IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v8y2020i4p124-d446482.html
   My bibliography  Save this article

Pricing, Risk and Volatility in Subordinated Market Models

Author

Listed:
  • Jean-Philippe Aguilar

    (Covéa Finance, Quantitative Research Team, 8-12 rue Boissy d’Anglas, FR75008 Paris, France)

  • Justin Lars Kirkby

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30318, USA)

  • Jan Korbel

    (Section for the Science of Complex Systems, Center for Medical Statistics, Informatics, and Intelligent Systems (CeMSIIS), Medical University of Vienna, Spitalgasse 23, 1090 Vienna, Austria
    Complexity Science Hub Vienna, Josefstädterstrasse 39, 1080 Vienna, Austria
    Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University, 11519 Prague, Czech Republic
    The Czech Academy of Sciences, Institute of Information Theory and Automation, Pod Vodárenskou Věží 4, 182 00 Prague 8, Czech Republic)

Abstract

We consider several market models, where time is subordinated to a stochastic process. These models are based on various time changes in the Lévy processes driving asset returns, or on fractional extensions of the diffusion equation; they were introduced to capture complex phenomena such as volatility clustering or long memory. After recalling recent results on option pricing in subordinated market models, we establish several analytical formulas for market sensitivities and portfolio performance in this class of models, and discuss some useful approximations when options are not far from the money. We also provide some tools for volatility modelling and delta hedging, as well as comparisons with numerical Fourier techniques.

Suggested Citation

  • Jean-Philippe Aguilar & Justin Lars Kirkby & Jan Korbel, 2020. "Pricing, Risk and Volatility in Subordinated Market Models," Risks, MDPI, vol. 8(4), pages 1-27, November.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:4:p:124-:d:446482
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/8/4/124/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/8/4/124/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jean-Philippe Aguilar, 2020. "Explicit option valuation in the exponential NIG model," Papers 2006.04659, arXiv.org, revised Oct 2020.
    2. Jean-Philippe Aguilar & Cyril Coste & Jan Korbel, 2017. "Series representation of the pricing formula for the European option driven by space-time fractional diffusion," Papers 1712.04990, arXiv.org, revised Oct 2018.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    2. Anselm Hudde & Ludger Rüschendorf, 2023. "European and Asian Greeks for Exponential Lévy Processes," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-24, March.
    3. Jean-Philippe Aguilar & Jan Korbel & Nicolas Pesci, 2021. "On the Quantitative Properties of Some Market Models Involving Fractional Derivatives," Mathematics, MDPI, vol. 9(24), pages 1-24, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-Philippe Aguilar & Jan Korbel & Nicolas Pesci, 2021. "On the Quantitative Properties of Some Market Models Involving Fractional Derivatives," Mathematics, MDPI, vol. 9(24), pages 1-24, December.
    2. Jean-Philippe Aguilar & Jan Korbel, 2019. "Simple Formulas for Pricing and Hedging European Options in the Finite Moment Log-Stable Model," Risks, MDPI, vol. 7(2), pages 1-14, April.
    3. Pedro Febrer & João Guerra, 2021. "Residue Sum Formula for Pricing Options under the Variance Gamma Model," Mathematics, MDPI, vol. 9(10), pages 1-29, May.
    4. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:8:y:2020:i:4:p:124-:d:446482. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.