Forest of Stochastic Trees: A Method for Valuing Multiple Exercise Options

Round 1

Reviewer 1 Report

The paper "Forest of Stochastic Trees: A Method for Valuing Multiple Exercise Options” intends to fill in a method for pricing multiple exercise options by simulation the forest of stochastic trees (FOST). The proposed method uses stochastic trees in place of binomial trees in the forest of trees algorithm originally proposed to value swing options (a type of multiple exercise option).

The paper consists of five sections: Introduction, Results, Discussion, Material and Methods, and Conclusions.

The abstract must contains the main purpose of the paper, the research method used in the research, and the main contributions.

It would be very useful to add into the "Introduction" section the purpose, objectives, and hypothesis of the research. We consider that the introduction should specify the novelty of the paper compared to other papers published in this area. The authors should refer to other papers published in the Sustainability Journal. Also, Also, we consider the literature is very old (1995, 1997, 2001, etc) and that is why we recommend the authors refer to other recent works indexed in Web of Science, Scopus, Emerald, Cambridge, etc. We consider the literature review and introduction should be presented as separate sections. The conclusions must be developed because a single conclusion is not relevant to this research.

Author Response

Point 1: The paper consists of five sections: Introduction, Results, Discussion, Material and Methods, and Conclusions.

Response 1: We have removed Section 5 (Conclusions) and now have Section 3 serving as both discussion and conclusion. As per the editor’s suggestion, we have also moved Section 4 (Materials and Methods) which proves the main results of the paper to Appendix B.1. This leaves the paper with 3 sections, plus an Appendix.

Point 2: The abstract must contains the main purpose of the paper, the research method used in the research, and the main contributions.

Response 2: We have re-written the abstract that (hopefully) makes things more clear.

Point 3: It would be very useful to add in the "Introduction" section the purpose, objectives, and hypothesis of the research. We consider that the introduction should specify the novelty of the paper compared to other papers published in this area. The authors should refer to other papers published in the Sustainability Journal. Also, Also, we consider the literature is very old (1995, 1997, 2001, etc) and that is why we recommend the authors refer to other recent works indexed in Web of Science, Scopus, Emerald, Cambridge, etc. We consider the literature review and introduction should be presented as separate sections. The conclusions must be developed because a single conclusion is not relevant to this research.

Response 3: The Introduction has been re-written (with a separate section for the literature review). We have tried to make it clearer the novelty of our contribution compared to other papers in the areas (e.g., Table 1 on page 2). We have updated the reference list and note that is the Journal of Risk and Financial Management, not the Sustainability Journal. We have searched for references in JRFM that focus on the pricing of multiple exercise options and found none. However, we did find a reference in Energy, another MDPI journal. As noted above, we have removed Section 5, with Section 3 now serving as the discussion and conclusion.

Reviewer 2 Report

I think that this is an interesting article. I hope that my comments will be of some help for authors to revise the document. 

1. The literature review should be extended. The authors should cite more recent articles. 

2. The results should be discussed and compared with other studies.

3. Conclusions should be improved. The authors should explain the similarity and differences between the existing literature and their findings. Policy implications should be added.

Author Response

Point 1: The literature review should be extended. The authors should cite more recent articles.

Response 1: We have revised our literature review and list of references to include some more recent articles.

Point 2: The results should be discussed and compared with other studies.

Response 2: The theoretical results are extensions of the results appearing in Broadie and Glasserman (1997). We believe this is made clear in our paper, particularly in the first paragraph of Section 2.2 and the last paragraph of Section 2.3. In Section 2.4.1, the “binomial” values are computed using the Forest of binomial trees of Lari et al (2001) and are compared with the values from FOST. In Section 2.4.2 we use the trinomial model in Jaillet et al (2004) from which we simulate prices in the FOST method and compare the pricing results (see Figure 4). We do not compare the pricing results for the five-dimensional example in Section 2.4.3 as no benchmark is readily available.

Point 3: Conclusions should be improved. The authors should explain the similarity and differences between the existing literature and their findings. Policy implications should be added.

Response 3: We have made more clear the contribution of our paper (Table 1 on Page 2). Additionally, we removed Section 5 and now have Section 3 serving as Discussion and Conclusion. In this work, we have not attempted to estimate/investigate the properties of the estimated optimal exercise policy and compare our estimates with those of other studies. Here, we have shown the theoretical properties of the high- and low-biased estimators along with some numerical examples to illustrate the method. We do not focus on estimating the optimal exercise policy or on its theoretical properties. As such we view policy implications as a different study than this current submission.

Round 2

Reviewer 2 Report

I think that the current version of this manuscript has been well revised. I am glad to recommend that this article can be accepted for publication.