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Estimating the Wishart Affine Stochastic Correlation Model using the empirical characteristic function

Author

Listed:
  • Da Fonseca José

    () (Department of Finance, Auckland University of Technology, Private Bag 92006, 1142 Auckland, New Zealand)

  • Grasselli Martino

    (Università degli Studi di Padova, Dipartimento di Matematica, Via Trieste 63, Padova, Italy; ESILV, Ecole Supérieure d’Ingénieurs Léonard de Vinci, Département Mathématiques et Ingénierie Financière, Paris La Défense, France; and QUANTA FINANZA S.R.L., Via Cappuccina 40, Mestre (Venezia), Italy)

  • Ielpo Florian

    (Lombard Odier Asset Management, avenue des Morgines 6, 1213 Petit Lancy, Switzerland and Université Paris 1 Sorbonne, 106 Boulevard de l’Hopital, 75013 Paris, France)

Abstract

This paper provides the first estimation strategy for the Wishart Affine Stochastic Correlation (WASC) model. We provide elements showing that the use of empirical characteristic function-based estimates is advisable as this function is exponential affine in the WASC case. We use a GMM estimation strategy with a continuum of moment conditions based on the characteristic function. We present the estimation results obtained using a dataset of equity indexes. The WASC model captures most of the known stylized facts associated with financial markets, including leverage and asymmetric correlation effects.

Suggested Citation

  • Da Fonseca José & Grasselli Martino & Ielpo Florian, 2014. "Estimating the Wishart Affine Stochastic Correlation Model using the empirical characteristic function," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(3), pages 1-37, May.
  • Handle: RePEc:bpj:sndecm:v:18:y:2014:i:3:p:37:n:1
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Francesca Biagini & Alessandro Gnoatto & Maximilian Hartel, 2013. "Affine HJM Framework on $S_{d}^{+}$ and Long-Term Yield," Papers 1311.0688, arXiv.org, revised Aug 2015.
    2. Chiarella, Carl & Da Fonseca, José & Grasselli, Martino, 2014. "Pricing range notes within Wishart affine models," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 193-203.
    3. Chiarella, Carl & Hsiao, Chih-Ying & Tô, Thuy-Duong, 2016. "Stochastic correlation and risk premia in term structure models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 59-78.
    4. Alfonsi, Aurélien & Kebaier, Ahmed & Rey, Clément, 2016. "Maximum likelihood estimation for Wishart processes," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3243-3282.
    5. Da Fonseca, José & Gnoatto, Alessandro & Grasselli, Martino, 2013. "A flexible matrix Libor model with smiles," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 774-793.
    6. repec:kap:apfinm:v:24:y:2017:i:3:d:10.1007_s10690-017-9231-4 is not listed on IDEAS
    7. Jan Baldeaux & Eckhard Platen, 2012. "Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods," Papers 1204.1126, arXiv.org.
    8. José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, vol. 10(2), pages 151-180, May.
    9. Alessandro Gnoatto & Martino Grasselli, 2011. "The explicit Laplace transform for the Wishart process," Papers 1107.2748, arXiv.org, revised Aug 2013.
    10. repec:wsi:ijtafx:v:15:y:2012:i:08:n:s0219024912500562 is not listed on IDEAS
    11. Alessandro Gnoatto, 2012. "The Wishart Short Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-24.
    12. repec:kap:revdev:v:21:y:2018:i:1:d:10.1007_s11147-017-9132-8 is not listed on IDEAS
    13. repec:eee:dyncon:v:86:y:2018:i:c:p:49-71 is not listed on IDEAS
    14. Branger, Nicole & Muck, Matthias, 2012. "Keep on smiling? The pricing of Quanto options when all covariances are stochastic," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1577-1591.

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