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Density Approximations for Multivariate Affine Jump-Diffusion Processes

Author

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  • Damir Filipovi'c
  • Eberhard Mayerhofer
  • Paul Schneider

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 credit risk, likelihood inference, and option pricing highlight the usefulness of our expansions. The approximations are extremely fast to evaluate, and they perform very accurately and numerically stable.

Suggested Citation

  • Damir Filipovi'c & Eberhard Mayerhofer & Paul Schneider, 2011. "Density Approximations for Multivariate Affine Jump-Diffusion Processes," Papers 1104.5326, arXiv.org, revised Oct 2011.
  • Handle: RePEc:arx:papers:1104.5326
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    File URL: http://arxiv.org/pdf/1104.5326
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    References listed on IDEAS

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    1. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    2. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
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    Citations

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    Cited by:

    1. Hlouskova, Jaroslava & Sögner, Leopold, 2015. "GMM Estimation of Affine Term Structure Models," Economics Series 315, Institute for Advanced Studies.
    2. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2011. "Realized Laplace transforms for estimation of jump diffusive volatility models," Journal of Econometrics, Elsevier, vol. 164(2), pages 367-381, October.
    3. repec:oup:rasset:v:7:y:2017:i:1:p:2-42. is not listed on IDEAS
    4. 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.
    5. Sander Willems, 2018. "Asian Option Pricing with Orthogonal Polynomials," Papers 1802.01307, arXiv.org.
    6. Damien Ackerer & Damir Filipovic, 2017. "Option Pricing with Orthogonal Polynomial Expansions," Papers 1711.09193, arXiv.org, revised Dec 2017.
    7. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2013. "Stationarity and ergodicity for an affine two factor model," Papers 1302.2534, arXiv.org, revised Sep 2013.
    8. Márcio Poletti Laurini & Luiz Koodi Hotta, 2016. "Generalized moment estimation of stochastic differential equations," Computational Statistics, Springer, vol. 31(3), pages 1169-1202, September.
    9. Damir Filipovi'c & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Papers 1711.08043, arXiv.org.
    10. 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.
    11. Damien Ackerer & Damir Filipovi'c, 2016. "Linear Credit Risk Models," Papers 1605.07419, arXiv.org, revised Jan 2018.
    12. Damien Ackerer & Damir Filipovic & Sergio Pulido, 2017. "The Jacobi Stochastic Volatility Model," Working Papers hal-01338330, HAL.
    13. 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, revised May 2018.
    14. repec:oup:rapstu:v:7:y:2017:i:1:p:2-42. is not listed on IDEAS
    15. Choi, Seungmoon, 2015. "Explicit form of approximate transition probability density functions of diffusion processes," Journal of Econometrics, Elsevier, vol. 187(1), pages 57-73.
    16. Damien Ackerer & Damir Filipovi'c & Sergio Pulido, 2016. "The Jacobi Stochastic Volatility Model," Papers 1605.07099, arXiv.org, revised Mar 2018.
    17. 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.
    18. Schneider, Paul, 2015. "Generalized risk premia," Journal of Financial Economics, Elsevier, vol. 116(3), pages 487-504.
    19. 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.
    20. 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.

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