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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
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    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.
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    Citations

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    Cited by:

    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. 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. 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.

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