From Stochastic to Rough Volatility: A New Deep Learning Perspective on Hedging
Round 1
Reviewer 1 Report
see attachment
Comments for author File: 
Comments.pdf
Author Response
We would like to thank Reviewer 1 for his/her thoughtful and detailed comments on our paper. Please see the attachment for the response.
Author Response File: Author Response.pdf
Reviewer 2 Report
This paper investigates the GRU-NN architecture using the entropic risk measure with those deep calibrated parameters and gives the deep hedging performance. The primary goal of this paper is to analyze the implications under volatilities with different regularities for option hedging purposes, obtain the deep hedging performance under volatility models with different regularities, and compare them with multiple characteristics. The topic is interesting, however, in the current form, there are multiple unclear points in the manuscript. I suggest the authors to revise this work and improve its clarity. The specific comments below are provided corresponding to this issue.
1. The English needs to be polished in a great care, especially in the abstract. The abstract should be updated with more details on proposed method with concise language, to highlight the main contributions of this paper.
2. Why authors to submit this paper to this special issue “Stability Analysis and Control of Fractional-Order Markovian Jump Systems”?
3. In Induction part, references (within five years) should be cited one by one, not in “which includes [2], [3], [4], [5] and [6]”, in order to highlight the contributions of the proposed results, ending with a brief organizational overview.
4. How to obtain Eq.(17)? It is suggested to give more details on notations of equations in this paper.
5. There is a corollary in page 6 on convex risk measure, however, little comments on this corollary can be found. It seems that authors choose to use entropic risk measure as the convex risk measure.
6. Through my reading, some writing errors and small typos were found in the manuscript, please correct and check all the probable errors and mistakes.
Author Response
We would like to thank Reviewer 2 for his/her thoughtful and detailed comments on our paper. Please see the attachment for the response.
Author Response File: Author Response.pdf
Reviewer 3 Report
See the enclosed review report form below
Comments for author File: Comments.pdf
Author Response
We would like to thank Reviewer 3 for his/her thoughtful and detailed comments on our paper. Please see the attachment for the response.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
see attachment
Comments for author File: Comments.pdf
Author Response
Thank you for taking the necessary time and effort to review the manuscript. We sincerely appreciate all your valuable comments and concerns, which helped us improve the quality of the manuscript. We have added the comparison with FRNN, optimal neuron number selection and the detailed architecture description in the new version. Please see the attached file for more details.
Author Response File: Author Response.pdf
Reviewer 2 Report
The paper has been improved a lot. However, there are still some minor issues that need to be addressed further. As stated in Abstract, this paper investigates the gated recurrent unit neural network architecture for hedging with different-regularity volatility and these gates are updated adaptively in the learning process and thus outperform conventional deep learning techniques in the non-Markovian environment. Can the proposed method be used in Markovian environment? More comments are suggested to be given on this issue. Furthermore, the font and size of the text in Figures should be uniform with the text in the body.
Author Response
Many thanks to you for your good comments.
1. Can the proposed method be used in Markovian environment? More comments are suggested to be given on this issue.
Yes, our method can be used in Markovian environment, such as the BS model and the SV model. We have added the following sentence in Page 12 to emphasis this point.
"The embedded gating network signals of the GRU-NN can use the preceding memory and present inputs to generate the current state. Besides, the gating weights are updated adaptively in the learning process. Consequently, these models empower successful learning not only in the Markovian environment, but also in the non-Markovian environment."
2. The font and size of the text in Figures should be uniform with the text in the body.
Thank you for pointing this out. We have made the adjustments.
Round 3
Reviewer 1 Report
- I appreciate all the changes made, however, I am afraid that they are not significant enough to change my mind that the paper brings sufficient novelty.
Author Response
We thank Reviewer 1 for reviewing our paper. The novelties are introduced in the attached file.
Author Response File: Author Response.pdf
