Bayesian Sensitivity Analysis for VaR and CVaR Employing Distorted Band Priors
, MarÃa Isabel Parra 1,†, Mario M. Pizarro 2,*,†and Eva L. Sanjuán 1,†Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper defined sensitivity measures for Value at Risk and Conditional Value at Risk based on distorted band priors. Simulation study and an illustrative example were also proposed. Overall, the contents of this paper demonstrate sufficiency and present some novel results. However, several areas for improvement have been identified.
1. The revision has made an attempt to highlight the contribution of the present work, but it turned out to be bare mentioning of some previous works without pointing out how the present work is different. It needs a better description with few lines of clarification in relation to the present work.
2. It is unfortunate that the authors of this paper do not compare their model and estimation method with the existing work. I suggest that authors expand their simulation work to include the comparison and to demonstrate the gains of using the proposed model over the existing models.
3. Punctuation is missing in many places, like line 113 in P4, line 120 in P4, and almost every formula.
4. Line 141 in P5, formula (15) must have been written wrong.
5. To maintain the paper's relevance, it is imperative to include discussions on recent advances in parametric estimation methods. Notably, insights from Wang et al.'s regression analysis of clustered panel count data (Statistical Papers, 2023, DO1:10.1007/s00362-023-01511-3) and Luo et al's work on system reliability modeling (Reliability Engineering and System Safety, 2022, 218.108136) should be integrated. Besides, some recent advances on Bayesian methods, for example,
Zhou S, Xu A, Tang Y, Shen L. Fast Bayesian inference of reparameterized gamma process with random effects. IEEE Transactions on Reliability. (2023). DOI: 10.1109/TR.2023.3263940.
Zhuang L, Xu A, Wang X. A prognostic driven predictive maintenance framework based on Bayesian deep learning. Reliability Engineering and System Safety. 2023, 234, 109181.
Author Response
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Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors may wish to connect their work with other attempts at measuring extreme risk such as Risk-adjusted probability measures in portfolio optimization with coherent measures of risk
N Miller, A Ruszczyński - European Journal of Operational Research, 2008 - Elsevier Comments on the Quality of English LanguageEnglish is fine
Author Response
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Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for Authorssee attached file.
Comments for author File: Comments.pdf
Author Response
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Author Response File: Author Response.pdf
Reviewer 4 Report
Comments and Suggestions for AuthorsThe manuscript presented the use of distorted band priors for sensitivity analysis of Value at Risk and Conditional Value at Risk. The manuscript is overall clearly presented, but some revisions and clarifications are needed before publication. Please see details below:
1. What's the main innovation of the paper? Others have used distorted bands, so the authors need to clarify what's new in this paper.
2. More analysis and plots are needed for the data you are using. In section 5, what does the dataset look like? What does the extreme look like? How well does GPD fit the extreme values?
3. How does your method compare to others? Comparisons to existing methods are needed to justify the contribution.
4. The text fonts for X and Y labels, legends, and axes are too small to be readable. Please enlarge them for readability.
Author Response
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Author Response File: Author Response.pdf
Reviewer 5 Report
Comments and Suggestions for AuthorsThe article explores sensitivity analysis for the Generalized Pareto Distribution in the context of varying the prior distribution for the shape parameter within distorted bands. Proposed sensitivity measures for extreme values and Conditional Value at Risk allow for assessing the impact of prior distribution variability on these crucial risk measures. The paper also extends the definitions of sensitivity measures to other distributions that satisfy appropriate likelihood ratio order conditions. Simulation studies confirm the interaction between parameters and demonstrate the practical application of sensitivity measures using data from the IBEX35 stock index. The article addresses a topic that could have practical applications.
The article is written in correct and understandable language. However, it would be beneficial for the authors to clarify the following issues:
1) Have the authors considered the potential impacts of employing different forms of distorted bands on the results of sensitivity analysis? It would be worthwhile to investigate whether the choice of a specific type of distorting function influences the stability of the obtained results.
2) The article discusses sensitivity analysis for GPD, but have the authors considered comparing the results with other popular distributions used in risk analysis to assess whether the findings are specific to GPD?
3) Have the authors investigated potential effects of sample size on the stability and reliability of the obtained sensitivity measures? Sensitivity analysis can be particularly sensitive to small sample sizes, and this should be considered in the context of the conclusions drawn from the study.
4) In the text, there is mention of applying sensitivity measures to data from the IBEX35 stock index. Have the authors considered differences in the results of sensitivity analysis based on the specificity of the data used in the study?
5) The analysis addressed the issue of interaction between parameters theta and p for sensitivity measures SVaR and SCVaR. Have the authors considered potential methods to minimize this interaction or applied additional corrections to obtain more conclusive results?
Additionally, the authors should enhance the introduction and emphasize novel elements in the work. It would be beneficial to improve the figures as the font size on them is very small and poorly visible.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have revised the paper well.
Reviewer 3 Report
Comments and Suggestions for AuthorsBy including Proposition 3 and its proof, the authors have addressed the main issue that I brought up in my previous review. They have also magnified Fig. 1-5 as requested.
Reviewer 4 Report
Comments and Suggestions for AuthorsThe manuscript has improved a lot and I recommend publication.
