In September, Daniel Stašek, a graduate of the doctoral program at ECON MUNI, received the Dean's Award for outstanding dissertation work. In his research focused on volatility prediction, he demonstrated that more reliable results can be achieved through a sophisticated combination of hundreds of models. It is also advisable to include market liquidity indicators in predictive models and to consider that underestimating volatility is more costly than overestimating it. The result is more realistic and economically accurate predictions.
Your Doctoral Thesis deals with volatility prediction. What is its specific contribution to the existing literature?
Volatility, meaning the degree of uncertainty associated with price movements, plays a key role for example in the valuation of financial derivatives, in risk management and investment decision-making. Where we can predict this variable more accurately, we can for example manage investment risks more effectively.
This is why my Doctoral Thesis focuses on improving the accuracy of these predictions through three different but interconnected approaches. All three studies succeeded in improving predictions compared to standard models.
In your first study you tested innovative methods for increasing the accuracy of predictions on key market indices. Can you explain what these methods were and how they are innovative?
We adopted what is known as ensemble models. These models do not rely on a single best model but combine hundreds of different variants. The selection of variables for the individual models is done using the full subset method, with the resulting models predicting either volatility itself or its probability distribution. Each model is weighted according to its past performance, and the resulting prediction is a weighted average of all models. This makes our approach more resilient to extreme fluctuations and changes in the data generation process. This then eliminates the problem of selecting a single "best" model.
What results did this study bring? Did ensemble models prove to perform better than simpler approaches?
Yes, the results showed that our ensemble models predict volatility more accurately than traditional approaches. The differences were smaller for short-term predictions, but the advantage of ensemble approaches increased significantly as the time horizon extended. This suggests that these models are better at capturing longer-term volatility dynamics.
As part of the study, we also compared two types of ensemble models that differ in their complexity. It turned out that the more complex variant, which uses the prediction of the entire probability distribution, is not significantly more accurate than the simpler one, which predicts volatility itself. For practical use, a simpler and less computationally demanding model is often sufficient.
The second study extends volatility models with variables related to market liquidity. What conclusions did you reach and which findings interested you the most?
In the second study we analysed the predictive power of twenty-five different liquidity indicators. The difference between the bid and ask prices, known as the quoted spread, was found to be the strongest predictor of future volatility. This reflects market makers' expectations of future uncertainty. If these expectations are correct, then our model achieves greater prediction accuracy thanks to them. This information value remains significant even after considering other variables, such as the VIX index, known as the "fear index."
What attracted my attention was that the predictive power of liquidity indicators varies depending on trading volume, the size of the quoted spread, and the level of market uncertainty. Liquidity indicators work best for less traded stocks with a larger difference between the bid and ask prices, especially in times of increased market uncertainty.
The focus of the third study is on asymmetric loss functions in economic decision-making. What led you to this focus and what is the advantage of an asymmetric model?
It was as early as 1969 when Clive Granger pointed out that loss functions are rarely symmetric in economic applications, yet models often ignore this fact. Our approach takes this asymmetry into account in the model estimation itself, which we then use in volatility trading using option contracts.
In this area the loss function is naturally asymmetric. Underestimating volatility leads to significantly higher financial losses than overestimating it. Standard volatility models that use symmetric loss functions therefore do not lead to optimal results in practice. Our study shows that when a model takes this asymmetry into account, it achieves significantly better results and traders obtain higher risk-adjusted returns.
What insights does this study provide? What can an asymmetric model capture better and how would you illustrate this with a practical example?
The study brought several important findings. I believe the most interesting is the potential explanation of the so-called volatility risk premium – a phenomenon where market volatility is on average higher than the volatility realised. This difference is commonly explained by investors' risk aversion, but we show that cost asymmetry also plays a role. We can explain the dynamics of market volatility by predicting realised volatility, which is generated by a model that takes cost asymmetry into account, and it is precisely the magnitude of asymmetry that maximises risk-adjusted returns in options trading. This suggests that market option prices already implicitly reflect traders' asymmetric losses, offering an alternative explanation for the phenomenon.
How can the results of your research be used in practice?
The results can be used to predict volatility more accurately, which is essential for financial derivative pricing, risk management, portfolio optimisation, and a range of other financial applications. Findings on asymmetric loss functions are particularly useful for option traders and market makers. Models that more strictly penalise volatility underestimation provide predictions that better match the actual risk profile of the market and lead to higher risk-adjusted returns.
Portfolio managers can use these insights to develop investment strategies that better reflect their aversion to losses. The liquidity study also provides practical recommendations on which indicators to choose. Large institutions can use detailed data on quoted spreads, while smaller investors can use simpler indicators calculated from daily data.
