Modelling Asset Price Volatility Over Time Using LSTM

This note explores machine learning based modelling approach over classical quantitative methods with a focus on modelling realized volatility of asset price over time. Initially, a few modelling assumptions of classical quantitative finance are examined using recent market data. Daily stock data of S&P500, DJIA (Dow Jones), a few technology-sector stocks (AAPL, MSFT) are used and some of their distribution characteristics are highlighted. These characteristics under stressed and non-stressed periods deserves attention. Standard time series models are used for price and volatility forecasting over time and prediction accuracy is observed. In a subsequent section, machine learning based modelling technique is explored and a Long short-term memory (LSTM) model is trained to make multi-step look-ahead return forecast to calculate realized volatility. LSTM approach has already gained momentum for stock price prediction. Hyper-parameter variations of the model are explored to achieve better fit and develop intuition for optimum parameter tuning. The effectiveness of this model over some of the classical methods are noted