Research on Pricing Methods of Convertible Bonds Based on Deep Learning GAN Models

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Editor,

I am pleased to read the manuscript entitled "Research on Pricing Methods of Convertible Bonds Based on 2 Deep Learning GAN Models" The topic is very interesting, and the approach used is justified in the literature. The paper is well written. In my opinion, it also represents an unexplored, interesting topic to be investigated. This paper is well presented and can be accepted after addressing these major recommendations.

1. In order to establish the significance and value of the study, it is necessary to provide a comprehensive rationale for the research, which emphasizes its relevance and unique contributions to the current scholarly discourse. This will strengthen the study's originality and scholarly impact Following are useful suggested studies to get the benefit to update this part: https://doi.org/10.1007/s11356-021-17438-x ; https://DOI:10.4172/2167-0234.1000370; https://doi.org/10.1016/j.resourpol.2022.102730 ;

2. I suggest authors to improve the abstract, because it is presented poorly (Key aim-methods-findings-policy suggestion).

3. I suggest the authors improve the Introduction section by adding one paragraph “methodological choices and why this method is used”. In addition, also add flow chart of methodology.

4. English check/editing: I found major typos/ grammatical, this study was presented with depraved English language usage.

5. Recheck throughout the paper and ensure that all abbreviations are defined the first time they are used.

6. The paper clearly lacks the sense of paragraphing; some paragraphs are too shorting and consist of only few lines. Kindly rearrange your paragraphs and provide arguments about one main theme in each paragraph.

7. The Results and described with reference to the references of the parameters that influence the results of the research will make it more original. The purpose of the study and the reasons clearly set forth.

8. Please increase the pixel size of all Figures.

9. The policy perspectives are inadequate. I recommend the authors to re-write the policy suggestions systematically and separately for developing and developed countries. Besides, it would also be useful if the authors could also suggest policies for oil importing and oil exporting nations respectively. Similarly, specific policies for fossil fuel dependent and renewable energy dependent nations can be provided

10.  Also, please consistent in data sources of all Tables. It should be in proper referenced shape.

11.  The conclusion is sufficiently discussed with some useful policy implications. However, limitations and future directions of research should have a reasonably sized paragraph instead of just a few lines written half-heartedly at the end of the conclusion.

Comments on the Quality of English Language

Dear Editor,

I am pleased to read the manuscript entitled "Research on Pricing Methods of Convertible Bonds Based on 2 Deep Learning GAN Models" The topic is very interesting, and the approach used is justified in the literature. The paper is well written. In my opinion, it also represents an unexplored, interesting topic to be investigated. This paper is well presented and can be accepted after addressing these major recommendations.

1. In order to establish the significance and value of the study, it is necessary to provide a comprehensive rationale for the research, which emphasizes its relevance and unique contributions to the current scholarly discourse. This will strengthen the study's originality and scholarly impact Following are useful suggested studies to get the benefit to update this part: https://doi.org/10.1007/s11356-021-17438-x ; https://DOI:10.4172/2167-0234.1000370; https://doi.org/10.1016/j.resourpol.2022.102730 ;

2. I suggest authors to improve the abstract, because it is presented poorly (Key aim-methods-findings-policy suggestion).

3. I suggest the authors improve the Introduction section by adding one paragraph “methodological choices and why this method is used”. In addition, also add flow chart of methodology.

4. English check/editing: I found major typos/ grammatical, this study was presented with depraved English language usage.

5. Recheck throughout the paper and ensure that all abbreviations are defined the first time they are used.

6. The paper clearly lacks the sense of paragraphing; some paragraphs are too shorting and consist of only few lines. Kindly rearrange your paragraphs and provide arguments about one main theme in each paragraph.

7. The Results and described with reference to the references of the parameters that influence the results of the research will make it more original. The purpose of the study and the reasons clearly set forth.

