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Option pricing in a subdiffusive constant elasticity of variance (CEV) model

Author

Listed:
  • Kevin Z. Tong

    (Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, K1N 6N5, Canada)

  • Allen Liu

    (#x2020;Enterprise Risk and Portfolio Management, Bank of Montreal, First Canadian Place, Toronto, Ontario, M5X 1A3, Canada)

Abstract

In this paper, we extend the classical constant elasticity of variance (CEV) model to a subdiffusive CEV model, where the underlying CEV process is time changed by an inverse α-stable subordinator. The new model can capture the subdiffusive characteristics of financial markets. We find the corresponding fractional Fokker–Planck equation governing the PDF of the new process. We also derive the analytical formula for option prices in terms of eigenfunction expansion. This method avoids the evaluation of PDF of an inverse α-stable variable and also eliminates the need for numerical integration to calculate the option prices. We numerically investigate the sensitivities of the option prices to the key parameters of the newly developed model.

Suggested Citation

  • Kevin Z. Tong & Allen Liu, 2019. "Option pricing in a subdiffusive constant elasticity of variance (CEV) model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-21, June.
    • Handle: RePEc:wsi:ijfexx:v:06:y:2019:i:02:n:s242478631950018x
    DOI: 10.1142/S242478631950018X
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    References listed on IDEAS

    as
    1. Lingfei Li & Vadim Linetsky, 2015. "Discretely monitored first passage problems and barrier options: an eigenfunction expansion approach," Finance and Stochastics, Springer, vol. 19(4), pages 941-977, October.
    2. Vadim Linetsky, 2004. "Lookback options and diffusion hitting times: A spectral expansion approach," Finance and Stochastics, Springer, vol. 8(3), pages 373-398, August.
    3. Dmitry Davydov & Vadim Linetsky, 2003. "Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach," Operations Research, INFORMS, vol. 51(2), pages 185-209, April.
    4. Marcin Magdziarz & Sebastian Orzel & Aleksander Weron, 2011. "Option pricing in subdiffusive Bachelier model," HSC Research Reports HSC/11/05, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    5. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    6. Zhigang Tong & Allen Liu, 2018. "Analytical pricing of discrete arithmetic Asian options under generalized CIR process with time change," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-21, March.
    7. Zhigang Tong & Allen Liu, 2017. "Analytical pricing formulas for discretely sampled generalized variance swaps under stochastic time change," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-24, June.
    8. repec:bla:jfinan:v:44:y:1989:i:1:p:211-19 is not listed on IDEAS
    9. Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
    10. Karipova, Gulnur & Magdziarz, Marcin, 2017. "Pricing of basket options in subdiffusive fractional Black–Scholes model," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 245-253.
    11. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    12. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
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    Cited by:

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