TRADING USING DEEP LEARNING MAN VS MACHINE Orders By Algorithms - - PowerPoint PPT Presentation

TRADING USING DEEP LEARNING

MAN VS MACHINE

TRADING USING DEEP LEARNING

84%

Orders By Algorithms

16%

Orders By Human

Artificial Neural Networks

Neural networks are a family of models inspired by biological brain structure and are used to estimate or approximate functions that can depend on a large number

• f inputs and are generally unknown.

Recent breakthroughs in artificial neural networks led to a modern renascence in AI.

TRADING USING DEEP LEARNING

DEEP LEARNING SUPERIORITY

96.92%

Deep Learning

94.9%

Human

DEEP META LEARNING

ref: http://www.image-net.org/challenges/LSVRC/

GRADIENT DESCENT

𝐹 = Error of the network

𝑥𝑢 = 𝑥𝑢−1 − 𝛿 𝜖𝐹 𝜖𝑥

𝑋 = Weight matrix representing the filters

DEEP META LEARNING

GRADIENT BASED MODELS

Legend

𝑦0

𝑔

0(𝑦0, 𝑥0)

𝑔

1(𝑦1, 𝑥1)

𝑔

2(𝑦2, 𝑥2)

𝑔

𝑜 𝑦𝑜, 𝑥𝑜 = ො

𝑧

𝑔

𝑜−1(𝑦𝑜−1, 𝑥𝑜−1)

𝑔

𝑜−2(𝑦𝑜−2, 𝑥𝑜−2)

𝑥0 𝑥1 𝑥𝑜 𝑥𝑜−1

𝐹 = 𝑚 ො 𝑧, 𝑧 𝑧

𝑚 ො 𝑧, 𝑧

• Loss Function

𝑦0 - Features Vector 𝑦𝑗 - Output of 𝑗 layer 𝑥𝑗 - Weights of 𝑗 layer 𝑧 – Ground Truth ො 𝑧 – Model Output 𝐹 – Loss Surface

𝜖𝐹 𝜖𝑦𝑜 = 𝜖𝑚 ො 𝑧, 𝑧 𝜖𝑦𝑜 𝜖𝐹 𝜖𝑥𝑜 = 𝜖𝐹 𝜖𝑦𝑜 𝜖𝑔

𝑜 𝑦𝑜−1, 𝑥𝑜

𝜖𝑥𝑜 𝜖𝐹 𝜖𝑦𝑜−1 = 𝜖𝐹 𝜖𝑦𝑜 𝜖𝑔

𝑜 𝑦𝑜−1, 𝑥𝑜

𝑦𝑜−1

𝑔– Activation Function

𝜖𝐹 𝜖𝑦𝑜−2 = 𝜖𝐹 𝜖𝑦𝑜−1 𝜖𝑔

𝑜−1 𝑦𝑜−2, 𝑥𝑜−1

𝑦𝑜−2 𝜖𝐹 𝜖𝑥𝑜−1 = 𝜖𝐹 𝜖𝑦𝑜−1 𝜖𝑔

𝑜 𝑦𝑜−2, 𝑥𝑜−1

𝜖𝑥𝑜−1

… … 𝐺𝑝𝑠𝑥𝑏𝑠𝑒 𝑄𝑠𝑝𝑞𝑏𝑕𝑏𝑢𝑗𝑝𝑜

𝐶𝑏𝑑𝑙 𝑄𝑠𝑝𝑞𝑏𝑕𝑏𝑢𝑗𝑝𝑜

1: Forward Propagation 2: Loss Calculation 3: Optimization

DEEP META LEARNING

Supervised Learning in a nutshell.

CAT Learning From Examples.

FINNANCIAL PREDICTION PITFALLS

Much Data

Possible relevant data from many markets is incredibly large.

No Theory

Complex non-linear interactions in the data are not well specified by financial theory.

Noisy Data

Noise In financial data Is very common and sometimes distinguishing noise from behavior is hard.

Importance

Data Importance is questionable and determination of meaningful data is hard.

Overfitting

Overfitted easily, most models have poor predictive capabilities On financial data.

Behavior

Behavior of financial markets change all the time and can be really unpredictable. TRADING USING DEEP LEARNING

WHY DEEP LEARNING?

Much Data

Possible relevant data from many markets is incredibly large.

No Theory

Complex non-linear interactions in the data are not well specified by financial theory.

Noisy Data

Noise In financial data Is very common and sometimes distinguishing noise from behavior is hard.

Importance

Data Importance is questionable and determination of meaningful data is hard.

