Newton–Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities

Round 1

Reviewer 1 Report

The paper proposes to use well known Python libraries to speed up a Newton-Raphson algorithm applied to implied volatility estimation.

The manuscript is well written. The main goals are clearly and properly described.

The numerical test section is adequate to show possible limitations (accuracy) and advantages (speed) of the proposed algorithm.

As a minor issue, there is a typo on line 82: the expression "networkIt" should be replaced with "network".

Author Response

Thanks much for reviewing our paper. We have corrected the typo.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors empirically assess two algorithms to extract implied volatilities from option prices.

The authors should improve the description of the algorithm run on the GPU: it is not simple to understand the main details needed to replicate the proposed approach.

In my view the comparison between the two algorithms is not fair for the following reasons.

1) The authors should consider a standard processor: the Intel Xeon Silver 4216 is a CPU designed for servers and it is even more expensive than the GeForce RTX 2080. I suggest to execute the code on a standard desktop.

2) While the Newton-Raphson (NR) algorithm uses a single core, the proposed approach is run in parallel on a GPU. Is there an implementation of the NR algorithm that can be executed in parallel? The authors should elaborate on this point.

3) There are well-known algorithms to extract volatilities from option prices: the blsimpv function implemented in Matlab, and other faster algorithm implemented in Matlab, Python or R. The authors should compare the proposed algorithm with possible alternatives implemented in Matlab, Python or R.

Extensive editing of English language and style is required.

Finally, it would be useful if the authors could share their Python code.

Author Response

1. The authors should improve the description of the algorithm run on the GPU: it is not simple to understand the main details needed to replicate the proposed approach.

- We appreciate your valuable review. We uploaded the Python code to GitHub (https://github.com/thix-is/Newton-Raphson-emulation) for better reusability.

2. The authors should consider a standard processor: the Intel Xeon Silver 4216 is a CPU designed for servers and it is even more expensive than the GeForce RTX 2080. I suggest to execute the code on a standard desktop.

- Thanks for your comment. For now, we only have a GPU server to test our model on. But next time we will be uploading new benchmark results for various hardware to GitHub. Thanks for your understanding.

3. While the Newton-Raphson (NR) algorithm uses a single core, the proposed approach is run in parallel on a GPU. Is there an implementation of the NR algorithm that can be executed in parallel? The authors should elaborate on this point. There are well-known algorithms to extract volatilities from option prices: the blsimpv function implemented in Matlab, and other faster algorithm implemented in Matlab, Python or R. The authors should compare the proposed algorithm with possible.

- We agree with the reviewer for a fair comparison. Therefore, we added another benchmark 'py_vollib_vectorized', released in 2021. This Python package was developed to calculate the implied volatility faster in parallel on the CPU. To our best knowledge, this package currently outperforms the other related packages in terms of accuracy and computational speed. We think that this comment has improved our results considerably. Thanks much.

4. Extensive editing of English language and style is required.

- We tried to improve this paper by editing it as much as possible. We would appreciate it if you are considering the review period is limited.

5. Finally, it would be useful if the authors could share their Python code.

- Thanks for the suggestion. This suggestion helped our method achieve reusability.

Author Response File: Author Response.pdf

Reviewer 3 Report

I am pleased to have the opportunity to review this research paper. This study attempted to explore a Newton–Raphson Emulation Network for Highly Efficient Computation of Numerous Implied Volatilities. Although the topic of this research study is interesting and fits within the journal scope, I think authors should apply the comments indicated below to increase the quality of research justification, contributions and findings. The manuscript know lacks in scientific style and structure.

First of all, paper research gap. Please improve this part in introduction section. Introduction is very general and lacked alignment to the research findings, no discussion was provided to derive the implication from. Theoretical and pragmatics implication are vague and need to be better aligned with this paper theoretical underpinnings and proposed process. Furthermore, there is insufficient support and weak arguments in support of the objective that is proposed as well as the model developed. In the final part of the introduction the objectives proposed, originality and gap that would be better covered. Also how the author will perform the methodology.

 

the topic of this research study is interesting and fits within the journal scope, I think authors should apply the comments indicated to increase the quality of research justification, contributions and findings

What is the originality of this research?  Paper research gap and originality should be better presented at the end of introduction section

Please consider this structure for manuscript final part.

-Discussion

-Conclusion

-Managerial Implication

-Practical/Social Implications

-Discussion needs to be a coherent and cohesive set of arguments that take us beyond this study in particular, and help us see the relevance of what authors have proposed. Authors should create an independent “Discussion” section. Author need to contextualize the findings in the literature, and need to be explicit about the added value of your study towards that literature. Also other studies should be cited to increase the theoretical background of each of the method used. Findings should be contextualized in the literature and should be explicit about the added value of the study towards the literature. Limitations and future research

Questions to be answered:

What practical/professional and academic consequences will this study have for the future of scientific literature (theoretical contributions)?

Why is this study necessary? should make clear arguments to explain what is the originality and value of the proposed model. This should be stated in the final paragraphs of introduction and conclusion sections.

Author Response

We sincerely appreciate your comment. We tried to improve the paper by supplementing the introduction and conclusion and rewriting several sentences concisely. Sentences added or modified are highlighted in the revised version.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Tha authors tried to improve their papers by following the suggestions of my previous report.

Even if the authors did not improve the description of the algorithm run on the GPU, they post the code on GitHub.

 

Author Response

Thank you very much for reviewing our paper. Your comments have helped us achieve better results.

Reviewer 3 Report

congrats! your work is now much better, I just ask you to add literature that supports the need for the study

Author Response

Thank you very much for reviewing our paper. As pointed out, we added two works of literature. Your comments have helped us achieve better results.

Author Response File: Author Response.pdf