Deep_Learning_In_Limited_Order_Books

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Deep_Learning_In_Limited_Order_Books

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:moneybag:Deep learning models for high-frequency financial data (limited order book)

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# Deep Learning Model for High-frequency Financial Data
## Introduction
Nowadays, deep learning has shown its power in tramendous areas, like computer vision, natural languange processing, etc. However, this project focuses on applying deep learning methods in high-frequency financial data --- Limited Order Books, to predict the next mid price move direction and magnitude.

## Task
Our task is to predict the next best ask price's **conditional** probability of moving direction and magnitude. We are not caring about the circumstance that the next best ask price do not move. We will say if the price **do** move, then what's the probability of it going up and going down, and further more, what's the probability of it going up 1 cent, 2 cents, ... ?

## Data
The data we use for this project is fixed time interval data, it can be requested on https://lobsterdata.com/. 
The data file contains three keys:
* `X_date`: records the limited order book
* `Y_date`: records the next best ask and bid price in Fixed Time Scale
* `T_date`: 
  * a. Time stamp(Start from the first row and keep adding the time interval);
  * b. transaction time just after the current time stamp;
  * c. current accumulated transaction number( Corresponding to the row numbers in the original limited order book)
 
## Preprocessing
The raw limited order book state has 40 dimensions. The format is like this:

| Col 1        | Col 2           | Col3  | Col4 | Col5 | Col6 | ...
|:-------------:|:-------------:|:-----:|:-----:|:-----:|:-----:|:-----:|
| Best ask price | Best ask size | Best bid price | Best bid size | 2nd ask price | 2nd ask size | ...

However, the spread of ask and bid prices changes through time, and the price magnitude barely have meaningful information we need. Therefore, we have to:
1. Binning the price spread. Here we set 20 bins ( 10 for ask price, 10 for bid price )
2. Put the corresponding sizes into the bins.

## Model
Since the limited order book state has inherent time dependency, it would be beneficial to utilize a sequence of state when we do the prediction job. Hence, we decide to use **LSTM** model for this project.
PyTorch has a built-in module so we do not have to write the LSTM layer on our own. The model structure is shown below:
``` python
class LSTM_model(nn.Module):
    def __init__(self, num_layers, input_size, hidden_size, fc_size, output_size):
        super(LSTM_model, self).__init__()
        self.input_size = input_size
        self.hidden_size = hidden_size
        self.lstm = nn.LSTM(num_layers=num_layers,
                            input_size = self.input_size,
                            hidden_size = self.hidden_size,
                            batch_first = True,
                            dropout =  0.2)
        self.fc = nn.Linear(hidden_size, fc_size)
        self.decoder = nn.Linear(fc_size, output_size)

def forward(self, order_book_data):
        """
        order_book_data: [batch_size, sequence_len, dims]
        """
        lstm_output, _ = self.lstm(order_book_data, None)
        output = F.relu(self.fc(lstm_output))
        output = self.decoder(output)
        return F.log_softmax(output, dim=2)
```
When we return the output, we do a `log_softmax` operation, since we need the output to be the probability of each class the input data can be, and the `log` operation is for the later on loss calculation's convenience.

## Training
* **Optimizer**: `Adam`
* **Loss function**: `nll_loss`
* **Learning rate**: 0.001
* **Truncation Length**: 20
* **Batch size**: 256
* **Hidden units**: 200

### Output classes
In our experiment, we set up **<font color="red">9 classes</font>**, they are:
best ask price move down 1 cent, 2 cents, 3 cents, 4 or more cents, not move, move up 1 cent, 2 cents, 3 cents, 4 or more cents.

## Results
### Accuracy on different stocks
After some experiments, we found that the performance of our model varies from different stocks. We used traditional **feed-forward neural network** as baseline. I put a table below to show the Evaluation accuracy on different stocks.

|        | AAPL | AMD  | CBS |
|:-------------:|:-------------:|:-----:|:-----:|
| LSTM | 62.23% | 72.84% | 47.82% |
| Neural Network | 58.52% | 67.29% | 45.13% |

### Training/Evaluation loss and accuracy plot
Here is the loss and accuracy trends throughout training/evaluation steps on `AMD` stock:

![image](https://raw.githubusercontent.com/MingyuZha/Deep_Learning_In_Limited_Order_Books/master/images/AMD.acc&loss.sl=20.png)

We can see that there is a little bit overfitting here, we are trying to imporve this further.

### Model Performance on different truncation length
We also experimented with different truncation length:

![image](https://raw.githubusercontent.com/MingyuZha/Deep_Learning_In_Limited_Order_Books/master/images/AMD.acc.sl=20&30&40&50.png)

Larger truncation length do have positive influence on the model performance, though not very large.

### Precision and Recall
**Precision and Recall**  is a very import metric for a classification model, since most of time we care more about model's performance on a certain category input. However, the data we used to train our model is highly imbalanced, which is very very common in limit order books, because the time interval is only **one second**! Therefore, most of the time the best mid price would remain the same or just move a very small magnitude.

|   Class   | 0 | 1  | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| Num of records | 4 | 6 | 70 | 1341 | 60349 | 1353 | 49 | 5 | 3 |
| **Precision** | 0% | 0% | 0% | 78.82% | - | 79.38% | 0% | 0% | 0% |

|   Class   | 0 | 1  | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|:---:|
| Num of records | 0 | 0 | 1 | 1405 | - | 1425 | 0 | 0 | 0 |
| **Recall** | - | - | 0% | 75.23% | - | 75.37% | - | - | - |

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