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On the Pricing of Power and Other Polynomial Options

Author

Listed:
  • Stefan Macovschi

    (EM - EMLyon Business School)

  • François Quittard-Pinon

Abstract

Options with non-linear payoffs offer flexibility to investors, but there are few closed formulas known for European options with non-linear payoffs. An adapted decomposition of the payoff can facilitate pricing with closed-form formulas. We show that it is possible to price a polynomial option by expressing it as a combination of several power options with adapted strikes. The general result is independent of the particular dynamics followed by the underlying. Several packages and parabolic calls are studied, along with an example of polynomial options in portfolio selection.

Suggested Citation

  • Stefan Macovschi & François Quittard-Pinon, 2006. "On the Pricing of Power and Other Polynomial Options," Post-Print hal-02313166, HAL.
    • Handle: RePEc:hal:journl:hal-02313166
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    Citations

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    Cited by:

    1. Jean-Philippe Aguilar, 2021. "The value of power-related options under spectrally negative Lévy processes," Review of Derivatives Research, Springer, vol. 24(2), pages 173-196, July.
    2. Lee, Jung-Kyung, 2020. "A simple numerical method for pricing American power put options," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.
    4. Marcos Escobar-Anel & Eric Molter & Rudi Zagst, 2024. "The power of derivatives in portfolio optimization under affine GARCH models," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 151-181, June.
    5. 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.
    6. Zagst, Rudi & Kraus, Julia & Bertrand, Philippe, 2019. "Option-Based performance participation," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 44-61.
    7. Julia Kraus & Philippe Bertrand & Rudi Zagst, 2013. "Theory of Performance Participation Strategies," Papers 1302.5339, arXiv.org.
    8. Jean-Philippe Aguilar, 2019. "The value of power-related options under spectrally negative L\'evy processes," Papers 1910.07971, arXiv.org, revised Jan 2021.
    9. Kim, Jerim & Kim, Bara & Moon, Kyoung-Sook & Wee, In-Suk, 2012. "Valuation of power options under Heston's stochastic volatility model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1796-1813.
    10. 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.
    11. Huang, Chun-Sung & O'Hara, John G. & Mataramvura, Sure, 2022. "Highly efficient Shannon wavelet-based pricing of power options under the double exponential jump framework with stochastic jump intensity and volatility," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    12. Ricardo Pachón, 2018. "Numerical pricing of European options with arbitrary payoffs," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(02), pages 1-31, June.

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