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Pricing Options with Extendible Maturities: Analysis and Applications

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  • Longstaff, Francis A

Abstract

Many common types of financial contracts incorporates options with extendible maturities. This paper derives closed-form expressions for options that can be extended by the optionholder and presents a number of applications including the valuation of American options with stochastic dividends, junk bonds, and shared-equity mortgages. We also derive closed-form expressions for writer-extendible options and discuss the writer's economic incentives for extending an out-of-the-money option. We apply these results to show that corporate debtholders have a strong incentive to extend the maturity of defaulting debt if there are liquidation costs. We model and solve the debtholders' optimal extension problem and show that the possibility of an extension can induce shareholders in highly levered firms to accept negative NPV projects. Copyright 1990 by American Finance Association.

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  • Longstaff, Francis A, 1990. "Pricing Options with Extendible Maturities: Analysis and Applications," Journal of Finance, American Finance Association, vol. 45(3), pages 935-957, July.
    • Handle: RePEc:bla:jfinan:v:45:y:1990:i:3:p:935-57
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    Cited by:

    1. Darsinos, T. & Satchell, S.E., 2002. "On the Valuation of Warrants and Executive Stock Options: Pricing Formulae for Firms with Multiple Warrants/Executive Options," Cambridge Working Papers in Economics 0218, Faculty of Economics, University of Cambridge.
    2. Antill, Samuel & Grenadier, Steven R., 2019. "Optimal capital structure and bankruptcy choice: Dynamic bargaining versus liquidation," Journal of Financial Economics, Elsevier, vol. 133(1), pages 198-224.
    3. Wu, Wei-Hwa, 2021. "Extendible stock loan," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    4. Hauser, Shmuel & Lauterbach, Beni, 1996. "Empirical tests of the Longstaff extendible warrant model," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 1-14, May.
    5. Bergman, Yaacov & Callen, Jeffrey L., 1995. "Rational deviations from absolute priority rules," International Review of Financial Analysis, Elsevier, vol. 4(1), pages 1-18.
    6. Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
    7. Epps, T. W. & Pulley, Lawrence B. & Humphrey, David B., 1996. "Assessing the FDIC's premium and examination policies using 'Soviet' put options," Journal of Banking & Finance, Elsevier, vol. 20(4), pages 699-721, May.
    8. Moraux, Franck & Navatte, Patrick, 2015. "How do reservation prices impact distressed debt rescheduling?," Economic Modelling, Elsevier, vol. 46(C), pages 269-282.
    9. Chateau, J.-P. & Wu, J., 2007. "Basel-2 capital adequacy: Computing the `fair' capital charge for loan commitment `true' credit risk," International Review of Financial Analysis, Elsevier, vol. 16(1), pages 1-21.
    10. Pavel V. Shevchenko, 2010. "Holder-extendible European option: corrections and extensions," Papers 1010.0090, arXiv.org, revised Sep 2014.
    11. Liu, Yu-hong & Jiang, I-Ming & Hsu, Wei-tze, 2018. "Compound option pricing under a double exponential Jump-diffusion model," The North American Journal of Economics and Finance, Elsevier, vol. 43(C), pages 30-53.
    12. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    13. Koussis, Nicos & Martzoukos, Spiros H. & Trigeorgis, Lenos, 2013. "Multi-stage product development with exploration, value-enhancing, preemptive and innovation options," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 174-190.
    14. Moraux, Franck & Silaghi, Florina, 2014. "Inside debt renegotiation: Optimal debt reduction, timing, and the number of rounds," Journal of Corporate Finance, Elsevier, vol. 27(C), pages 269-295.
    15. Veld, C.H., 1991. "Warrant pricing : A review of theoretical and empirical research," Other publications TiSEM ac252bad-d1c0-45d6-832a-f, Tilburg University, School of Economics and Management.
    16. Hyong-Chol O & Mun-Chol KiM, 2013. "The Pricing of Multiple-Expiry Exotics," Papers 1302.3319, arXiv.org, revised Aug 2013.
    17. Chung, Y. Peter & Johnson, Herb, 2011. "Extendible options: The general case," Finance Research Letters, Elsevier, vol. 8(1), pages 15-20, March.
    18. Windcliff, H. & Forsyth, P. A. & Vetzal, K. R., 2001. "Valuation of segregated funds: shout options with maturity extensions," Insurance: Mathematics and Economics, Elsevier, vol. 29(1), pages 1-21, August.
    19. Abínzano, Isabel & Seco, Luis & Escobar, Marcos & Olivares, Pablo, 2009. "Single and Double Black-Cox: Two approaches for modelling debt restructuring," Economic Modelling, Elsevier, vol. 26(5), pages 910-917, September.
    20. Marco Antônio Guimarães Dias & Katia Maria Carlos Rocha, 2015. "Petroleum Concessions with Extendible Options: Investment Timing and Value Using Mean Reversion and Jump Processes for Oil Prices," Discussion Papers 0082, Instituto de Pesquisa Econômica Aplicada - IPEA.
    21. Tedeschi, Gabriele & Vidal-Tomás, David & Delli-Gatti, Domenico & Gallegati, Mauro, 2021. "The macroeconomic effects of default and debt restructuring: An agent based exploration," International Review of Economics & Finance, Elsevier, vol. 76(C), pages 1146-1163.
    22. Marco Realdon, "undated". "About Debt and the Option to Extend Debt Maturity," Discussion Papers 03/20, Department of Economics, University of York.
    23. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    24. Foad Shokrollahi, 2017. "Pricing compound and extendible options under mixed fractional Brownian motion with jumps," Papers 1708.04829, arXiv.org.

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