IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i10p1449-d1390624.html
   My bibliography  Save this article

Quadratic American Strangle Options in Light of Two-Sided Optimal Stopping Problems

Author

Listed:
  • Tsvetelin S. Zaevski

    (Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, Bulgaria
    Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, Boul. James Boucher 5, 1164 Sofia, Bulgaria)

Abstract

The aim of this paper is to examine some American-style financial instruments that lead to two-sided optimal hitting problems. We pay particular attention to derivatives that are similar to strangle options but have a quadratic payoff function. We consider these derivatives in light of much more general payoff structures under certain conditions which guarantee that the optimal strategy is an exit from a strip. Closed-form formulas for the optimal boundaries and the fair price are derived when the contract has no maturity constraints. We obtain the form of the optimal boundaries under the finite maturity horizon and approximate them by maximizing the financial utility of the derivative holder. The Crank–Nicolson finite difference method is applied to the pricing problem. The importance of these novel financial instruments is supported by several features that are very useful for financial practice. They combine the characteristics of the power options and the ordinary American straddles. Quadratic strangles are suitable for investors who need to hedge strongly, far from the strike positions. In contrast, the near-the-money positions offer a relatively lower payoff than the ordinary straddles. Note that the usual options pay exactly the overprice; no more, no less. In addition, the quadratic strangles allow investors to hedge the positions below and above the strike together. This is very useful in periods of high volatility when large market movements are expected but their direction is unknown.

Suggested Citation

  • Tsvetelin S. Zaevski, 2024. "Quadratic American Strangle Options in Light of Two-Sided Optimal Stopping Problems," Mathematics, MDPI, vol. 12(10), pages 1-27, May.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1449-:d:1390624
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/10/1449/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/10/1449/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhang, Xiang & Li, Lingfei & Zhang, Gongqiu, 2021. "Pricing American drawdown options under Markov models," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1188-1205.
    2. Zhang, Zhiqiang & Liu, Weiqi & Sheng, Yuhong, 2016. "Valuation of power option for uncertain financial market," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 257-264.
    3. Lee, Jung-Kyung, 2020. "A simple numerical method for pricing American power put options," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    4. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    5. Shi Qiu, 2020. "American Strangle Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(3), pages 228-263, May.
    6. Junkee Jeon & Jeonggyu Huh & Kyunghyun Park, 2020. "An Analytic Approximation for Valuation of the American Option Under the Heston Model in Two Regimes," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 499-528, August.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    8. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    9. Jérôme Detemple & Weidong Tian, 2002. "The Valuation of American Options for a Class of Diffusion Processes," Management Science, INFORMS, vol. 48(7), pages 917-937, July.
    10. Woo, Min Hyeok & Choe, Geon Ho, 2020. "Pricing of American lookback spread options," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6300-6318.
    11. Broadie, Mark & Detemple, Jerome, 1995. "American Capped Call Options on Dividend-Paying Assets," The Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 161-191.
    12. Tsvetelin S. Zaevski, 2023. "American strangle options with arbitrary strikes," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 880-903, July.
    13. Madi, Sofiane & Cherif Bouras, Mohamed & Haiour, Mohamed & Stahel, Andreas, 2018. "Pricing of American options, using the Brennan–Schwartz algorithm based on finite elements," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 846-852.
    14. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    15. Stefan Macovschi & François Quittard-Pinon, 2006. "On the Pricing of Power and Other Polynomial Options," Post-Print hal-02313166, HAL.
    16. Lu, Xiaoping & Putri, Endah R.M., 2020. "A semi-analytic valuation of American options under a two-state regime-switching economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    17. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103, World Scientific Publishing Co. Pte. Ltd..
    18. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    19. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    20. Tsvetelin S. Zaevski, 2022. "Pricing cancellable American put options on the finite time horizon," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1284-1303, July.
    21. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    22. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    2. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    3. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    4. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    5. 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.
    6. Lee, Jung-Kyung, 2020. "A simple numerical method for pricing American power put options," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Zaevski, Tsvetelin S., 2022. "Pricing discounted American capped options," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    8. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    9. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    10. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
    11. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    12. Muthuraman, Kumar, 2008. "A moving boundary approach to American option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3520-3537, November.
    13. Zhongkai Liu & Tao Pang, 2016. "An efficient grid lattice algorithm for pricing American-style options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 36-55.
    14. Yacin Jerbi, 2016. "Early exercise premium method for pricing American options under the J-model," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 2(1), pages 1-26, December.
    15. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    16. Simon Scheidegger & Adrien Treccani, 2021. "Pricing American Options under High-Dimensional Models with Recursive Adaptive Sparse Expectations [Telling from Discrete Data Whether the Underlying Continuous-Time Model Is a Diffusion]," Journal of Financial Econometrics, Oxford University Press, vol. 19(2), pages 258-290.
    17. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
    18. 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.
    19. Cassimon, D. & Engelen, P.J. & Thomassen, L. & Van Wouwe, M., 2007. "Closed-form valuation of American call options on stocks paying multiple dividends," Finance Research Letters, Elsevier, vol. 4(1), pages 33-48, March.
    20. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1449-:d:1390624. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.