This package uses convolutional neural networks (implemented in PyTorch) to train mixture models to model the volatility of stock prices.

A single model is trained on a number of different stock symbols. Internally, an embedding is learned for each symbol. In other words, a convolutional neural network learns general features of time series of daily returns that predict the volatilty along with an embedding that tunes the result for different symbolsl.

The volatility of stock returns changes daily. The models produced by this package predict the distribution of the log returns for the next trading date. The actual turn is virtually impossible to predict, but predicting the distribution of return has several uses:

1. The distribution can be sampled to generate simulated sequences of returns that can be used as synthetic data to test various trading algorithms. Datasets with historic daily returns are very small so testing algorithms using historic data is very prone to overfitting.

2. Knowing the distribution of the daily returns (especially the volatility) can be used to determine fair prices for stock options. The famous Black-Scholes formula predicts fair option prices. However, it assumes the daily returns to be stationary and normally distributed. However, observed daily returns are not stationary (the variance varies with time) and the returns are not normally distributed. They tend to have "long tails" compared to a normal distrubution (i.e., kurtosis) and they are not always symmetric (i.e., skew). It's possible to estimate the variances by computing the variance of a trailing sample. However, during periods of increasing volatility this would underestimate the volatility since the volatility today can be significantly greater than the volatility of the past N days. Likewise, during periods of decreasing volatility this would overestimate the volatility. The goal is to determine the instantaneous volatility to provide estimates of the distribution of daily returns during the next trading day (or the next few trading days)

This package can be installed by running pip install . in the top level directory of a git clone checkout

 pip install .

Ideally you would train models on a larger set of symbols. Here we use a small set for demo purposes:

python -m deep_volatility_models.train_univariate -s SPY -s QQQ -s BND 

This script will produce a table and a plot with volatility and mean predictions for the past and for the trading day.

python -m deep)volatility_models.evaluate_model -s SPY -s BND

Models generated as described above do not model correlations between symbols. It's possible to generate multivariate models that represent the correlations between symbols.

The inference code described above infers the parameters of a mixture model representing the distribution of daily returns. No code has been provided here to sample these distributions to generate synthetic data.