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This paper analyzes the predictability and tradability of volatility in the large S&P500 index and SPY ETF, VIX index and VXX ETN. Although there is a large literature on predicting high frequency fluctuations, most of the predictions are evaluated only on the basis of statistical errors. In practice, this analysis is only a small indication of the actual economic significance of the projections that have been made. Therefore, in our methodology, we also test our forecasts by trading appropriate volatility derivatives.
Introduction to the
Volatility plays a central role in asset pricing and allocation and in risk management, such as value at risk and expected shortfalls. Modelling and forecasting volatility is of great interest to econometricians, statisticians and practitioners, hence the financial and economic literature. However, the traditional generalized autoregressive conditional heteroscedasticity (GARCH) and stochastic volatility (SV) models are not suitable for applications using high frequency data.
In this paper, HAR-RV-J is compared with recursive neural network (RNN) and hybrid HAR-RV-J-RNN models to predict volatility and thereby analyze predictability.
Recurrent neural network
Artificial neural network is a powerful nonparametric tool for signal filtering, pattern recognition and interpolation. It can also tolerate data with errors and find nonlinear correlations between model parameters. While most econometric models are developed by capturing specific features of time series (such as long memory) or functional relationships between hypothetical variables, the main advantage of artificial neural networks is that they contain nonlinearity and include all variables.
A single output RNN model with a hidden layer
Hybrid model
The hybrid model is also designed for RNN. However, as additional input, we feed the prediction of the linear model to the RNN. We also retained four basic inputs. Thus, in the case of the mixed model, the total number of inputs increases to five.
All other model parameters remain unchanged. Specifically, determine the number of hidden neurons above. In addition, the model architecture remains the same.
The motivation for using hybrid models stems from the desire to use each model in a way that exploits its specific capabilities. By feeding linear predictions to the RNN, we can remove any linear components from the prediction task. This should leave more room to better match nonlinear residuals of linear prediction errors.
data
Our underlying data set includes headline data from Thomson Reuters Tick History (TRTH) for the S&P 500 from January 2, 1996 to the beginning of June 2, 2016.
The results of
Daily S&P500 RV. Note: The top panel shows the daily realized volatility and its logarithmic transformation,
conclusion
This paper analyzes the potential of heterogeneous autoregressive models, including jump prediction realized volatility (RV). For this approach, we calculate the RV based on a 20-year history of 5-year intraday data for the S&P 500. Our results show that the basic HAR-RV-J model can indeed provide satisfactory RV prediction.