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Polynomial diffusions and applications in finance

Author

Listed:
  • Damir Filipović

    (EPFL and Swiss Finance Institute)

  • Martin Larsson

    (ETH Zurich)

Abstract

This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility, commodities and electricity. Uniqueness of polynomial diffusions is established via moment determinacy in combination with pathwise uniqueness. Existence boils down to a stochastic invariance problem that we solve for semialgebraic state spaces. Examples include the unit ball, the product of the unit cube and nonnegative orthant, and the unit simplex.

Suggested Citation

  • Damir Filipović & Martin Larsson, 2016. "Polynomial diffusions and applications in finance," Finance and Stochastics, Springer, vol. 20(4), pages 931-972, October.
    • Handle: RePEc:spr:finsto:v:20:y:2016:i:4:d:10.1007_s00780-016-0304-4
    DOI: 10.1007/s00780-016-0304-4
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    References listed on IDEAS

    as
    1. Filipović, Damir & Gourier, Elise & Mancini, Loriano, 2016. "Quadratic variance swap models," Journal of Financial Economics, Elsevier, vol. 119(1), pages 44-68.
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    8. Damien Ackerer & Damir Filipovi'c, 2016. "Linear Credit Risk Models," Papers 1605.07419, arXiv.org, revised Jul 2019.
    9. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
    10. Damien Ackerer & Damir Filipovic & Sergio Pulido, 2017. "The Jacobi Stochastic Volatility Model," Working Papers hal-01338330, HAL.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Polynomial diffusions; Polynomial diffusion models in finance; Stochastic invariance; Boundary attainment; Moment problem;
    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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