Overfitting

Overfitted easily, most models have poor predictive capabilities On financial data.

Behavior

Behavior of financial markets change all the time and can be really unpredictable. TRADING USING DEEP LEARNING

160.5 161 161.5 162 162.5 163 163.5 164 35:09.9 36:57.2 38:04.2 40:03.3 41:06.0 42:41.7 44:12.7 45:35.9 47:39.1 49:05.9 50:17.6 51:31.1 53:04.0 54:36.3 56:31.8 58:07.0 59:29.3 00:57.2 02:31.0 04:05.5 08:16.0 10:11.6 12:09.7 17:17.8 20:37.3 22:09.9 28:36.1 30:52.1 33:07.0 36:46.1 39:29.7 42:05.1 46:26.1 49:55.8 53:08.2 54:59.0 57:12.2 00:35.6 04:10.1 06:56.1 09:30.2 12:35.7 15:44.1 19:03.8 21:05.0 23:13.6 28:12.2 32:33.9 38:22.9 43:34.5 46:47.4 52:54.0 00:33.2 09:54.6 22:43.6 33:06.1 44:02.0 59:27.2 03:38.7 14:35.6 .5 1 .5 2 .5 3 .5 4 35:09.9 37:08.7 38:59.2 40:38.7 42:17.6 43:49.0 45:35.9 47:55.2 49:32.2 51:02.2 52:25.6 54:24.2 56:31.8 58:27.3 59:58.8 01:43.3 03:22.2 08:03.3 10:11.6 14:04.0 17:37.5 21:19.2 26:03.8 30:46.0 33:07.0 36:54.2 40:00.4 43:27.5 48:22.7 52:26.2 54:59.0 57:33.4 01:00.6 04:41.4 08:23.5 11:20.4 15:44.1 19:15.9 21:24.3 25:00.7 30:25.5 37:26.4 43:34.5 47:56.6 53:40.0 01:46.4 21:12.6 31:31.7 44:02.0 59:33.3 12:50.0

BACK TO FINANCE

?

TRADING USING DEEP LEARNING

Strategy Universe

Strategy Configurations Configuration

DEEP REINFORCEMENT LEARNING

Trading Decision Utility

1 - buy 0 - hold

• 1 - Sell

P&L / Drawdown

DEEP LEARNING IN FINANCE

Technical analysis Might of might not work, One thing for sure: Very hard to generalize.

Technical Analysis

talib.SMA(… talib.MOM(…

TA-Lib : Technical Analysis Library

Successful Technical Trading Agents Using Genetic Programming Farnsworth , 2004

DEEP LEARNING IN FINANCE

Surprisingly, Genetic programing can be very successful when It comes to financial strategies gp = SymbolicRegressor(... gp.fit(X_train, y_train)

DEEP LEARNING IN FINANCE

APPLYING DEEP LEARNING TO ENHANCE MOMENTUM TRADING STRATEGIES IN STOCKS

DEEP LEARNING IN FINANCE

APPLYING DEEP LEARNING TO ENHANCE MOMENTUM TRADING STRATEGIES IN STOCKS L Takeuchi, 2013

𝑌𝑗: σ𝑢−12

𝑢+𝑗

𝑐𝑗𝑒𝑢−𝑏𝑡𝑙𝑢−12 𝑏𝑡𝑙𝑢−12

−𝜈 𝜏

| 𝑗 ∈ (1,11), ∪ 1 𝑗𝑔 𝑢 𝑗𝑜 𝑘𝑏𝑜𝑣𝑏𝑠𝑧 𝑓𝑚𝑡𝑓 0

𝐺𝑓𝑏𝑢𝑣𝑠𝑓 𝑊𝑓𝑑𝑢𝑝𝑠

FEATURE ENGINEERI NG MODEL RESULT S

DEEP LEARNING IN FINANCE

𝑌𝑗: σ𝑢−12

𝑢+𝑗

𝑐𝑗𝑒𝑢−𝑏𝑡𝑙𝑢−12 𝑏𝑡𝑙𝑢−12

−𝜈 𝜏

| 𝑗 ∈ (1,11), ∪ 1 𝑗𝑔 𝑢 𝑗𝑜 𝑘𝑏𝑜𝑣𝑏𝑠𝑧 𝑓𝑚𝑡𝑓 0

𝐻𝑠𝑝𝑣𝑜𝑒 𝑈𝑠𝑣𝑢ℎ

40 33 4 50 2 40 33 𝑌:

