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

Author

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  • 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
    DOI: 10.1515/snde-2012-0009
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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. H. Bertholon & A. Monfort & F. Pegoraro, 2008. "Econometric Asset Pricing Modelling," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 407-458, Fall.
    3. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    4. Carrasco, Marine & Kotchoni, Rachidi, 2017. "Efficient Estimation Using The Characteristic Function," Econometric Theory, Cambridge University Press, vol. 33(2), pages 479-526, April.
    5. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    6. Jiang, George J & Knight, John L, 2002. "Estimation of Continuous-Time Processes via the Empirical Characteristic Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 198-212, April.
    7. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    8. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(4), pages 537-572.
    9. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    10. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    12. Jun Yu, 2004. "Empirical Characteristic Function Estimation and Its Applications," Econometric Reviews, Taylor & Francis Journals, vol. 23(2), pages 93-123.
    13. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    14. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
    15. Garcia, René & Lewis, Marc-André & Pastorello, Sergio & Renault, Éric, 2011. "Estimation of objective and risk-neutral distributions based on moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 22-32, January.
    16. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    17. 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.
    18. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
    19. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
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    Cited by:

    1. Hiroaki Hata & Jun Sekine, 2017. "Risk-Sensitive Asset Management in a Wishart-Autoregressive Factor Model with Jumps," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(3), pages 221-252, September.
    2. 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.
    3. Long Teng & Matthias Ehrhardt & Michael Günther, 2016. "On The Heston Model With Stochastic Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-25, September.
    4. José Da Fonseca & Martino Grasselli & Florian Ielpo, 2011. "Hedging (Co)Variance Risk With Variance Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(06), pages 899-943.
    5. Jan Baldeaux & Eckhard Platen, 2012. "Computing Functionals of Multidimensional Diffusions via Monte Carlo Methods," Papers 1204.1126, arXiv.org.
    6. 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.
    7. 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.
    8. Alessandro Gnoatto & Martino Grasselli, 2011. "The explicit Laplace transform for the Wishart process," Papers 1107.2748, arXiv.org, revised Aug 2013.
    9. Escobar, Marcos & Ferrando, Sebastian & Rubtsov, Alexey, 2018. "Dynamic derivative strategies with stochastic interest rates and model uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 86(C), pages 49-71.
    10. Gaetano Bua & Daniele Marazzina, 2021. "On the application of Wishart process to the pricing of equity derivatives: the multi-asset case," Computational Management Science, Springer, vol. 18(2), pages 149-176, June.
    11. 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.
    12. Marcos Escobar & Christoph Gschnaidtner, 2018. "A multivariate stochastic volatility model with applications in the foreign exchange market," Review of Derivatives Research, Springer, vol. 21(1), pages 1-43, April.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Song, Jian & Yao, Jianfeng & Yuan, Wangjun, 2022. "Recent advances on eigenvalues of matrix-valued stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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