slice_size': None})"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.fit(input_fn=get_data, steps=100)"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'accuracy': 0.54913604,\n",
" 'accuracy/baseline_label_mean': 0.52429807,\n",
" 'accuracy/threshold_0.500000_mean': 0.54913604,\n",
" 'auc': 0.56181008,\n",
" 'global_step': 100,\n",
" 'labels/actual_label_mean': 0.52429807,\n",
" 'labels/prediction_mean': 0.52496111,\n",
" 'loss': 0.68702751,\n",
" 'precision/positive_threshold_0.500000_mean': 0.54815865,\n",
" 'recall/positive_threshold_0.500000_mean': 0.7971164}"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"model.evaluate(input_fn=get_data, steps=1)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data['dnn_pred'] = list(model.predict(input_fn=get_data))\n",
"data['dnn_pred'] = np.where(data['dnn_pred'] > 0, 1.0, -1.0)"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"data['dnn_returns'] = data['returns'] * data['dnn_pred']"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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AY46Z22U5OTnBRyyrqiopLy/jF7/4KRCc27Rw4aIO7ztyy5ucnNzQ8ZQpdgDS0zNxu4Pr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"text/plain": [
"<matplotlib.figure.Figure at 0x10bf11e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"data[['returns', 'ols_returns', 'log_returns', 'dnn_returns']].cumsum(\n",
" ).apply(np.exp).plot(figsize=(10, 6));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src=\"http://hilpisch.com/tpq_logo.png\" width=350px align=\"right\">"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
@stef296
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stef296 commented Aug 3, 2017

Hi Yves, thanks for the great session. There is a small bug in the paths() function. I think it should be something like this:

def paths2(S0=S0,r=r,sigma=sigma,dt=dt):
    rn = rng()
    rn[0] = 0.0
    S = np.zeros_like(rn)
    S[0] = S0
    S[1:] = S0 * np.exp(((r - 0.5 * sigma ** 2) * dt +
            sigma * dt ** 0.5 * rn[1:]).cumsum(axis=0))
    return S; 

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