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A new closed-form formula for pricing European options under a skew Brownian motion

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  • Song-Ping Zhu
  • Xin-Jiang He

Abstract

In this paper, we present a new pricing formula based on a modified Black–Scholes (B-S) model with the standard Brownian motion being replaced by a particular process constructed with a special type of skew Brownian motions. Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options.” The European Journal of Finance 13 (6): 523–544] have worked on this model, the results they obtained are incorrect. In this paper, not only do we identify precisely where the errors in Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options”. The European Journal of Finance 13 (6): 523–544] are, we also present a new closed-form pricing formula based on a newly proposed equivalent martingale measure, called ‘endogenous risk neutral measure’, by which only endogenous risks should and can be fully hedged. The newly derived option pricing formula takes the B-S formula as a special case and it does not induce any significant additional burden in terms of numerically computing option values, compared with the effort involved in computing the B-S formula.

Suggested Citation

  • Song-Ping Zhu & Xin-Jiang He, 2018. "A new closed-form formula for pricing European options under a skew Brownian motion," The European Journal of Finance, Taylor & Francis Journals, vol. 24(12), pages 1063-1074, August.
    • Handle: RePEc:taf:eurjfi:v:24:y:2018:i:12:p:1063-1074
    DOI: 10.1080/1351847X.2017.1339104
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    Cited by:

    1. Ben-zhang Yang & Xinjiang He & Nan-jing Huang, 2019. "Equilibrium price and optimal insider trading strategy under stochastic liquidity with long memory," Papers 1901.00345, arXiv.org, revised Jan 2019.
    2. Pasricha, Puneet & He, Xin-Jiang, 2022. "Skew-Brownian motion and pricing European exchange options," International Review of Financial Analysis, Elsevier, vol. 82(C).
    3. Che Guo & Xingchun Wang, 2022. "Pricing vulnerable options under correlated skew Brownian motions," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(5), pages 852-867, May.
    4. Zaniar Ahmadi & Xiaowen Zhou, 2024. "A note on Skew Brownian Motion with two-valued drift and an application," Papers 2407.09321, arXiv.org, revised Nov 2024.

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