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Polynomial Jump-Diffusion Models

Author

Listed:
  • Damir Filipović

    (Ecole Polytechnique Fédérale de Lausanne and Swiss Finance Institute)

  • Martin Larsson

    (ETH Zurich)

Abstract

We develop a comprehensive mathematical framework for polynomial jump-diffusions, which nest affine jump-diffusions and have broad applications in finance. We show that the polynomial property is preserved under exponentiation and subordination. We present a generic method for option pricing based on moment expansions. As an application, we introduce a large class of novel financial asset pricing models that are based on polynomial jump-diffusions.

Suggested Citation

  • Damir Filipović & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Swiss Finance Institute Research Paper Series 17-60, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1760
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    Citations

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    Cited by:

    1. Christa Cuchiero & Martin Larsson & Sara Svaluto-Ferro, 2018. "Probability measure-valued polynomial diffusions," Papers 1807.03229, arXiv.org.
    2. Filipović, Damir & Larsson, Martin & Pulido, Sergio, 2020. "Markov cubature rules for polynomial processes," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 1947-1971.
    3. Christa Cuchiero & Sara Svaluto-Ferro, 2019. "Infinite dimensional polynomial processes," Papers 1911.02614, arXiv.org.
    4. Damien Ackerer & Damir Filipovic, 2017. "Option Pricing with Orthogonal Polynomial Expansions," Papers 1711.09193, arXiv.org, revised May 2019.
    5. Damir Filipovi'c & Kathrin Glau & Yuji Nakatsukasa & Francesco Statti, 2019. "Weighted Monte Carlo with least squares and randomized extended Kaczmarz for option pricing," Papers 1910.07241, arXiv.org.
    6. Damir Filipovi'c & Sander Willems, 2018. "A Term Structure Model for Dividends and Interest Rates," Papers 1803.02249, arXiv.org, revised May 2020.
    7. Damien Ackerer & Damir Filipović, 2020. "Linear credit risk models," Finance and Stochastics, Springer, vol. 24(1), pages 169-214, January.
    8. Damir Filipovi'c & Martin Larsson & Sergio Pulido, 2017. "Markov cubature rules for polynomial processes," Papers 1707.06849, arXiv.org, revised Jun 2019.

    More about this item

    Keywords

    polynomial jump-diffusions; affine jump-diffusions; exponentiation; subordination; asset pricing models; stochastic volatility;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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