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Density approximations for multivariate affine jump-diffusion processes

Author

Listed:
  • Filipović, Damir
  • Mayerhofer, Eberhard
  • Schneider, Paul

Abstract

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial moments. We establish parametric conditions which guarantee existence and differentiability of transition densities of affine models and show how they naturally fit into the approximation framework. Empirical applications in option pricing, credit risk, and likelihood inference highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:econom:v:176:y:2013:i:2:p:93-111
    DOI: 10.1016/j.jeconom.2012.12.003
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Sander Willems, 2018. "Asian Option Pricing with Orthogonal Polynomials," Papers 1802.01307, arXiv.org.
    2. repec:eee:ejores:v:262:y:2017:i:3:p:1116-1135 is not listed on IDEAS
    3. Sarno, Lucio & Schneider, Paul & Wagner, Christian, 2016. "The economic value of predicting bond risk premia," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 247-267.
    4. repec:gam:jrisks:v:6:y:2018:i:2:p:28-:d:138299 is not listed on IDEAS
    5. Damien Ackerer & Damir Filipovic & Sergio Pulido, 2017. "The Jacobi Stochastic Volatility Model," Working Papers hal-01338330, HAL.
    6. Jaroslava Hlouskova & Leopold Sogner, 2015. "GMM Estimation of Affine Term Structure Models," Papers 1508.01661, arXiv.org.
    7. Damien Ackerer & Damir Filipovic, 2017. "Option Pricing with Orthogonal Polynomial Expansions," Papers 1711.09193, arXiv.org, revised Dec 2017.
    8. Damien Ackerer & Damir Filipovi'c, 2016. "Linear Credit Risk Models," Papers 1605.07419, arXiv.org, revised Jan 2018.
    9. repec:oup:rapstu:v:7:y:2017:i:1:p:2-42. is not listed on IDEAS
    10. Damir Filipović & Martin Larsson, 2016. "Polynomial diffusions and applications in finance," Finance and Stochastics, Springer, vol. 20(4), pages 931-972, October.
    11. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2017. "Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations," Papers 1711.02140, arXiv.org.
    12. Andrea Barletta & Paolo Santucci de Magistris & Francesco Violante, 2016. "Retrieving Risk-Neutral Densities Embedded in VIX Options: a Non-Structural Approach," CREATES Research Papers 2016-20, Department of Economics and Business Economics, Aarhus University.
    13. esposito, francesco paolo & cummins, mark, 2015. "Filtering and likelihood estimation of latent factor jump-diffusions with an application to stochastic volatility models," MPRA Paper 64987, University Library of Munich, Germany.
    14. Márcio Poletti Laurini & Luiz Koodi Hotta, 2016. "Generalized moment estimation of stochastic differential equations," Computational Statistics, Springer, vol. 31(3), pages 1169-1202, September.
    15. Li, Chenxu & Chen, Dachuan, 2016. "Estimating jump–diffusions using closed-form likelihood expansions," Journal of Econometrics, Elsevier, vol. 195(1), pages 51-70.
    16. Andrea Barletta & Paolo Santucci de Magistris & Francesco Violante, 0404. "A Non-Structural Investigation of VIX Risk Neutral Density," CREATES Research Papers 2017-15, Department of Economics and Business Economics, Aarhus University.
    17. Juan Arismendi, 2014. "A Multi-Asset Option Approximation for General Stochastic Processes," ICMA Centre Discussion Papers in Finance icma-dp2014-03, Henley Business School, Reading University.
    18. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.
    19. repec:oup:rasset:v:7:y:2017:i:1:p:2-42. is not listed on IDEAS
    20. repec:eee:spapps:v:128:y:2018:i:4:p:1135-1164 is not listed on IDEAS
    21. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2016. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Papers 1609.05865, arXiv.org, revised Aug 2017.

    More about this item

    Keywords

    Affine processes; Asymptotic expansion; Density approximation; Orthogonal polynomials;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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