8. Please increase the pixel size of all Figures.

9. The policy perspectives are inadequate. I recommend the authors to re-write the policy suggestions systematically and separately for developing and developed countries. Besides, it would also be useful if the authors could also suggest policies for oil importing and oil exporting nations respectively. Similarly, specific policies for fossil fuel dependent and renewable energy dependent nations can be provided

10.  Also, please consistent in data sources of all Tables. It should be in proper referenced shape.

11.  The conclusion is sufficiently discussed with some useful policy implications. However, limitations and future directions of research should have a reasonably sized paragraph instead of just a few lines written half-heartedly at the end of the conclusion.

Author Response

1. In order to establish the significance and value of the study, it is necessary to provide a comprehensive rationale for the research, which emphasizes its relevance and unique contributions to the current scholarly discourse. This will strengthen the study's originality and scholarly impact Followingare useful suggested studies to get the benefit to update this part: https://doi.org/10.1007/s11356-021-17438-x ; https://DOI:10.4172/2167-0234.1000370; https://doi.org/10.1016/j.resourpol.2022.102730 ;

Solution and thanks for your revision suggestion: Theoretically, the study of this paper enriches the existing pricing theory, and discusses the shortcomings, what needs to be improved, and applies the new method to the traditional pricing model, so that it can overcome the pre-defect, and then better complete its pricing task. due to the differences between the terms of domestic and foreign convertible bonds and the limitations of traditional models, it is found empirically that directly applying these methods to the pricing of domestic convertible bonds is not a good way to price convertible bonds. Considering some defects of the above models, this paper adopts a data-driven method (including LSTM model and GAN model) to price convertible bonds, so as to solve the pricing imprecision problem of traditional methods. This method can discard some strict restrictions in traditional models and include more influential factors. According to the characteristics of different industries, reasonable influence factors can be selected for scientific pricing.

2. I suggest authors to improve the abstract, because it is presented poorly (Key aim-methods-findings-policy suggestion).

Solution and thanks for your revision suggestion: This paper proposes two data-driven models (including LSTM pricing model, WGAN pricing model) and an improved model of LSM based on GAN to analyze the pricing of convertible bonds. By applying the generative deep learning model GAN to the pricing of convertible bonds can avoid the strict pre-assumptions and significantly improve the pricing effect of the traditional model. The scope of application of each model is different. Therefore, this paper proves the feasibility of GAN model applied to the pricing of convertible bonds, and enriches the pricing function of derivatives in the financial field.

3. I suggest the authors improve the Introduction section by adding one paragraph “methodological choices and why this method is used”. In addition, also add flow chart of methodology.

Solution and thanks for your revision suggestion: Yes, we did this part of  "methodological choices and why this method is used" as the following: Because the traditional convertible bond pricing theory can be roughly divided into four categories: B-S (Black-Scholes) option pricing model, tree graph pricing model, finite difference method and least square Monte Carlo pricing model (LSM).

However, due to the differences between the terms of domestic and foreign convertible bonds and the limitations of traditional models, it is found empirically that directly applying these methods to the pricing of domestic convertible bonds is not a good way to price convertible bonds. Considering some defects of the above models, this paper adopts a data-driven method (including LSTM model and GAN model) to price convertible bonds, so as to solve the pricing imprecision problem of traditional methods. This method can discard some strict restrictions in traditional models and include more influential factors. According to the characteristics of different industries, reasonable influence factors can be selected for scientific pricing.

4. English check/editing: I found major typos/ grammatical, this study was presented with depraved English language usage.

Solution and thanks for your revision suggestion: Yes, we did double check on your suggest and request by even Native English Speakers.

5. Recheck throughout the paper and ensure that all abbreviations are defined the first time they are used.

Solution and thanks for your revision suggestion: Yes, we re-checked all abbreviations and terminology for some of them are not first used by the author in common sense.  

6. The paper clearly lacks the sense of paragraphing; some paragraphs are too shorting and consist of only few lines. Kindly rearrange your paragraphs and provide arguments about one main theme in each paragraph.

