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Pricing, no-arbitrage bounds and robust hedging of instalment options

Author

Listed:
  • M. H. A. Davis
  • W. Schachermayer
  • R. G. Tompkins

Abstract

An instalment option is a European option in which the premium, instead of being paid up-front, is paid in a series of instalments. If all instalments are paid the holder receives the exercise value, but the holder has the right to terminate payments on any payment date, in which case the option lapses with no further payments on either side. We discuss pricing and risk management for these options, in particular the use of static hedges, and also study a continuous-time limit in which premium is paid at a certain rate per unit time.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:6:p:597-610
    DOI: 10.1080/713666004
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    Citations

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    Cited by:

    1. Ben-Ameur, Hatem & de Frutos, Javier & Fakhfakh, Tarek & Diaby, Vacaba, 2013. "Upper and lower bounds for convex value functions of derivative contracts," Economic Modelling, Elsevier, vol. 34(C), pages 69-75.
    2. Deng Guohe & Xue Guangming, 2016. "Valuation of American Continuous-Installment Options Under the Constant Elasticity of Variance Model," Journal of Systems Science and Information, De Gruyter, vol. 4(2), pages 149-168, April.
    3. Chung, San-Lin & Shih, Pai-Ta & Tsai, Wei-Che, 2013. "Static hedging and pricing American knock-in put options," Journal of Banking & Finance, Elsevier, vol. 37(1), pages 191-205.
    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.
    5. Pierangelo Ciurlia & Ilir Roko, 2005. "Valuation of American Continuous-Installment Options," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 143-165, February.
    6. Joanna Goard & Mohammed AbaOud, 2022. "Pricing European and American Installment Options," Mathematics, MDPI, vol. 10(19), pages 1-27, September.
    7. Tumellano Sebehela, 2016. "Portfolio Formation Memory," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 1-16, June.
    8. Kimura, Toshikazu, 2010. "Valuing continuous-installment options," European Journal of Operational Research, Elsevier, vol. 201(1), pages 222-230, February.
    9. Jan Obłój & Thaleia Zariphopoulou, 2021. "In memoriam: Mark H. A. Davis and his contributions to mathematical finance," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1099-1110, October.
    10. Ben-Ameur, Hatem & Breton, Michele & Francois, Pascal, 2006. "A dynamic programming approach to price installment options," European Journal of Operational Research, Elsevier, vol. 169(2), pages 667-676, March.
    11. Hansjörg Albrecher & Philipp Mayer, 2010. "Semi-Static Hedging Strategies For Exotic Options," World Scientific Book Chapters, in: Rüdiger Kiesel & Matthias Scherer & Rudi Zagst (ed.), Alternative Investments And Strategies, chapter 14, pages 345-373, World Scientific Publishing Co. Pte. Ltd..

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