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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": [
"# LSM Algorithm with Machine Learning"
]
},
{
"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",
"from pylab import plt\n",
"plt.style.use('seaborn')\n",
"%matplotlib inline\n",
"import warnings\n",
"warnings.simplefilter('ignore')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Random Number Generation "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"M = 50"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"I = 10000"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"rn = np.random.standard_normal((M+1, I))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[-0.28364418, -0.45291348, 1.22343853, 0.7823462 , -0.58229015],\n",
" [ 0.74218088, -0.68603758, -0.05851018, 1.80353156, -0.9411742 ],\n",
" [ 0.05790127, 1.10559574, 0.7983463 , -0.05257768, -0.3110397 ],\n",
" [-1.05650266, -0.68168332, -0.100843 , -0.44411644, 0.42445042],\n",
" [ 0.62767664, -2.44087068, -0.78945214, 0.17290842, -1.35785665]])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rn[:5, :5]"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-0.00097121035643966936"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rn.mean()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.99920118330691687"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rn.std()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"rn -= rn.mean()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-1.2594718296610403e-17"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rn.mean()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"rn /= rn.std()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.0"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rn.std()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def rng(M=M, I=I):\n",
" # np.random.seed(1)\n",
" rn = np.random.standard_normal((M+1, I))\n",
" rn -= rn.mean()\n",
" rn /= rn.std()\n",
" return rn"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulating Geometric Brownian Motion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Black-Scholes-Merton model is given by the SDE:\n",
"\n",
"$$\n",
"dS_t = rS_tdt + \\sigma S_t dZ_t\n",
"$$\n",
"\n",
"$S_t$ is the stock price at time $t$, $r$ is the constant risk-less short rate, $\\sigma$ the constant volatility factor and $Z_t$ a standard Brownian motion."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An Euler discretization of the model for MCS is given by:\n",
"\n",
"$$\n",
"S_t = S_{t-\\Delta t} \\cdot \\exp \\left(\\left(r - \\frac{\\sigma^2}{2}\\right)\\Delta t + \\sigma \\sqrt{\\Delta t} z_t\\right)\n",
"$$\n",
"\n",
"Here, $\\Delta t = \\frac{T}{M}$ (with $T$ being the time horizon) is the discrete, homogenous time interval and $z_t$ is a standard normally distributed rv."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"S0 = 36.0\n",
"r = 0.06\n",
"sigma = 0.2\n",
"T = 1.0\n",
"dt = T / M"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.02"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dt"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"rn = rng()"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(51, 10000)"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rn.cumsum(axis=1).shape"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"a = np.arange(15).reshape((3, 5))"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0, 1, 2, 3, 4],\n",
" [ 5, 6, 7, 8, 9],\n",
" [10, 11, 12, 13, 14]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0, 1, 2, 3, 4],\n",
" [ 5, 7, 9, 11, 13],\n",
" [15, 18, 21, 24, 27]])"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.cumsum(axis=0)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0, 1, 3, 6, 10],\n",
" [ 5, 11, 18, 26, 35],\n",
" [10, 21, 33, 46, 60]])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a.cumsum(axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
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QBKhZk0dBSSqH3m3m8HvNCAKUPkRtnyVRf8ho8gTwxuJszDShVcgZGzxJJNCH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amQSATqK/tQqWTEJs2vuMrF/NinIyAG2FX1PE6fiwey75rWOAuCgEGhJz04hc0x68gJycTt81A9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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x115419e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(rn.cumsum(axis=0)[:, :10]);"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"S = np.zeros_like(rn)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0., 0., 0., 0., 0.],\n",
" [ 0., 0., 0., 0., 0.],\n",
" [ 0., 0., 0., 0., 0.],\n",
" [ 0., 0., 0., 0., 0.],\n",
" [ 0., 0., 0., 0., 0.]])"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"S[:5, :5]"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(51, 10000)"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"S.shape"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"rn[0] = 0.0"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"S = S0 * np.exp((r - 0.5 * sigma ** 2) * dt + sigma * dt ** 0.5 *\n",