Solution and thanks for your revision suggestion: Yes, we have adjusted according to your suggestion rearrange some of the paragraphs and provide arguments about one main theme in each paragraph.

7. The Results and described with reference to the references of the parameters that influence the results of the research will make it more original. The purpose of the study and the reasons clearly set forth.

Solution and thanks for your revision suggestion: Yes, we have checked the results and described with reference to the references of the parameters that influence the results of the research will make it more original. The purpose of the study and the reasons clearly set forth.

8. Please increase the pixel size of all Figures.

Solution and thanks for your revision suggestion:  Yes, we increased the pixel size by importing the original charts of the Figures.

9. The policy perspectives are inadequate. I recommend the authors to re-write the policy suggestions systematically and separately for developing and developed countries. Besides, it would also be useful if the authors could also suggest policies for oil importing and oil exporting nations respectively. Similarly, specific policies for fossil fuel dependent and renewable energy dependent nations can be provided

Solution and thanks for your revision suggestion: Thanks for your suggestion, but what you have mentioned for the developing and developed counties DO NOT FIT for our methodology topics. As for the "suggest policies for oil importing and oil exporting nations respectively. Similarly, specific policies for fossil fuel dependent and renewable energy dependent nations can be provided", which we don't think this suggestion are not suitable for our topics. Sorry, we cannot accept this suggestion, and this may for other paper.

10. Also, please consistent in data sources of all Tables. It should be in proper referenced shape.

 Solution and thanks for your revision suggestion:  Yes, we did check the consistent in data sources of all Tables, whihch are in proper referenced shape.

11. The conclusion is sufficiently discussed with some useful policy implications. However, limitations and future directions of research should have a reasonably sized paragraph instead of just a few lines written half-heartedly at the end of the conclusion.

 Solution and thanks for your revision suggestion:  We used this form because we want to emphasize what we have done in this empirical process and results which heavily take up the whole paper. Among the four pricing models, LSTM pricing model and WGAN pricing model have the best pricing effect. From the perspective of MAPE index, the pricing effect of WGAN pricing model (0.14%) is better than that of LSTM pricing model (0.21%), and the pricing effect of LSM improved model (1.17%) is better than that of traditional LSM model (2.26%). Though there are some limitation of the existing research in this paper, the prospects for the future research direction we also put forward at the end.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper proposes two data-driven models (including LSTM pricing model, WGAN

pricing model) and an improved model of LSM based on GAN to analyze the pricing of convertible bonds. However, there is still some work that needs to be polished. Here are the details of my suggestions:

1. The description of innovation is not enough. It is suggested that the author explain where this method differs from previous studies about. Please explain the innovation and breakthrough of this method in the abstract or introduction explicitly. It is suggested that the author introduce some excellent latest research results. For example: A distributed message passing algorithm for computing perfect demand matching; Lookback option pricing models based on the uncertain fractional-order differential equation with Caputo type; 𝑃_𝑘 -factors in squares and line graphs of trees.

2. Equation 3.5 looks very strange, such a formula should be composed of mathematical expressions, please modify in detail.

3. Some of the mathematical formulas seem not fit in the format. Some of them are center aligned, and some of them seem not. Mathematical formulas are necessities of the manuscript for our journal, a uniform format is more acceptable. What is recommended is that using Mathtype to write the mathematical formulas.

4. Moreover, language expressions need to be polished. Please check over the whole manuscript and polish the language. Less errors on these will make the paper more readable.

Comments on the Quality of English Language

Language expressions need to be polished. Please check over the whole manuscript and polish the language. Less errors on these will make the paper more readable.

Author Response

1. The description of innovation is not enough. It is suggested that the author explain where this method differs from previous studies about. Please explain the innovation and breakthrough of this method in the abstract or introduction explicitly. It is suggested that the author introduce some excellent latest research results. For example: A distributed message passing algorithm for computing perfect demand matching; Lookback option pricing models based on the uncertain fractional-order differential equation with Caputo type;?_?-factors in squares and line graphs of trees.