𝑐𝑗𝑒𝑢+1 − 𝑏𝑡𝑙𝑢−12 𝑏𝑡𝑙𝑢−12 > ෍

𝑢−12 𝑢+𝑗 𝑐𝑗𝑒𝑢 − 𝑏𝑡𝑙𝑢−12

𝑏𝑡𝑙𝑢−12

𝐻𝑠𝑝𝑣𝑜𝑒 𝑈𝑠𝑣𝑢ℎ

12 Monthly Returns For every month: Daily cumulative returns Z-score Against other cumulative returns of other stocks Flag if January Layers Structure Hyper Parameters

K - Fold Stacked RBMs Layers size found by grid search Not Written

Confusion Matrix

True False

Predicted True Predicted False 22.38% 19.19% 30.97% 27.45%

Precision: 61.224% Recall: 53.659% Accuracy: 53.061%

DEEP MODELING COMPLEX COUPLINGS WITHIN FINANCIAL MARKETS

DEEP LEARNING IN FINANCE

DEEP MODELING COMPLEX COUPLINGS WITHIN FINANCIAL MARKETS

𝑌𝑗: 𝑇𝑗 ∪ 𝐺𝑗

𝐺𝑓𝑏𝑢𝑣𝑠𝑓 𝑊𝑓𝑑𝑢𝑝𝑠

FEATURE ENGINEERI NG MODEL RESULT S

DEEP LEARNING IN FINANCE

R B M

S T O C K

Used Deep Belief Network to find hidden couplings between markets Used Past Prices of stocks and forex as features Unsupervised Learning Model Layers Structure Hyper Parameters

DBN of Stacked RBMs Optimizer: SGD Loss: Negative Log Likelihood Note: No Cross Validation in paper

F O R E X

R B M R B M R B M

DEEP LEARNING FOR MULTIVARIATE FINANCIAL TIME SERIES

DEEP LEARNING IN FINANCE

DEEP LEARNING FOR MULTIVARIATE FINANCIAL TIME SERIES

𝑌𝑗:

log

−𝜈 𝜏

| 𝑗 ∈ (−33, −2), ∪ 1 𝑗𝑔 𝑢 𝑗𝑜 𝑘𝑏𝑜𝑣𝑏𝑠𝑧 𝑓𝑚𝑡𝑓 0

𝐺𝑓𝑏𝑢𝑣𝑠𝑓 𝑊𝑓𝑑𝑢𝑝𝑠

FEATURE ENGINEERI NG MODEL RESULT S

DEEP LEARNING IN FINANCE

𝑍: 1 𝑗𝑔 𝑄𝑠𝑗𝑑𝑓 𝑗𝑡 𝑝𝑤𝑓𝑠 𝑛𝑓𝑒𝑗𝑏𝑜 𝑏𝑢 𝑢 + 1 𝐻𝑠𝑝𝑣𝑜𝑒 𝑈𝑠𝑣𝑢ℎ

D E N S e

1

𝐻𝑠𝑝𝑣𝑜𝑒 𝑈𝑠𝑣𝑢ℎ

Matrix of log returns over all the stocks Z-score Against other stocks log returns Flag if January Layers Structure Hyper Parameters

DBN Connected to MLP Optimizer: ADAGrad CrosVal: Tarining: 70%, Valid: 15%, Test:

15%

Loss: Negative Log Likelihood

R B M R B M R B M

“Deep” Belief Net Fully Connected

Activation: 𝑢𝑏𝑜ℎ Regularization: 𝑀1

IMPLEMENTING DEEP NEURAL NETWORKS FOR FINANCIAL MARKET PREDICTION

DEEP LEARNING IN FINANCE

IMPLEMENTING DEEP NEURAL NETWORKS FOR FINANCIAL MARKET PREDICTION

𝑌: ራ

𝑗 𝑗−100 𝑞𝑢 − 𝑞𝑢−1

𝑞𝑢−1 ∪ ራ

𝑔=5 100

𝑁𝐵( 𝑌, 𝑔) ∪ ራ

𝑘=1 𝑏

𝜍(𝑌, 𝑌

𝑘)

𝐺𝑓𝑏𝑢𝑣𝑠𝑓 𝑊𝑓𝑑𝑢𝑝𝑠

FEATURE ENGINEERI NG MODEL RESULT S

DEEP LEARNING IN FINANCE

𝑍 ∈ 1,0, −1 𝑔𝑝𝑠 𝑐𝑣𝑧, 𝑡𝑓𝑚𝑚, ℎ𝑝𝑚𝑒 𝐻𝑠𝑝𝑣𝑜𝑒 𝑈𝑠𝑣𝑢ℎ

1

𝐻𝑠𝑝𝑣𝑜𝑒 𝑈𝑠𝑣𝑢ℎ

All moving averages from 5 to 100 List of 100 lagged prices Pearson correlation between the returns (all 100) of the stock and all the other stocks(45) Layers Structure Hyper Parameters

