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Pricing Path-Dependent Options under Stochastic Volatility via Mellin Transform

Author

Listed:
  • Jiling Cao

    (Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand)

  • Xi Li

    (Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand)

  • Wenjun Zhang

    (Department of Mathematical Sciences, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1142, New Zealand)

Abstract

In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model using an asymptotic approach. To find the explicit closed-form formulas for the zero-order term and the first-order correction term, we use Mellin transform. We also conduct a sensitivity analysis on these formulas, and compare the option prices calculated by them with those generated by Monte-Carlo simulation.

Suggested Citation

  • Jiling Cao & Xi Li & Wenjun Zhang, 2023. "Pricing Path-Dependent Options under Stochastic Volatility via Mellin Transform," JRFM, MDPI, vol. 16(10), pages 1-17, October.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:10:p:456-:d:1264186
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    References listed on IDEAS

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    2. Sun-Yong Choi & Jean-Pierre Fouque & Jeong-Hoon Kim, 2013. "Option pricing under hybrid stochastic and local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1157-1165, July.
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    7. Boyle, Phelim P. & Tian, Yisong “Sam”, 1999. "Pricing Lookback and Barrier Options under the CEV Process," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(2), pages 241-264, June.
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