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Multi-stage real option evaluation with double barrier under stochastic volatility and interest rate

Author

Listed:
  • Michele Bufalo

    (Territory and Finance Università degli Studi di Roma “La Sapienza”)

  • Antonio Di Bari

    (University of Bari)

  • Giovanni Villani

    (University of Bari)

Abstract

This paper focuses on valuing R&D projects using a twofold compound real option by including two knock-out barriers. However, the valuation of R&D projects is not a simple task, since they are characterised by various risks and sequential decision-making. Specifically, we embed a double-barrier in the multi-stage real option in order to mitigate the risk of huge losses for the investor. In this way, our model incorporates the opportunity to abandon a project if its profitability falls below a benchmark level. We contribute to the existing literature in these ways: first we present a closed formula that allows evaluating this kind of project assuming the technical uncertainty of each research phase; secondly, we consider the scenario in which the volatility and the interest rate are both stochastic. Finally, we provide an application for a wind farm case.

Suggested Citation

  • Michele Bufalo & Antonio Di Bari & Giovanni Villani, 2022. "Multi-stage real option evaluation with double barrier under stochastic volatility and interest rate," Annals of Finance, Springer, vol. 18(2), pages 247-266, June.
    • Handle: RePEc:kap:annfin:v:18:y:2022:i:2:d:10.1007_s10436-021-00403-6
    DOI: 10.1007/s10436-021-00403-6
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    1. C. F. Lo & H. C. Lee & C. H. Hui, 2003. "A simple approach for pricing barrier options with time-dependent parameters," Quantitative Finance, Taylor & Francis Journals, vol. 3(2), pages 98-107.
    2. Loncar, Dragan & Milovanovic, Ivan & Rakic, Biljana & Radjenovic, Tamara, 2017. "Compound real options valuation of renewable energy projects: The case of a wind farm in Serbia," Renewable and Sustainable Energy Reviews, Elsevier, vol. 75(C), pages 354-367.
    3. Venetsanos, Konstantinos & Angelopoulou, Penelope & Tsoutsos, Theocharis, 2002. "Renewable energy sources project appraisal under uncertainty: the case of wind energy exploitation within a changing energy market environment," Energy Policy, Elsevier, vol. 30(4), pages 293-307, March.
    4. Ritzenhofen, Ingmar & Spinler, Stefan, 2016. "Optimal design of feed-in-tariffs to stimulate renewable energy investments under regulatory uncertainty — A real options analysis," Energy Economics, Elsevier, vol. 53(C), pages 76-89.
    5. Jan Ericsson & Joel Reneby, 2003. "Stock options as barrier contingent claims," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(2), pages 121-147.
    6. Cassimon, D. & Engelen, P. J. & Thomassen, L. & Van Wouwe, M., 2004. "The valuation of a NDA using a 6-fold compound option," Research Policy, Elsevier, vol. 33(1), pages 41-51, January.
    7. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    8. Flavia Cortelezzi & Giovanni Villani, 2009. "Valuation of R&D Sequential Exchange Options Using Monte Carlo Approach," Computational Economics, Springer;Society for Computational Economics, vol. 33(3), pages 209-236, April.
    9. Jan Ericsson & Joel Reneby, 1998. "A framework for valuing corporate securities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(3-4), pages 143-163.
    10. Pennings, Enrico & Sereno, Luigi, 2011. "Evaluating pharmaceutical R&D under technical and economic uncertainty," European Journal of Operational Research, Elsevier, vol. 212(2), pages 374-385, July.
    11. Lee, Shun-Chung & Shih, Li-Hsing, 2011. "Enhancing renewable and sustainable energy development based on an options-based policy evaluation framework: Case study of wind energy technology in Taiwan," Renewable and Sustainable Energy Reviews, Elsevier, vol. 15(5), pages 2185-2198, June.
    12. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    13. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    14. Guglielmo D’Amico & Giovanni Villani, 2021. "Valuation of R&D compound option using Markov chain approach," Annals of Finance, Springer, vol. 17(3), pages 379-404, September.
    15. Conrad, Jon M. & Kotani, Koji, 2005. "When to drill? Trigger prices for the Arctic National Wildlife Refuge," Resource and Energy Economics, Elsevier, vol. 27(4), pages 273-286, November.
    16. Lee, Shun-Chung & Shih, Li-Hsing, 2010. "Renewable energy policy evaluation using real option model -- The case of Taiwan," Energy Economics, Elsevier, vol. 32(Supplemen), pages 67-78, September.
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    Cited by:

    1. Michele Bufalo & Antonio Di Bari & Giovanni Villani, 2023. "A Compound Up-and-In Call like Option for Wind Projects Pricing," Risks, MDPI, vol. 11(5), pages 1-13, May.
    2. Guglielmo D’Amico & Shakti Singh & Dharmaraja Selvamuthu, 2023. "Analysis of fair fee in guaranteed lifelong withdrawal and Markovian health benefits," Annals of Finance, Springer, vol. 19(3), pages 383-400, September.

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    More about this item

    Keywords

    Down-and-out barrier option; Compound real options approach; Wind farm projects;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
    • K32 - Law and Economics - - Other Substantive Areas of Law - - - Energy, Environmental, Health, and Safety Law
    • O30 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - General

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