Simple Fully Connected Optimizer: SGD CrosVal: Tarining: 80%, Test:

20%

Loss: Categorical Cross Entropy

100 135

Fully Connected

Activation: ReLU, 𝑡𝑝𝑔𝑢𝑛𝑏𝑦

Training Algorithm: Walk forward

Accuracy: 73% F1 Score: 0.4

DEEP LEARNING IN FINANCE

DEEP LEARNING IN FINANCE

DEEP LEARNING IN FINANCE Heaton et al, 2016

𝑞𝑗𝑘: | 𝑗 ∈ (0,365), j ∈ (1,500)

𝐺𝑓𝑏𝑢𝑣𝑠𝑓 𝑊𝑓𝑑𝑢𝑝𝑠

FEATURE ENGINEERI NG MODEL RESULT S

DEEP LEARNING IN FINANCE

𝑞𝑗𝑘: | 𝑗 ∈ (0,365), j ∈ (1,500)

𝐻𝑠𝑝𝑣𝑜𝑒 𝑈𝑠𝑣𝑢ℎ

50

4 4 2

𝑞𝑗𝑘

𝑡&𝑞500: | j ∈ (1,500) 𝐻𝑠𝑝𝑣𝑜𝑒 𝑈𝑠𝑣𝑢ℎ

Trained an auto encoder Used it to find stock close to the market encoded Used those with deep architecture to find s&p500

Layers Structure Hyper Parameters

AutoEncod er DFP Policy Sparsity indicator: 0.1

50

Stationarity

Definition

Let 𝑦𝑢 be a stochastic process and let 𝐺

𝑦 𝑦𝑢1+𝜐, . . . . , 𝑦𝑢𝑙+𝜐 represent the cumulative distribution

function of the joint distribution of 𝑦𝑢 at times 𝑢1 + 𝜐, . . . . . . . , 𝑢𝑙 + 𝜐. 𝒚𝒖 is said to be strictly stationary if, for all k, for all 𝜐 and for all 𝑢1. . . . . . 𝑢𝑙

𝑮𝒚 𝒚𝒖𝟐+𝝊, . . . . , 𝒚𝒖𝒍+𝝊 = 𝑮𝒀 𝒚𝒖𝟐, . . . . , 𝒚𝒖𝒍

In other words

Shifting the time origin by an amount 𝜐 has no effect on the joint distribution which depends only on the intervals between 𝑢1 . . . . . . . 𝑢𝑙

Stationarizing A Time Series

V A L U E F O R E C A S T I N G

"Stationarizing" A Time Series

V A L U E F O R E C A S T I N G

𝑧𝑗 = 𝑧𝑝𝑠𝑗𝑕𝑗 𝑧𝑗 = [ln(𝑧𝑝𝑠𝑗𝑕𝑗)]′

Algorithm Structure

Learning Model Logarithm & Differentiation

Integration & Exponentiation

V A L U E F O R E C A S T I N G

Segmentation Concatenation

𝑧𝑗 = [ln(𝑧𝑝𝑠𝑗𝑕𝑗)]′ 𝑧𝑞𝑠𝑓𝑒𝑗 = 𝑓׬ ො

𝑧𝑗

Features Prediction

Nonstationary Stochastic Series Stationary Stochastic Series Segments Regression Prediction Stationary Stochastic Prediction Nonstationary Final Stochastic Prediction

4D Financial Graph Data

Assets

DEEP REINFORCEMENT LEARNING

Time Features

DEEP LEARNING IN PRODUCTION

ALGOTRADING PITFALLS

Slippage is the difference between where the computer signaled the entry and exit for a trade and where actual clients, with actual money, entered and exited.

Slippage

Commission is a service charge assessed by a broker

• r investment advisor in return

for providing investment advice and/or handling the purchase or sale of a security.

Commission

DEEP LEARNING IN FINANCE

Theoretical Motivations

Smoothness Assumption

Points that are close to each other are more likely to share a label.

• Allow to easily interpolate between examples.
• The root for the curse of dimensionality

Depth Assumption

Depth is a double edge sword.

• Depth can add exponentially (comparing to width) more predictive power to the network but only

if done right.

Distributed Representations

Localist models are very inefficient whenever the data has componential structure

• Distributed representations are useful for efficient combining of features to learn the underlying

mechanism that the labels are derived from.