" rn.cumsum(axis=0))"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"S[0] = S0"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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cY66eAYsXu+vWi2YwFOFU0zCJGhXueDk1Njcf91puuR3LibgYBZsr03G4A9R3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S0LwXXoIMTjGK/emTC0UimqvPwE7/E5bbjng9sZ4JWnW4jF4lx/RxUFJRcuQLwUJAoFxi1bMW6Z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\nnWTOjsXLW0lkjJbQcPfX6oiM0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vUmGlqN1OkMXGrqRupdlX98sYkjufVkJoUQEhWGta0N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\nTGcAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11949b438>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(S[:, :10]);"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def paths():\n",
" rn = rng()\n",
" rn[0] = 0.0\n",
" S = np.zeros_like(rn)\n",
" S = S0 * np.exp(((r - 0.5 * sigma ** 2) * dt + sigma * dt ** 0.5 *\n",
" rn).cumsum(axis=0))\n",
" S[0] = S0\n",
" return S"
]
},
{
"cell_type": "raw",
"metadata": {
"collapsed": true
},
"source": [
"def paths():\n",
" rn = rng()\n",
" rn[0] = 0.0\n",
" S = np.zeros_like(rn)\n",
" S[0] = S0\n",
" for t in range(1, M+1):\n",
" S[t] = S[t-1] * np.exp((r - 0.5 * sigma ** 2) * dt +\n",
" sigma * dt ** 0.5 * rn[t])\n",
" return S"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 47.1 ms, sys: 13.8 ms, total: 61 ms\n",
"Wall time: 68.3 ms\n"
]
}
],
"source": [
"%time S = paths()"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38.226115675632947"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"S0 * np.exp(r * T)"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"38.235502683378009"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"S[-1].mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## LSM for American Option Pricing"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"K = 40.0"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df = np.exp(-r * dt)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def lsm():\n",
" S = paths()\n",
" h = np.maximum(K - S, 0)\n",
" V = h[-1]\n",
" for t in range(M-1, 0, -1):\n",
" reg = np.polyfit(S[t], V * df, deg=5)\n",
" C = np.polyval(reg, S[t])\n",
" V = np.where(h[t] > C, h[t], V * df)\n",
" return V.mean() * df"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 285 ms, sys: 18.5 ms, total: 304 ms\n",
"Wall time: 223 ms\n"
]
}
],
"source": [
"%%time\n",
"P0 = lsm()\n",
"P0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Logistic Regression for the Exercise Decision"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from sklearn import linear_model"
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
"def clm(otype='put'):\n",
" S = paths()\n",
" lm = linear_model.LogisticRegression(C=1.0)\n",
" if otype == 'put':\n",
" h = np.maximum(K - S, 0)\n",
" else:\n",
" h = np.maximum(S - K, 0)\n",
" V = h[-1]\n",
" def create_fc(deg=3):\n",
" l = [h[t]]\n",
" for d in range(1, deg+1):\n",
" l.append(S[t] ** d)\n",
" return np.array(l).T\n",
" for t in range(M-1, 0, -1):\n",
" ex = (h[t] > V * df).astype(int)\n",
" fc = create_fc()\n",
" lm.fit(fc, ex)\n",
" exc = lm.predict(fc)\n",
" V = np.where(exc, h[t], V * df)\n",
" return V, V.mean() * df"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def clm(otype='put'):\n",
" # np.random.seed(1000)\n",
" S = paths()\n",
" lm = linear_model.LogisticRegression(C=1.0)\n",
" if otype == 'put':\n",
" h = np.maximum(K - S, 0)\n",
" elif otype == 'call':\n",
" h = np.maximum(S - K, 0)\n",
" else:\n",
" return 'Option type not known.'\n",
" def create_fc(deg=5):\n",
" l = [h[t]]\n",
" for o in range(1, deg+1):\n",
" l.append(S[t] ** o)\n",
" l.append(S[t-1] ** o)\n",
" return np.array(l).T\n",
" V = h[-1]\n",
" for t in range(M-1, 0, -1):\n",
" ex = (h[t] > V * df).astype(int)\n",
" fc = create_fc(deg=5)\n",
" lm.fit(fc, ex)\n",
" exc = lm.predict(fc)\n",
" V = np.where(exc, h[t], V * df)\n",
" return V, df * V.mean()"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"4.06276636741\n",
"4.10544238347\n",
"4.04925059654\n",
"4.12907140423\n",
"4.08535487619\n",
"CPU times: user 19.2 s, sys: 385 ms, total: 19.6 s\n",
"Wall time: 10.3 s\n"
]
}
],
"source": [
"%%time\n",
"for _ in range(5):\n",
" V, P0c = clm()\n",
" print(P0c)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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/Hcbfj2HMDH/MXbf8m57cfQfwIHBBZn6vWv1ARHwiMzcBxwObgU3A5yNiCe13BAcATzU5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\nCmPxS1JhLH5JKozFL0mFsfglqTD/BxD/VZyrDfeRAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11a1ecc50>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(V, bins=35);"
]
},
{
"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
}
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@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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