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Pricing European continuous-installment strangle options

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  • Jeon, Junkee
  • Kim, Geonwoo

Abstract

This paper investigates the valuation of European continuous-installment strangle options written on dividend-paying underlying assets in the standard Black-Scholes framework. In this pricing problem, the premium of the strangle option is paid continuously instead of up-front. Since the holder of this option has the right to surrender installment payments at any time, the valuation of installment strangle option can be formulated as an optimal stopping problem with two surrender boundaries. Based on the Mellin transform approaches, we derive the integral equation representations for the value function and the two optimal surrender boundaries. By using the recursive integration method, we obtain efficiently the numerical solution for the integral equations and illustrate the optimal surrender boundaries with respect to the significant parameters.

Suggested Citation

  • Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing European continuous-installment strangle options," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    • Handle: RePEc:eee:ecofin:v:50:y:2019:i:c:s1062940819301962
    DOI: 10.1016/j.najef.2019.101049
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    References listed on IDEAS

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    1. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. Ji-Hun Yoon, 2014. "Mellin Transform Method for European Option Pricing with Hull-White Stochastic Interest Rate," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-7, October.
    4. Laminou Abdou, Souleymane & Moraux, Franck, 2016. "Pricing and hedging American and hybrid strangles with finite maturity," Journal of Banking & Finance, Elsevier, vol. 62(C), pages 112-125.
    5. Andrew Ziogas & Carl Chiarella, 2005. "Pricing American Options under Stochastic Volatility," Computing in Economics and Finance 2005 77, Society for Computational Economics.
    6. Kim, Geonwoo & Koo, Eunho, 2016. "Closed-form pricing formula for exchange option with credit risk," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 221-227.
    7. Franck Moraux, 2009. "On perpetual American strangles," Post-Print halshs-00393811, HAL.
    8. Jeon, Junkee & Kim, Geonwoo, 2019. "Pricing of vulnerable options with early counterparty credit risk," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 645-656.
    9. Kimura, Toshikazu, 2010. "Valuing continuous-installment options," European Journal of Operational Research, Elsevier, vol. 201(1), pages 222-230, February.
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    Cited by:

    1. Jeon, Junkee & Kim, Geonwoo, 2022. "Pricing European continuous-installment currency options with mean-reversion," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    2. Junkee Jeon & Geonwoo Kim, 2022. "Analytic Valuation Formula for American Strangle Option in the Mean-Reversion Environment," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    3. Zhou Yang & Junkee Jeon, 2023. "A Problem of Finite-Horizon Optimal Switching and Stochastic Control for Utility Maximization," Papers 2309.12588, arXiv.org.

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