Credit Spreads, Leverage and Volatility: A Cointegration Approach

Round 1

Reviewer 1 Report

A file with the report is attached.

Comments for author File: Comments.pdf

Author Response

Dear reviewer,

please find  below the point-by-point response to your comments.

1) The formula is correct. It is the payoff of the firm's equity in a compound option model a la Geske (1977, Journal of Financial and Quantitative Analysis) and, in fact, applying risk-neutral valuation, leads to a Geske-like pricing formula. By model assumptions, default cannot occur between t_i and t_i+1, but only a fixed (and known) reimbursement dates, that is only at t_i and t_i+1 (the default barrier is discrete). This is clearly a limitation of such class of models. I can surely stress this features further.

2) This is a structural model of default in which the state variable is the value of the firm, V. Any other claim, both S and D, will be functions of such state variable only. Equity cannot be function of debt (nor debt can be a function of equity). This would go against the Modigliani-Miller proposition I (without taxes) which states the indifference of the value of the firm being financed with equity versus debt. The composition of the capital structure does not influence the value of the firm. The only thing that matters is the value of the asset. Mathematically, this can be appreciated in the following way: by assumption, equity is a function of the firm's assets, that is S = f(V). V follows a geometric brownian motion and, applying Ito's lemma, it is evident that stochastic process driving S depends on V (and the parameters related to V) only.

3) This directly connect to the point above. Applying Ito's Lemma to S allows to find the drift and diffusion components of the process driving S; in this way, the formula for sigmaS is found. Delta_S is the delta of the equity: since equity is an option on the firm's assets, Delta_S is dS/dV. If you think it may be useful, I can explicitly show the application of Ito's Lemma and the derivation of the formula for sigmaS.

4) Pi is the payoff of the CDS contract, which is essentially a contract written on the firm's debt. Here, what matters are the risk-neutral probabilities of default which can be extracted directly from the CDS spreads in a model-free way. Essentially, every model of default (structural or reduced-form) should aim at reproducing such probabilities. Since in the compound option model the state variable is V, that is default can be formulated in terms of events of V, and it must be V = S + D, default events impact the price of equity too. Hence, the justification to use (indirectly S, as it is observable) to calibrate such probabilities. This is done using equation 8 (second row of the system).

5) Thank you. I will update both section and Appendix.

Reviewer 2 Report

The article is well supported. However, it is highly technical and needs to hold the readers' attention.

In our opinion, the manuscript should be rewritten. Namely, the author should present a section on the literature review, where he should give state of art.

Conclusions should be rewritten, presenting policy implications and impacts on society.

Author Response

Dear reviewer, thank you for your comments. I have added a section for the literature review (as suggested by another referee), and modified the conclusion. All the changes are visible as written in blue (the latex package for managing the changing was clashing with the template of the journal). I hope these changes meet your expectations.

Best regards

Reviewer 3 Report

Research subject and problem

The article's topic corresponds to the special issue's area of interest. The research problem has been correctly formulated and is original.

Objectives and tasks

The purpose was stated descriptively in the introduction. It is worth explicitly highlighting it. Similarly, this applies to the research tasks. The intention is to connect them with the description of the article structure - briefly, as a bullet point.

Research gaps

The research deficits are given in the introduction descriptively, as the background and reasons for the research. This description is a surrogate for the literature review. It is advisable to clearly, and briefly bullet them: the theoretical, methodological and empirical gaps. See also the notes on the structure.

Questions and hypotheses

Research questions and hypotheses are implicit and result from the content of the introduction, including the methodological part of the article. It is advisable to formulate them explicitly and present them as enumerated. This will facilitate their later verification.

Methodology (selection of methods and tools)

The study used the original author's model. In the review, I confirm the authenticity that: “using a novel structural model in which equity is modelled as a compound option on the firm’s assets, a new methodology for estimating the unobservable market value of the firm’s assets and volatility is developed”.

Data and research test

The empirical data is sufficient and broad. It is 64 US listed companies from the S&P100 index. The selection of objects for the study is reliable. The research period is long-term (2013-2017), and the periodization of observations is weekly. This provides research for 16,640 object-observations.

Interpretation of the results

The results are presented in detail in an orderly manner. Their interpretation is not in doubt. They clearly prove the achievement of the stated goals. Therefore, it is worthwhile, after the proposed formulation of hypotheses by the review, to add their final verification.

Discussion and conclusions

There is no discussion of the results in the article. Partly this fact explains the originality of the method and research. Nevertheless, it is advisable to add a polemic with the results of other studies - both as to the method used and the results achieved. In conclusion, it is necessary to add remarks containing the author's recognized limitations of the research, as well as an indication of its further direction.

Structure and composition

In line with the editorial pattern and the universal structure of a scientific article, this one under review requires some changes precisely in its structure. In the introduction, the background of the research, and its location in a broader perspective, should be left out. Also leave a hint of their purpose and research problem, as well as the structure of the article. Add a chapter as a literature review (partly as a remixing of the text of the introduction). This is the one that is supposed to provide strong evidence of research gaps: theoretical, methodological and empirical. From these deficits, the author's formulation of the research problem, research objective and hypotheses should be made explicit (sequence: research gaps > research object > research objective > research problem > hypotheses > methodology > results > discussion). Adding a chapter as a literature review would cause the expected expansion of the article's bibliography by at least a dozen more items. The second comment on the structure of the article is the addition of a chapter as a discussion, so a polemic with the results of other studies.

Formal requirements (language, edition)

Language and writing style are generally correct. Standard editorial correction is required.

General opinion

The research problem, as well as the research methodology, are original and valuable. The research sample is proper, and broad, including on a long-term basis. The logic of the text and the causal sequence is correct. The scientific discussion is conducted reliably. The research is valuable and, as a reviewer, I congratulate the author. The comments raised in the review of the article should be seen as a way to enhance its value.

Author Response

Dear reviewer, thank you very much for your comments. 

I have added a section for the literature review (as suggested by another referee) and made all the required changes. All the changes are visible as written in blue (the latex package for managing the changing was clashing with the template of the journal). I hope these changes meet your expectations.

Best regards

Round 2

Reviewer 1 Report

A file with the report is attached.

Comments for author File: Comments.pdf

Author Response

Dear reviewer,

I added the reference to the derivation.

In particular, I added lines 604-5 in pag. 33 which states "Further details on the derivations of equations (A1), (A2) and (A3) can be found in [25]."

Best regards,