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Valuation of American Continuous-Installment Options

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  • Pierangelo Ciurlia
  • Ilir Roko

Abstract

In an American continuous-installment option the premium, instead of being paid up-front, is paid at a certain rate per unit time. At any time at or before maturity date, the holder has the right to terminate payments and either exercise the option or "walk away" from deal. Under the standard Black-Scholes assumptions, we can construct an instantaneous riskless dynamic hedging portfolio and derive a Partial Differential Equation (PDE) for the value of this option. This key result enables us to derive valuation formulas for American continuous-installment options using the well-known integral representation along the early exercise boundary. The finite difference approach to solve the PDE is also examined, and numerical techniques to implement the valuation formulas are presented

Suggested Citation

  • Pierangelo Ciurlia & Ilir Roko, 2004. "Valuation of American Continuous-Installment Options," Computing in Economics and Finance 2004 345, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:345
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    References listed on IDEAS

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    1. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
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    3. Carl Chiarella & Adam Kucera & Andrew Ziogas, 2004. "A Survey of the Integral Representation of American Option Prices," Research Paper Series 118, Quantitative Finance Research Centre, University of Technology, Sydney.
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    5. M. H. A. Davis & W. Schachermayer & R. G. Tompkins, 2001. "Pricing, no-arbitrage bounds and robust hedging of instalment options," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 597-610.
    6. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14, April.
    7. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 541-552, November.
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    Cited by:

    1. Joanna Goard & Mohammed AbaOud, 2022. "Pricing European and American Installment Options," Mathematics, MDPI, vol. 10(19), pages 1-27, September.
    2. Kimura, Toshikazu, 2010. "Valuing continuous-installment options," European Journal of Operational Research, Elsevier, vol. 201(1), pages 222-230, February.
    3. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing European continuous-installment strangle options," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    4. 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.

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    More about this item

    Keywords

    Option pricing; Hedging;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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