On the Class of Risk Neutral Densities under Heston’s Stochastic Volatility Model for Option Valuation

Round 1

Reviewer 1 Report

This paper introduced a class of scale-parameter distributions with mean being the forward spot price to price option, which is used instead of the Heston stochastic volatility model. A large number of theoretical analysis and practical numerical examples verify the effectiveness of the proposed method. Due to the practical effects of the opinions involved in the paper, I personally believe that the paper is suitable for publication in this journal.

Page 1,line 11, generally, parameterρshouold be represent by ρ ∈ [-1, 1]

Author Response

Thank you for your kind and favorable review. Please see the attached letter . 

Author Response File: Author Response.pdf

Reviewer 2 Report

Please see on the report.

Comments for author File: Comments.pdf

Author Response

Please see the attached letter . 

Author Response File: Author Response.pdf

Reviewer 3 Report

The author shows that any member of the class of scale-parameter distributions could be used for the direct risk-neutral valuation of the option price under Heston’s stochastic volatility model.

I have some comments for better paper.

1. Author should provide 'Conclusion' or 'Concluding remarks' to present the novelty of the paper well.

 

2.  Author compared the option prices in Table 2. Provide the computational time.

 

3. Minor

(1) Example: ODAX: -> Example  (ODAX):

(2) Example: AMD: -> Example  (AMD):

(3) On page 14, Table III???

(4) On page 15, Table 4???

Author Response

Thank you for your kind and favorable review. Please see the attached letter . 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Dear Editor,

I would like to give a review for a revised manuscript of the article “On the class of risk neutral densities under Heston’s stochastic volatility model for option valuation” as follows.

 

The author has cited the papers of Ait-Sahalia et al and other related papers, and also explained more clearly the proposed method comparing to the approaches for calibrating or estimating the Heston’s model parameters in literatures.

Then, I move to the simulation results of the paper as shown in Figure 1c, demonstrating the PDF of V*(t) which is stated by the author to follow (27), a non-central chi-square distribution. Using the parameter values which are set by the author (from line 276-277), the author should clarify that the Feller condition is satisfied or not, and the PDF shown in Figure 1c, is the PDF of the non-central chi-square distribution corresponding to this parameter setting. If so, V*(t) =V(t) *b/a when t=56/365 should be a non-central chi-square random variable with degree of freedom = 1.05851 and non-centrality parameter = 0.291788. Is it correct?

I am not clear this point because the PDF shown in Figure 1c does not look like the PDF of the non-central chi-square distribution with degree of freedom = 1.05851 and non-centrality parameter = 0.291788. So, I need the author to explain more.

According to the above comment, I recommend with a major revision the manuscript for considering in Mathematics if the comment is discussed and taken into account.

Best Regards,

 

Author Response

Thank you for your second round review -- please see attached letter. 

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Several typos have been corrected, and I have no further comments. I recommend that the Academic Editors conduct a final review and check the manuscript.