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How fundamental is the one-period trinomial model to European option pricing bounds. A new methodological approach

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  • Braouezec, Yann

Abstract

We offer a new simple approach to price European options in incomplete markets using the sole no-arbitrage principle and this only requires to make use of a one-period model; introducing a stochastic process is unnecessary. We show that determining the range of arbitrage-free prices with a trinomial model only consists in locating two points on a triangle. As this range of prices may be lower than the classical ones, the parameters of the model can be implied from the quoted bid and ask prices of liquid European options, used in turn to estimate the volatility bounds. A simple example is provided using options on the S & P 500.

Suggested Citation

  • Braouezec, Yann, 2017. "How fundamental is the one-period trinomial model to European option pricing bounds. A new methodological approach," Finance Research Letters, Elsevier, vol. 21(C), pages 92-99.
    • Handle: RePEc:eee:finlet:v:21:y:2017:i:c:p:92-99
    DOI: 10.1016/j.frl.2016.11.001
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    References listed on IDEAS

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    1. Yann Braouezec & Cyril Grunspan, 2016. "A new elementary geometric approach to option pricing bounds in discrete time models," Post-Print hal-01744439, HAL.
    2. Moriggia, V. & Muzzioli, S. & Torricelli, C., 2009. "On the no-arbitrage condition in option implied trees," European Journal of Operational Research, Elsevier, vol. 193(1), pages 212-221, February.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Farzad Fard & Tak Siu, 2013. "Pricing and managing risks of European-style options in a Markovian regime-switching binomial model," Annals of Finance, Springer, vol. 9(3), pages 421-438, August.
    5. Braouezec, Yann & Grunspan, Cyril, 2016. "A new elementary geometric approach to option pricing bounds in discrete time models," European Journal of Operational Research, Elsevier, vol. 249(1), pages 270-280.
    6. Ernst Eberlein & Jean Jacod, 1997. "On the range of options prices (*)," Finance and Stochastics, Springer, vol. 1(2), pages 131-140.
    7. Xiao, Shuang & Ma, Shihua, 2016. "Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani," Finance Research Letters, Elsevier, vol. 19(C), pages 67-74.
    8. Shi, Guangping & Liu, Xiaoxing & Tang, Pan, 2016. "Pricing options under the non-affine stochastic volatility models: An extension of the high-order compact numerical scheme," Finance Research Letters, Elsevier, vol. 16(C), pages 220-229.
    9. Donald Brown & Rustam Ibragimov & Johan Walden, 2015. "Bounds for path-dependent options," Annals of Finance, Springer, vol. 11(3), pages 433-451, November.
    10. Energy Sonono, Masimba & Phillip Mashele, Hopolang, 2016. "Estimation of bid-ask prices for options on LIBOR based instruments," Finance Research Letters, Elsevier, vol. 19(C), pages 33-41.
    11. Varian, Hal R, 1987. "The Arbitrage Principle in Financial Economics," Journal of Economic Perspectives, American Economic Association, vol. 1(2), pages 55-72, Fall.
    12. Carr, Peter & Wu, Liuren, 2016. "Analyzing volatility risk and risk premium in option contracts: A new theory," Journal of Financial Economics, Elsevier, vol. 120(1), pages 1-20.
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    More about this item

    Keywords

    Incomplete markets; No arbitrage; Option pricing bounds; Bid-ask spread; Volatility bounds;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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