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The sub-fractional CEV model

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  • Axel A. Araneda
  • Nils Bertschinger

Abstract

The sub-fractional Brownian motion (sfBm) is a stochastic process, characterized by non-stationarity in their increments and long-range dependency, considered as an intermediate step between the standard Brownian motion (Bm) and the fractional Brownian motion (fBm). The mixed process, a linear combination between a Bm and an independent sfBm, called mixed sub-fractional Brownian motion (msfBm), keeps the features of the sfBm adding the semi-martingale property for H>3/4, is a suitable candidate to use in price fluctuation modeling, in particular for option pricing. In this note, we arrive at the European Call price under the Constant Elasticity of Variance (CEV) model driven by a mixed sub-fractional Brownian motion. Empirical tests show the capacity of the proposed model to capture the temporal structure of option prices across different maturities.

Suggested Citation

  • Axel A. Araneda & Nils Bertschinger, 2020. "The sub-fractional CEV model," Papers 2001.06412, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:2001.06412
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    References listed on IDEAS

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    1. Raffaello Morales & T. Di Matteo & Tomaso Aste, 2012. "Non stationary multifractality in stock returns," Papers 1212.3195, arXiv.org, revised May 2013.
    2. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    3. Morales, Raffaello & Di Matteo, T. & Aste, Tomaso, 2013. "Non-stationary multifractality in stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6470-6483.
    4. Bassler, Kevin E. & McCauley, Joseph L. & Gunaratne, Gemunu H., 2006. "Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets," MPRA Paper 2126, University Library of Munich, Germany.
    5. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
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    Cited by:

    1. Sutthimat, Phiraphat & Mekchay, Khamron & Rujivan, Sanae, 2022. "Closed-form formula for conditional moments of generalized nonlinear drift CEV process," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    2. Axel A. Araneda, 2022. "Credit Default Swaps and the mixed-fractional CEV model," Papers 2211.07564, arXiv.org.
    3. Axel A. Araneda, 2021. "Price modelling under generalized fractional Brownian motion," Papers 2108.12042, arXiv.org, revised Nov 2023.

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