Solution and thanks for your revision suggestion: Yes, as you suggest the description of innovation may not enough, but we want to emphasize out discovery, research process and result in our reaseach empirical analysis.  Especially when considering some defects of the traditional models, this paper adopts a data-driven method (including LSTM model and GAN model) to price convertible bonds, so as to solve the pricing imprecision problem of traditional methods. This method can discard some strict restrictions in traditional models and include more influential factors. According to the characteristics of different industries, reasonable influence factors can be selected for scientific pricing.

As for the examples as you given, such as the distributed message passing algorithm for computing perfect demand matching; Lookback option pricing models based on the uncertain fractional-order differential equation with Caputo type; ?_? -factors in squares and line graphs of trees, we may consider them in our next paper.

2. Equation 3.5 looks very strange, such a formula should be composed of mathematical expressions, please modify in detail.

Solution and thanks for your revision suggestion: all the formulas have been composed of mathematical expressions, such as this one as you mentioned of Equation 3.5.

3. Some of the mathematical formulas seem not fit in the format. Some of them are center aligned, and some of them seem not. Mathematical formulas are necessities of the manuscript for our journal, a uniform format is more acceptable. What is recommended is that using Mathtype to write the mathematical formulas.

Solution and thanks for your revision suggestion: we did some adjustment based on your suggestions, such as some of the mathematical formulas seem not fit in the format. Some of them are center aligned, and some of them seem not. We know that the Mathematical formulas are necessities of the manuscript for our journal, a uniform format is more acceptable. And thanks for your recommendation of using Mathtype to write the mathematical formulas, though there are Math typed.

4. Moreover, language expressions need to be polished. Please check over the whole manuscript and polish the language. Less errors on these will make the paper more readable.

Solution and thanks for your revision suggestion: yes, we did some polish work on the language expression by check the whole manuscript to descrease less typos or errors to increase the paper more readable.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

1. Table indication is mis-matched

2. Table 4-11 is missing

3. "A total of 33 characteristic variables are used as the input characteristics of the model" . It is necessary explanation of characterristic variables or more specific model specification of GAN.

4. The author mentions the limitation of this research at the last.

    It could be over-optimization problem. Do include Feb~Aug data prediction as a real predicion. 

Author Response

1. Table indication is mis-matched

Solution and thanks for your revision suggestion: Yes, we re-checked all the table indications and matched them all.

2. Table 4-11 is missing

Solution and thanks for your revision suggestion: We delete the table 4-11 due to some reason, which doesn't impact the whole paper's contribution.

3. "A total of 33 characteristic variables are used as the input characteristics of the model" . It is necessary explanation of characteristic variables or more specific model specification of GAN.

Solution and thanks for your revision suggestion: we delete the variables table due to the downsized requirement as the following:

4. The author mentions the limitation of this research at the last.

It could be over-optimization problem. Do include Feb~Aug data prediction as a real prediction. 

Solution and thanks for your revision suggestion: yes, as you mentioned to some extent, the research work have conducted to duplicate the empirical results and try to compare different models, some there could be optimization issue, but we want to emphasize what we have done in this empirical process and results which heavily take up the whole paper. Among the four pricing models, LSTM pricing model and WGAN pricing model have the best pricing effect. From the perspective of MAPE index, the pricing effect of WGAN pricing model (0.14%) is better than that of LSTM pricing model (0.21%), and the pricing effect of LSM improved model (1.17%) is better than that of traditional LSM model (2.26%). Though there are some limitation of the existing research in this paper, the prospects for the future research direction we also put forward at the end. For the missing data of Feb~Aug data just because of some missing data existed, we are try to do that in the future study.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Accepted for Publication 

Comments on the Quality of English Language

Accepted for publication 

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript can be accepted now.

Comments on the Quality of English Language

This manuscript can be accepted now.