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Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes

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  • Yuji Umezawa
  • Akira Yamazaki

Abstract

This paper proposes a pricing method for path-dependent derivatives with discrete monitoring when an underlying asset price is driven by a time-changed Lévy process. The key to our method is to derive a backward recurrence relation for computing the multivariate characteristic function of the intertemporal joint distribution of the time-changed Lévy process. Using the derived representation of the characteristic function, we obtain semi-analytical pricing formulas for geometric Asian, forward start, barrier, fader and lookback options, all of which are discretely monitored.

Suggested Citation

  • Yuji Umezawa & Akira Yamazaki, 2015. "Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(2), pages 133-161, April.
    • Handle: RePEc:taf:apmtfi:v:22:y:2015:i:2:p:133-161
    DOI: 10.1080/1350486X.2014.960529
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    Citations

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    Cited by:

    1. Kenichiro Shiraya, 2016. "An approximation method for pricing continuous barrier options under multi-asset local stochastic volatility models (Forthcoming in International Journal of Theoretical and Applied Finance.)," CARF F-Series CARF-F-397, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2018.
    2. Kenichiro Shiraya & Hiroki Uenishi & Akira Yamazaki, 2019. "A General Control Variate Method for Lévy Models in Finance (Published in European Journal of Operational Research.)," CARF F-Series CARF-F-455, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2020.
    3. Wendong Zheng & Chi Hung Yuen & Yue Kuen Kwok, 2016. "Recursive Algorithms For Pricing Discrete Variance Options And Volatility Swaps Under Time-Changed Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-29, March.
    4. Akira Yamazaki, 2016. "Generalized Barndorff-Nielsen And Shephard Model And Discretely Monitored Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-34, June.
    5. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2019. "A general framework for time-changed Markov processes and applications," European Journal of Operational Research, Elsevier, vol. 273(2), pages 785-800.
    6. Kenichiro Shiraya & Cong Wang & Akira Yamazaki, 2021. "A general control variate method for time-changed Lévy processes: An application to options pricing," CARF F-Series CARF-F-499, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    7. Shiraya, Kenichiro & Uenishi, Hiroki & Yamazaki, Akira, 2020. "A general control variate method for Lévy models in finance," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1190-1200.
    8. Yuan Li & Kenichiro Shiraya & Yuji Umezawa & Akira Yamazaki, 2022. "Moments of Maximum of Lévy Processes: Application to Barrier and Lookback Option Pricing," CARF F-Series CARF-F-536, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Pingping Zeng & Yue Kuen Kwok, 2016. "Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1375-1391, September.

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