Kitchen sink approach

Possible relevant features from many market can be incredibly large.

DEEP LEARNING IN FINANCE

UNDERFITTING

Finance models often have poor results

Solve this by smart risk management

“It works if you remove this situation”

Save yourself some money, it just doesn’t work.

Feature Engineering VS Raw Data

A good question. DEEP LEARNING IN FINANCE

Data: Unlimited

Image Finance

Overtraining : Hard Data: Limited Overtraining: Easy

$

“You are basically risking millions on something no

• ne in the world fully

understands?”

"Why Should I Trust You?": Explaining the Predictions of Any Classifier – Ribeiro, et al 2015

DEEP LEARNING IN FINANCE

MARKOV PROPERTY

𝑄 𝑌𝑜 = 𝑦𝑜 𝑌𝑜−1 = 𝑦𝑜−1, 𝑌𝑜−2 = 𝑦𝑜−2, . . . . , 𝑌0 = 𝑦0) = 𝑄(𝑌𝑜 = 𝑦𝑜|𝑌𝑜−𝑢 = 𝑦𝑜−𝑢)

Markov Property

DEEP LEARNING IN FINANCE

RNN PITFALLS

Example: Jane walked into the room John walked in too. It was late at night. Jane said hi to _____ The difficulty in training recurrent neural nets – Bengio, et al 2013 Tricks:

• Init the weight matrices to the identity Matrix
• Set the activation function to RELU
• Norm clipping the exploding gradient

ො 𝑕 ←

𝜖𝜁 𝜖𝑥

𝒋𝒈 𝑕 ≥ 𝑢ℎ𝑠𝑓𝑡ℎ𝑝𝑚𝑒 𝒖𝒊𝒇𝒐 ො 𝑕 ←

𝑢ℎ𝑠𝑓𝑡ℎ𝑝𝑚𝑒 || ො 𝑕||

ො 𝑕 A Simple Way to Initialize Recurrent Networks of Rectified Linear Units– Hinton, et al 2015

DEEP LEARNING IN FINANCE

DEBUGGING DEEP NETS

Understanding the difficulty in training deep feedforward neural nets– Bengio, et al 2013

Mean and standard deviation of the activation (output of the sigmoid) during learning, for 4 hidden layers . The top hidden layer quickly saturates at 0 (slowing down all learning), but then slowly desaturates ~ epoch 100.

Other Uses of Deep Learning

Extracting price impact of news

Stress signal on Individual Asset from text (Word2Vec) and fundamental data

Non-Linear Portfolio Replication

Using Fewer Instruments

Reinforcement Learning

For Continues Algo optimization

Space Embedding

For Correlation between Assets

DEEP LEARNING IN FINANCE

GOOG AAPL MMM

... ...

Deep Learning Orders

Trading / Training On Site

Research In House

Data Storage GPU CLUSTER Testing Data

Market Market

Under fitting

Underfitting occurs when a statistical model or machine learning algorithm cannot capture the underlying trend of the data. Intuitively, underfitting

• ccurs when the model or the algorithm does not fit

the data well enough.

Underftting is either caused by trying to fit a too simple model or by not training the model enough. Calculate 1+1 What is 1? I've

• nly seen

equations with 4

TRADING USING DEEP LEARNING

Represented As Tensor Multiplications Computed On NVidia GPUs Model Training Algorithm

USING THE GPU

TRADING USING DEEP LEARNING

X

THE IMPORTANCE OF POWER

TRADING USING DEEP LEARNING

Performance

Computational Speed allows us to further train our model to yield better accuracy in the finite amount of training time we have.

Memory Capacity

High Memory Capacity is crucial to our systems, allowing us to construct wider and deeper models and integrate more data into the models.

Interface Speed

The Speed of the card interface defines how many model “shifts” can we perform in one trading cycle.

CPU vs GPU

Compiled with .nvcc GDDR5 – 7.0 Gbps Compiled with .gcc DDR4 - 2400Mhz

TRADING USING DEEP LEARNING

Matrix multiplication complexity– 𝑃(𝑜3) Epoch takes: 7500 sec (avg) Matrix multiplication complexity– 𝑃(𝑜)

[1]

Epoch takes: 500 sec (avg)

[1] - Understanding the Efficiency of GPU Algorithms for Matrix-Matrix Multiplication - Fatahalian, et al, 2004

POWER TRAINING ACCURACY RETURNS = = =

Deep Learning Algorithmic Trading Paper Review GPU Based Trading Recap

Questions?