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Skew-Brownian motion and pricing European exchange options

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  • Pasricha, Puneet
  • He, Xin-Jiang

Abstract

This article derives a closed-form pricing formula for European exchange options under a non-Gaussian framework for the underlying assets, intending to resolve mispricing associated with a geometric Brownian motion. The dynamics of each of the two correlated underlying assets are assumed to be governed by the exponential of a skew-Brownian motion, which is specified as a sum of a standard Brownian motion and an independent reflected Brownian motion. The proposed pricing formula does not incur additional computational costs than the standard Black–Scholes framework, which one can quickly recover as a particular case of the proposed framework. Finally, we present some numerical experiments followed by a valuable discussion on the results.

Suggested Citation

  • Pasricha, Puneet & He, Xin-Jiang, 2022. "Skew-Brownian motion and pricing European exchange options," International Review of Financial Analysis, Elsevier, vol. 82(C).
    • Handle: RePEc:eee:finana:v:82:y:2022:i:c:s1057521922000886
    DOI: 10.1016/j.irfa.2022.102120
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    References listed on IDEAS

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    2. Lee, Hangsuck & Ha, Hongjun & Kim, Eunchae & Lee, Minha, 2024. "Quanto fund protection using partial lookback participation," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    3. Marta Biancardi & Michele Bufalo & Antonio Di Bari & Giovanni Villani, 2024. "A valuation of a corn ethanol plant through a compound options model under skew-Brownian motions," Annals of Operations Research, Springer, vol. 336(1), pages 1063-1087, May.
    4. Svetlozar Rachev & Nancy Asare Nyarko & Blessing Omotade & Peter Yegon, 2023. "Bachelier's Market Model for ESG Asset Pricing," Papers 2306.04158, arXiv.org.

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