Forecasting Realised Volatility in a Financial Market
Most of the studies about financial markets are to do with risks and returns. Realised volatility is a measure of risk expressed in terms of returns. If we can forecast realised volatility of any financial asset, we will be able to manage the risks we are exposed to in any financial market. There are many models to forecast realised volatility.
The Heterogeneous Autoregressive (HAR) model is arguably the one with better performance. It models tomorrow’s realised volatility as a linear function of today’s daily realised volatility, this week’s mean realised volatility and this month’s mean realised volatility. The HAR model captures two well-recognised properties of realised volatility. Firstly, realised volatility depends on activities of market participants who may have different trading frequencies. Secondly, short term realised volatility depends more on long term realised volatility than conversely. However, when we tested the HAR model with our data from S&P 500 index realised volatility, we found that the HAR model’s estimates and forecasts of realised volatilities are much flatter than the real data. One reason could be that the fixed autoregressive parameter does not capture market partcipants’ changing perceptions on how realised volatilities depends on its history.
The Heterogeneous Autoregressive State Space (HARS) model addresses this problem by adding a time varying component to the autoregressive parameter. The time varying component is a state variable driven by a latent Gaussian process. When we tested the HARS model with the same set of data, the HARS model performed much better. This provides empirical evidence for introducing state variable in a realised volatility model and offers us incentive to test a multivariate state space model for realised covariance matrix in which realised volatilities are the diagonal element.
Even though the Kalman Filter algorithm is commonly used to fit a state space model, the rapid increase in number of parameters to estimate in a multivariate model renders the Kalman Filter algorithm computationally infeasible. On the other hand, the Standardised Self-perturbed Kalman Filter(SPKF) algorithm is claimed to be more efficient. We used this algorithm on the HARS model to test if improvement in efficiency may entail accuracy loss in forecasting or estimation. The result suggested that, when fitting our data, SPKF seems to perform better than the Kalman Filter algorithm in estimation and was not subject to significant accuracy loss in forecasting.
The results of our findings drive us to apply the SPKF algorithm on a multivariate state space model for realised covariance matrix. We hope to bring some new insights in forecasting realised covariance matrix in the near future.
The AMSI vacation scholar program has offered me great opportunity to work with a very experienced and talented supervisor Dr Laleh Tafakori, and to meet with a group of amazing peers from all across Australia whom I share the same passion with and also have learned enormously from.
Bing Liu was one of the recipients of a 2017/18 AMSI Vacation Research Scholarship.