Advanced Statistical Analysis of the Predicted Volatility Levels in Crypto Markets

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper's introduction focuses on the significance and application of the GARCH Volatility Model in assessing and forecasting financial market volatility. It outlines the model's background, development over time, and pivotal role in financial econometrics. The paper sets the stage for a detailed exploration of the model's capabilities, limitations, and potential for innovation in volatility forecasting. 

However, the paper has some flaws as follows:

1.The GARCH model, as its innovative application or extension, is crucial for academic contributions. It is essential for the paper to clearly articulate how it adds new knowledge or understanding to the existing body of literature on the GARCH model. There are no authors' hypnotizes or clearly defined objectives. 2. A significant flaw is the absence of detailed practical examples. Practical examples not only demonstrate the applicability of the proposed methods but also help in validating the theoretical models against real-world data. 4. Figure 2 is critical for visualizing complex information and should be designed with clarity and detail. The figure is poorly designed or lacks necessary detail, which hinders the reader's understanding of key findings. Supplementing or replacing a complex figure with tables or a more accessible format can enhance clarity. THIS IS IMPORTANT; THE FIGURE NEEDS TO BE IMPROVED   

Please highlight changes in future edits.

 

Author Response

We have submitted the odf file with the response to Rewiever 1.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper makes two main contributions:

1) It proposes an additional probabilistic tool to complement conventional GARCH-based volatility prediction. Specifically, for a model-based predicted volatility level, the authors calculate the probability that the market volatility does not fall below that level. They call this the "probability of predicted volatility levels."

2) Since the exact calculation of this probability involves a complicated theoretical expression, the authors derive a more practical lower bound estimate that incorporates real market data. This results in a combined prediction approach with both model-based and data-driven elements.

The authors motivate their work by discussing the importance of volatility forecasting for various financial applications, such as derivative pricing, risk assessment, and trading strategy development. They explain how their proposed probability measure relates to crucial concepts like integrated volatility. Implementing their approach in a real-world volatility forecasting software module (Fig. 2) underscores the practical applicability of their ideas. Discussing how this tool could inform trading decisions and risk management is also valuable.

 

Analyzing the probability associated with predicted volatility levels appears novel, as this is the first time I have seen this specific approach in the volatility forecasting literature. The authors motivate the need for this complementary tool by discussing the limitations of the standard quasi-maximum likelihood (QML) estimation used in GARCH models when the normality assumption is violated, as is often the case with financial return data that exhibit fat tails and skewness.

Combining a stochastic volatility model to derive the exact probability expression and real market data to obtain an implementable lower bound is an interesting fusion of theoretical and empirical techniques. This two-pronged approach allows the limitations of each to be mitigated.

The authors put their work in the broader context of volatility modeling, discussing the importance of volatility forecasting for pricing derivatives, assessing risk, and informing trading strategies. They also tie their probability analysis to the concept of integrated volatility.

The authors make a convincing case for why this additional probabilistic measure can be helpful, particularly given the limitations of conventional QML estimation in GARCH models when dealing with non-normal financial return data.

 

The mathematical derivations in sections 4 and 5 are rigorous. Key steps are explained clearly. The authors analyze both the non-stationary and stationary cases.

Section 5 provides a practical approximation to the probability expression derived in section 4 by taking limits and incorporating real data through a volatility event count M. While the derivation makes sense, a concrete empirical example here would help show the usefulness of this bound and provide more significant intuition.

Figure 1 outlines how the proposed probability estimation can be integrated into a volatility forecasting module, but additional details on the "Decision-making/trading strategy" component would be helpful. How can this probability estimate inform trading decisions?

Figure 2 shows a screenshot of an actual software implementation by 1ex Trading Board, demonstrating the approach's real-world applicability. However, some of the interface elements are hard to parse visually. An enlarged and annotated screenshot focused only on the volatility-related aspects would be more impactful. Figure 2's small size and lack of annotation make it challenging to discern the critical elements related to volatility prediction.

While relevant, the two figures in the paper could be improved to convey the key ideas better.

The writing in sections 1-3 is effective, providing helpful background and building the case for the paper's contribution. However, sections 4-5 could be more varied and more accessible. While the derivations in sections 4 and 5 are rigorous, they are also quite thick and technical. The heavy mathematical notation is only sometimes accompanied by sufficient explanatory text, which may make these sections challenging for readers without a solid mathematical background. The readability of these sections could be improved by providing more intuition and interpretation alongside the equations.

 

This paper tackles a significant problem in financial volatility forecasting and makes a novel theoretical contribution. The proposed approach for analyzing the probability of predicted volatility levels is well-motivated and mathematically rigorous.

The main weakness is that the empirical application of the idea still feels preliminary. More could be done to demonstrate the practical usefulness of the probability bound through concrete examples and a discussion of how it affects trading strategies. While the theoretical derivations appear sound, the paper lacks an interesting empirical demonstration of the practical utility of the proposed probability bound. Section 5 introduces a lower bound that can be estimated from actual data but stops short of applying it to a concrete dataset and discussing the implications. An illustrative empirical example would help readers understand this new tool's potential applications and benefits. More discussion of how these probability estimates can inform real-world trading decisions would also be valuable.

The paper does not compare the proposed approach to existing volatility prediction or probability estimation methods. It would be informative to see how this new probability measure compares to or complements other commonly used techniques in the literature. This could help readers better situate this work within the broader landscape of volatility forecasting research.

The paper could benefit from a more extensive discussion of the limitations of the proposed approach and potential avenues for future research. For instance, are there certain types of financial data or market conditions where this probability measure is more or less effective? How might this technique be extended or improved in future work? Addressing these questions would provide valuable context and motivation for further research.

 

The writing and presentation also require polishing, particularly in the heavy mathematical sections.

Comments on the Quality of English Language

The paper has a logical flow and clear explanations of technical concepts. However, there are recurring grammatical issues, such as missing/extraneous commas and grammar errors.

 

Specifically, while the overall structure and flow of the paper are logical, there are many grammar, punctuation, and sentence structure issues throughout the manuscript. These errors do not substantially impede understanding, but they are frequent enough to be distracting and detract from the overall quality of the writing. A thorough copyedit would help polish the paper.

Author Response

We have attached the corresponding pdf file.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The paper provides an insightful exploration into the advanced statistical analysis of predicted volatility levels within cryptocurrency markets. The authors have thoroughly revised the manuscript based on earlier feedback, incorporating significant changes that have improved its overall quality and presentation with these adjustments.

Future research should apply the statistical methods discussed in the paper to different datasets varying in size, asset types, and characteristics. This would enhance the robustness of the findings and broaden the applicability of the proposed models in real-world scenarios across different types of financial data and market conditions. 

Reviewer 2 Report

Comments and Suggestions for Authors

Nothing else to add. Thank you for the revision.